## The Latent Structure of Job Characteristics of Men and Women

by
Gunn Elisabeth Birkelund, Leo A. Goodman, David Rose

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Title:

The Latent Structure of Job Characteristics of Men and Women

Author:

Gunn Elisabeth Birkelund, Leo A. Goodman, David Rose

Year:

1996

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The American Journal of Sociology

Volume:

102

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1

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80

End Page:

113

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English

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Abstract:

### The Latent Structure of Job Characteristics of Men and women1

Gunn Elisabeth Birkelund

University of Bergen

Leo A. Goodman

University of California, Berkeley

David Rose

University of Essex

Interesting gender differences are found in this article in the ob- served patterns of the job characteristics that are considered here, characteristics of men's jobs and characteristics of women's jobs. By applying the methods of latent structure analysis to analyze data on job characteristics obtained in a British national survey, the authors find that, for both the men and women employees consid- ered here, there are underlying latent variables that can explain the observed patterns of the job characteristics that pertain to (1) pay- ment conditions, (2) promotion prospects, and (3) autonomy at work. The article describes how the underlying latent variables associated with the men's job characteristics differ from the corre- sponding underlying latent variables associated with women's job characteristics.

INTRODUCTION

Various jobs can be described in terms of the employment relationships that they entail (Erikson and Goldthorpe 1992, p. 37). A key concept that is used sometimes in describing the different sorts of employment relationships is "trust," which differentiates to some extent between em- ployees who are involved in a service relationship with their employer and employees who are essentially regulated by a labor contract. These different employment relationships obtain commitment from the work-

'This paper is the written version of a talk presented at the conference, "Work, Employment, and Society in the 1990s: Changing Boundaries, Changing Experi- ences," at the University of Kent in Canterbury, September 1994, and at a meeting of the International Sociological Association Research Committee on Social Stratifica- tion and Social Mobility, in Zurich, May 1995. Direct correspondence to Leo A. Good- man, Department of Sociology, University of California, Berkeley, California 94720-1980.

O 1996 by The University of Chicago. All rights reserved. 0002-9602197110201-0003$01.50

80 AJS Volume 102 Number 1 (July 1996): 80-113

force in different ways. Performance in jobs based on a service relation-

ship is usually controlled and motivated by the possibility of advance-

ment and by the possibility of long-term career benefits, whereas

performance in jobs based on a labor contract is usually subject to super-

vision and the regulation of the contract.

Jobs can also be described in terms of the different ways that the employees receive payment for their work and in terms of other charac- teristics as well. The way in which employees receive their payment is related to the promotion prospects they face and to the degree of control and autonomy they have in their own work. These job characteristics may be interrelated in such a way that "meaningful distinctions can and should be made in class terms" (Erikson and Goldthorpe 1992, p. 41).

Using the methods of latent structure analysis (see, e.g., Goodman 1974a, 1974b), we shall examine in this article, separately for men and for women, the observed patterns of the job characteristics that pertain to these aspects of employment relationships; and we shall find that the ob- served patterns of the job characteristics can be explained in terms of some underlying latent variables. We shall compare the results obtained for men with those obtained for women. Since many labor markets are sex segre- gated (see, e.g., Rosenfeld 1983; Beller 1984; Reskin 1984; Bielby and Baron 1986; Tienda, Smith, and Ortiz 1987; England et al. 1988; Jacobs 1989; Crompton and Sanderson 1990; Birkelund 1992; Hakim 1992; Charles and Grusky 1995; Petersen and Morgan 1995), it is of interest to see whether the latent variables that explain the observed patterns of the job characteristics for men differ from the corresponding latent variables that explain the observed patterns of the job characteristics for women; and, if so, how these latent variables differ. We shall analyze data on these job characteristics obtained in a British national survey.

Class analysis in general, and the Erikson-Goldthorpe class schema in particular, has been criticized for not incorporating women's work into the analysis in a satisfactory way.' In the present article, we shall exam-

'The debate on the gender question within class theory has revealed at least two stances: On one side there are those who argue that class theory is concerned with class inequalities and not questions of gender, and that questions of class form an area of study of interest in its own right (see, e.g., Parkin 1972; Goldthorpe 1983,

1984; Erikson 1984; Lockwood 1986; Erikson and Goldthorpe 1988, 1992). On another side in this debate, there are those who claim that gender matters in the study of social stratification, and that women and women's work should be incorporated into class analysis in a way that will help to obtain a more complete understanding of class processes within present-day societies (see, e.g., Acker 1973; Garnsey 1982; Hartmann 1982; Murgatroyd 1982; Stanworth 1984; Heath and Britten 1984; Dale, Gilbert, and Arber 1985; Crompton and Mann 1986; Abbott 1987; Abbott and Saps- ford 1987; Leiulfsrud and Woodward 1987, 1988; Rose and Birkelund 1991). For a recent overview of the debate on women and the class structure, see, e.g., SzelCnyi (1994).

ine both the characteristics of men's jobs and the characteristics of

women's jobs, and we shall then see whether there are gender differences

in the observed patterns of the job characteristics and in the correspond-

ing underlying latent variables.

The particular set of job characteristics considered here is of interest in its own right, and it is also of interest in connection with the particular conceptualization of social class presented by Erikson and Goldthorpe. These particular job characteristics can be viewed as examples of rele- vant job characteristics, and the corresponding underlying latent vari- ables obtained with the latent structure analysis presented in the present article can be viewed as examples of possible underlying latent variables that can be used to describe the latent structure of job characteristics of men and women. The kind of latent structure analysis presented here can also be applied to other sets of job characteristics that may also be of interest in their own right, and that may also be of interest in connec- tion with other conceptualizations of social class.

CONCEPTUALIZATIONS OF SOCIAL CLASS

Although other conceptualizations of social class could also be considered in this section, our attention will be focused here mainly on the Erikson- Goldthorpe (E-G) class schema, one of the most influential and widely used conceptualizations of social class.3 The principles of differentiation adopted in the E-G class schema were derived mainly from classic sources, in particular, from Weber and Marx; and these principles were then adapted, under the influence of various later authors, for the pur- pose of analyzing contemporary class structures and class mobility. The E-G schema is concerned with the structural aspects of class, aiming to "differentiate positions within labor markets and production units . . . in terms of the employment relations that they entaileV4

30ther influential class schemata, which could also be considered in this section, are, e.g., the conceptualizations proposed by Wright (1979, 1985; Wright et al. 1989). These conceptualizations are related to recent developments in Marxist theory, and they are operationalized explicitly in term of job-level attributes, such as supervision, decision-making responsibility, authority, etc. As we noted earlier, the method used in the present article to explore the latent structure of job characteristics pertaining to payment conditions, promotion prospects, and job autonomy could also be applied to explore the latent structure of supervision, decision-making responsibility, author- ity, etc. This investigation would, however, go beyond the scope of this article. (See also Grusky [I9941 for an overview of various other approaches to research in the study of social stratification.)

4Although an earlier presentation of this class schema stated that the intention of the schema was to bring together individuals who have similar work and market situations (Goldthorpe 1980), the more recent formulation states that "it should be emphasized

These employment relations delineate three basic class positions: em-

ployers, self-employed workers, and employees. Within the employee

class, the E-G schema differentiates between "employment relationships

regulated by a labour contract [which] entail relatively short-term and

specific exchange of money for effort" and "employment relationships

within a bureaucratic context . . . [involving] a longer-term and generally

more diffuse exchange."'

In view of the stated importance of the associated employment relation- ships in differentiating among the classes in the E-G schema, it will be of interest to explore empirically the latent structure of job characteristics that underlie this class schema. In addition, since the original class schema was devised for use in a survey inquiry of men (Goldthorpe 1980), and subsequent application of the schema in studies of women's mobility prompted some refinement in the schema, it will also be of interest to examine whether the latent structure of the job characteristics for women corresponds to the latent structure of the job characteristics for men.

LATENT STRUCTURE ANALYSIS

Latent structure analysis is a technique for analyzing the latent structure of qualitative/categorical variables (see, e.g., Goodman 1974a, 1974b, 1987; Clogg 1977, 1994). This technique for the analysis of qualitative variables is analogous, in various ways, to factor analysis for the analysis of quantitative variables (Green 1952).

With latent structure analysis, we examine whether the observed rela- tionships among several dichotomous or polytomous manifest (observed) variables can be explained in terms of one (or more) latent (unobserved) variable(s). When it turns out that the observed relationships among the several manifest variables can be explained in terms of one (or more) latent variable(s), then the one (or more) latent variable(s) can be used to replace, in a certain sense, the several manifest variables (and the

that it is the [employment relationship] rather than the [content of work tasks and roles] that, for us, is decisive in determining class position" (Erikson and Goldthorpe 1992, pp. 37, 42).

'See Erikson and Goldthorpe (1992, p. 41). The line of division in the E-G schema, which stems from differences between the labor contract and the service relationship, follows Weber ([I9221 1968) and Dahrendorf (1959) among others. Various other bi- nary distinctions, formally similar to the labor vs. service distinction, can be found in other literature on stratification and mobility. See, e.g., the distinction between open and closed employment relations, the distinction between external and internal labor markets, andior other related kinds of distinctions in, e.g., Doeringer and Piore (1971), Berg (1981), Kalleberg and Berg (1987), Grusky (1994).

corresponding cross-classification of the several manifest variables). A chi-square test can be used to compare the actual frequencies found in the cross-classification of the manifest variables with the corresponding estimates of the frequencies expected under the latent class model. With this test, we can determine whether the model is congruent with the observed data. Various latent class models can be applied to a given cross-classification in order to compare the models with regard to their goodness of fit. In this article, we shall see that some simple latent class models are congruent with the empirical data analyzed here, and that these simple models help to describe and explain the empirical relation- ships observed among the manifest variables that are of interest. We also note here that, by using latent structure analysis to analyze the underlying (latent) pattern in the cross-classification of the responses pertaining to the several manifest variables of interest, we can discover patterns in the responses that could not be detected by the techniques usually used for analyzing such data. (For more about latent structure analysis, see, e.g., the section, "Some Additional Comments on Latent Structure Analysis," later herein; and for more details about the latent class model, see, e.g., app. A, "The Latent Class Model.")

Latent structure analysis is applicable in the study of a wide range of research topics in sociology and in the social sciences more generally, where the empirical analysis of qualitative/categorical data is of interest (see, e.g., Goodman 1974a, 1974b, 1978; Hagenaars and Halman 1989; Goodman and Clogg 1992; Clogg 1994).

DATA AND MANIFEST VARIABLES

The data used here are from a British survey of a national random sample of 1,770 respondents conducted in 1984. The survey, Social Class in Modern Britain (hereafter, SCMB), is described in detail in Marshall et al. (1988). We have restricted our sample to employees working 30 hours per week or more, which resulted in a sample of 580 men and 289 women. (Self-employed people and part-time workers were ~mitted.)~

6Self-employed respondents were asked only a limited number of questions pertaining to their job characteristics, so this group was excluded from the analysis due to lack of comparability. The part-time workers were excluded because previous research (see, e.g., Ellingsaeter 1992; Blossfeld 1994; Rosenfeld and Birkelund 1995) has shown that part-time work tends to be disadvantageous in many respects (pay, security, advancement opportunities, etc.), and so the inclusion of part-time workers with full-time workers would have required additional study of whether there are differ- ences in the underlying pattern of the job characteristics for part-time workers com- pared with full-time workers, which would have been beyond the scope of the present article.

The SCMB survey includes a number of questions pertaining to the work situation of employees. We have grouped some of these items into three categories: questions pertaining to the payment conditions, to pro- motion prospects, and to job autonomy. Our selection of these categories owes much to Evans (1992, 1994) who notes that these kinds of questions are relevant in studies that pertain to the class schema developed by Erikson and Goldthorpe, and-we would add-that would be relevant more generally in various kinds of studies that pertain to the work situ- ation.

The questions included here on the payment conditions are concerned with whether the respondent is working under a wage-earner contract or is in a salaried relationship, with the form in which he or she receives remuneration for his or her work, with whether he or she must clock on and off work, and with whether he or she is paid for overtime.

Promotion prospects are examined here using questions that are con- cerned with the subjective judgment of the respondent pertaining to his or her promotion prospects. The responses to questions about promotion prospects may or may not be realistic; they may be affected by personality characteristics as well as by job characteristics. The questions included here are concerned with the respondent's assessment of his or her chances for internal promotion, with the respondent's judgment about immediate and long-term ways to increase his or her level of pay, and with whether the respondent's job is a step on a recognized career or promotion ladder within the organization.

Finally, job autonomy is examined using a range of questions per- taining to the respondent's control over his or her work tasks. As with the questions on the payment conditions, these questions are more "ob- jective" than are the questions on promotion prospects. The questions on job autonomy are concerned with whether the respondent designs his or her own work, decides his or her day-to-day tasks at work, decides the amount or pace of work, decides the start and quit times, and with whether the respondent can reduce his or her work pace, and can initiate new tasks on the job.

For a more detailed description of the questions, see appendix B.

JOB CHARACTERISTICS OF MEN AND WOMEN

From table 1 we see that there are statistically significant gender differ- ences for two out of the three manifest variables considered here under payment conditions. With respect to the form in which remuneration is received, we find that 62% of the women receive a basic salary compared to 43% of the men, and that 34% of the men receive hourly pay compared to 23% of the women. Also, 68% of the men and 59% of the women are

TABLE 1

JOB CHARACTERISTICS BRITAIN 1984

BY GENDER,

Men Women

Payment conditions: Form of remuneration:

Hourly pay

..................

.......

Basic salary ...............................................................

Other .......................................................................

..................................

.........................

.......

Paid overtime ................................................................

Promotion prospects:

High chance of internal promotion ..................................

Promotion most likely immediate way to pay raise ................

Promotion most likely long-term way to pay raise .................

On career ladder .......................................................

Job autonomy: Design own work ...........................................................

Clock on

.................................

Decide day-to-day tasks ...................

......

Decide amount or pace ....................................................

Decide start and quit times ..........................................

Reduce work pace ..........................................................

Initiate new tasks on job ................................................

Range of sample size 542-66

NOTE.-For each item considered, this table presents the percentage of respondents who gave the response indicated, for male respondents (col. 2) and for female respondents (col. 3). *Statistically significant at 5% level. **Statistically significant at 1% level

paid for overtime work; 40% of the men and 33% of the women must clock on and off work.'

With respect to beliefs about promotion prospects, it is interesting to note that there are no statistically significant gender differences. For each of the four manifest variables considered under promotion prospects in table 1, the percentage describing the men's responses is similar (more or less) to the corresponding percentage describing the women's responses. We find that 81% of the men and 86% of the women do not think they have high chances of promotion within their workplace. Only 18% of the men and 18% of the women think that their most likely immediate way to a pay raise will be through promotion, and 24% of the men and 23% of the women think that their most likely long-term

.......................

'This last gender difference is not statistically significant at the usual 5% level of significance, but it is statistically significant at the 10% level.

way to a pay raise will be through promotion. Finally, 53% of the men

and 47% of the women report that their current job is on a career ladder.

In terms of these subjective evaluations of prospects, we see that there are

no statistically significant gender differences among the full-time working

employees considered here.

The responses pertaining to job autonomy reveal statistically signifi- cant gender differences for only two out of the six manifest variables on this subject. More men than women can decide their start and quit times at work (34% vs. 26%), and more men than women can reduce their own work pace (63% vs. 54%). There are no other statistically significant gender differences when we consider whether they can initiate new tasks on the job, whether they can decide the amount or pace of work, whether they can decide day-to-day tasks themselves, and whether they can de- sign their own work.

The results presented in table 1 were obtained by considering separately the responses on each of the manifest variables, and by examining separately the gender difference in the responses on each of the manifest variables. The relationships among the responses on two or more of the manifest variables (and the data in the cross-classification tables that describe the patterns of responses on two or more of the manifest vari- ables) were not considered in table 1. In the next section, we shall com- ment briefly on the use of latent structure analysis to explain the observed relationships in the cross-classijication tables that describe the patterns of responses on two or more of the manifest variables.

SOME ADDITIONAL COMMENTS ON LATENT STRUCTURE ANALYSIS

Let us now consider for a moment, say, two manifest variables, A and

B. When these two manifest variables are considered separately (as was done with the manifest variables in table I), it may be the case that the gender difference in the responses on variable A is negligible and the gender difference in the responses on variable B is negligible; but when the relationship between the responses on variables A and B is considered (in the two-way cross-classification table that describes the pattern of responses on both variables A and B), it may be the case that the gender difference in this relationship (between the responses on variables A and B) may be large and interesting.

Latent structure analysis is a method for determining whether the ob- served relationship between the responses on variables A and B can be explained in terms of an underlying latent variable. If in fact it turns out that the observed relationship between the responses on variables A and B can be explained in this way for the data obtained from the male respondents and also for the data obtained from the female respondents, then the underlying latent variable that can explain the observed relation- ship for the men's data could be compared with the underlying latent variable that can explain the observed relationship for the women's data.

The results presented in table 1indicated that, when each of the mani- fest variables is considered separately, there are statistically significant gender differences for two out of the three variables pertaining to pay- ment conditions, for none of the four variables pertaining to promotion prospects, and for two out of the six variables pertaining to job auton- omy. However, in the next two sections, a different perspective will be presented, and some surprising new results will be obtained. In these sections, latent structure analysis will be used to examine the observed relationships among the responses on the three variables pertaining to payment conditions, the observed relationships among the responses on the four variables pertaining to promotion prospects, and the observed relationships among the six variables pertaining to job autonomy. We shall find that each of these three sets of observed relationships can be explained by an underlying latent variable, for the data obtained from the male respondents and also for the data obtained from the female respondents. We shall also find in the next two sections interesting gender differences in the underlying latent variable pertaining to payment condi- tions, in the underlying latent variable pertaining to promotion prospects, and in the underlying latent variable pertaining to job autonomy.

THE ANALYSIS OF THE LATENT STRUCTURE OF JOB CHARACTERISTICS OF MEN AND WOMEN

In this section, we shall apply latent structure analysis separately to the data on men's job characteristics and to the data on women's job characteristics (see tables 2, 3, 4, and 5); then in the next section we shall apply this method of analysis in a different way in order to obtain some additional information pertaining to the gender differences in the under- lying pattern associated with these characteristics for men's work and women's work (see table 6).

We shall begin this section by first considering the data on payment conditions, that is, the three-way cross-classification table pertaining to the responses on the first three questions considered in table 1 (and de- scribed in app. B), one trichotomous manifest variable, and two dichotomous manifest variables. From the results presented in table 2, we take note of the fact that, for both men and women, the three variables considered under payment conditions are clearly related to each other,

TABLE 2 LATENT STRUCTURE MODELSPERTAININGTO JOB CHARACTERISTICS

Likelihood- | Goodness- | |
---|---|---|

Model df | Ratio x2 | of-Fit x2 |

Payment conditions: | ||

Men: | ||

Independence model ................................ 7 | 204.52 | 215.54 |

Model with two latent classes ........................ 2 | 4.27 | 3.45 |

Women: | ||

Independence model .................................... 7 | 49.53 | 56.74 |

Model with two latent classes ........................ 2 | .18 | .19 |

Promotion prospects: | ||

Men: | ||

Independence model .................................... 11 | 306.77 | 635.93 |

Model with two latent classes ........................ 7 | 8.13 | 7.55 |

Model with three latent classes ...................... 4 | 3.58 | 3.65 |

Model with four latent classes ....................... 0 | .16 | .15 |

Women: | ||

...........Independence model ...................... 11 | 177.73 | 467.22 |

Model with two latent classes ........................ 7 | 20.56 | 21.15 |

Model with three latent classes ...................... 3 | 11.29 | 10.51 |

Model with four latent classes ....................... 2 | .ll | .10 |

Job autonomy: | ||

Men: | ||

Independence model .................................... 5 7 | 625.96 | 1,279.05 |

Model with two latent classes ........................ 50 | 111.34 | 118.23 |

Model with three latent classes ...................... 43 | 50.48 | 47.73 |

Model with four latent classes ....................... 39 | 38.99 | 35.40 |

Model with five latent classes ........................ 33 | 26.51 | 24.34 |

Women: | ||

Independence model ................................. 57 | 395.86 | 735.15 |

Model with two latent classes ........................ 50 | 130.78 | 125.69 |

Model with three latent classes ...................... 44 | 82.60 | 76.90 |

Model with four latent classes ....................... 37 | 46.48 | 49.18 |

Model with five latent classes ........................ 36 | 35.93 | 41.52 |

although more so for men than for womene8 The form in which remunera- tion is received, whether by hourly pay (or pay for performance or piece- work), basic salary, or in other ways, is related to whether the respondent receives payment for overtime, and whether he or she must clock on and

-.

off. Both for men and women, the relationship among these three mani-

'For the model that states that responses on the three variables are statistically inde- pendent of each other (i.e., the independence model), the large chi-square values obtained in table 2 (e.g., the likelihood-ratio chi-square value of 204.52 on 7 df for men, and the corresponding value of 49.53 on 7 df for women) indicate that this model is contradicted by the data. Both the chi-square values for men and the chi-square

fest variables pertaining to payment conditions can be explained by a simple latent class model that has two latent classes. The two-class model fits the data very well for women, with a likelihood-ratio chi-square value of 0.18 on 2 degrees of freedom. For men, the likelihood-ratio chi-square value is 4.27 (on 2 df ); we find that this chi-square value is much less (dramatically less) than the corresponding chi-square value obtained for the model of independence. This dramatic reduction in the chi-square value obtained with the two-class model compared with the model of independence occurs for the men and also for the women (see table 2).9 For reasons that will become clear later in our exposition, the first latent class in the two-class model will be called the "salariat-type" latent class, and the second will be called the "non-salariat-type" latent class.

The variables pertaining to respondents7 beliefs about their promo- tion prospects are also related to each other, both for men and for women. (See the corresponding chi-square values for the model of independence applied to these variables in table 2.) Looking at men first, the model with two latent classes gives a satisfactory fit for these variables, with a likelihood-ratio chi-square value of 8.13 (on 7 df).lo For women, however, the two-class model does not give a satisfactory fit, and neither does the three-class model." The model with four latent classes does give a satisfactory fit for the women's data, with a likelihood-ratio chi-square value of 0.11 (on 2 df). Looking separately at the data on men's promotion prospects and women's promotion prospective, we conclude that these data can be described by a latent class model with two latent classes for men and a latent class model

values for women are statistically significant. Since the sample size for the men's data was approximately twice the sample size for the women's data, a rough comparison of the magnitude of these chi-square values can be made in this context by comparing the men's chi-square values with twice the women's chi-square values (see, e.g., Goodman 1991).

'There is a 98% reduction in the likelihood-ratio chi-square value obtained for the men and an even larger reduction for the women (4.271204.52 = 0.02 for men; 0.181

49.53 = 0.004 for women). Also, the men's chi-square value of 4.27 on 2 df, which

corresponds to a P-value of .12, indicates that the model fit to the men's data is

acceptable (if the usual statistical criteria are applied); and the women's chi-square

value of 0.18 on 2 df indicates that the model fits the women's data very well.

''Note here too the dramatic reduction in the chi-square values when the two-class

model is compared with the model of independence. Also, the chi-square value of

8.13 on 7 df corresponds to a P-value of .32.

"For men, the two-class model and the three-class model are congruent with the

data. Since the two-class model is more parsimonious than the three-class model,

there is no need here to use the three-class model for the men's data. For women,

neither the two-class model nor the three-class model is congruent with the data.

with four latent classes for women.12 This gender difference will be

considered further in the next section.

Finally, with respect to the various aspects of autonomy in the work- place, we find that the corresponding variables are also related to each other. (See the corresponding chi-square values for the model of indepen- dence applied to these variables in table 2.) The model with three latent classes is congruent with the data for men, with a likelihood-ratio chi- square value of 50.48 (on 43 df);13 but the three-class model does not provide a satisfactory fit for the data for women. For the women's data, the four-class model is acceptable, with a likelihood-ratio chi-square value of 46.48 (on 37 df).14

Having determined, from the results presented in table 2, how many latent classes are needed to obtain a latent class model that provides an acceptable fit to the data on men's and women's payment conditions (two latent classes for men and two latent classes for women), men's and women's promotion prospects (two latent classes for men and four latent classes for women), and men's and women's job autonomy (three latent classes for men and four latent classes for women), table 3 presents chi- square values for the more parsimonious latent class models that provide an acceptable fit. (Each model in table 3 either is an acceptable model presented earlier in table 2, or it is closely related to, but more parsimoni- ous than, a corresponding acceptable model in table 2.) From table 3, we see that the model with two latent classes for men's payment condi- tions now has a likelihood-ratio chi-square value of 4.52 (on 3 df), the

''The reader scrutinizing the results presented in table 2 may wonder why the three- class model has a different number of degrees of freedom for men's promotion pros- pects (4 df) and women's promotion prospects (3 df), why the four-class model has a different number of degrees of freedom for men's promotion prospects (0 df) and women's promotion prospects (2 df), and why differences of this kind also occur elsewhere in table 2 (where the number of degrees of freedom for a given latent class model for the men's data is different from the number of degrees of freedom for the corresponding model for the women's data). Even though the cross-classification table describing the data on men's promotion prospects has the same form as the corre- sponding table describing the data on women's promotion prospects (namely, a 2 x 2 x 2 x 2 table), and the latent class model under consideration (e.g., a three- class model) is the same for the men's data and for the women's data, the num- ber of parameters that were estimated as being equal to zero or estimated as being equal to one in the model for the men's data turned out to be different from the corresponding number of parameters that were so estimated in the model for the women's data, and the number of parameters that were so estimated affects the number of degrees of freedom. (For a more detailed explanation, see, e.g, Goodman 1974b.)

13The chi-square value of 50.48 (on 43 df) corresponds to a P-value of .20. 14The chi-square value of 46.48 (on 37 df) corresponds to a P-value of .14.

TABLE 3

Likelihood- | Goodness- | ||||
---|---|---|---|---|---|

Model | df | Ratio x2 | of-Fit xZ | ||

Payment conditions: | |||||

Men: | |||||

Model with two latent classes | ........................ | 3 | 4.52 | 3.63 | |

Women: | |||||

Model with two latent classes | ........................ | 2 | .18 | .19 | |

Promotion prospects: | |||||

Men: | |||||

Model with two latent classes | ........................ | 7 | 8.13 | 7.55 | |

Women: | |||||

Model with four latent classes | ....................... | 4 | 2.55 | 3.32 | |

Job autonomy: | |||||

Men: | |||||

Model with three latent classes | ...................... 47 | 51.62 | 47.63 | ||

Women: | |||||

Model with four latent classes | ....................... | 41 | 48.58 | 47.63 |

NOTE.-Each model in this table either is a model that was presented earlier in table 2 and that provided an acceptable fit to the data, or it is closely related to, but more parsimonious than, a corre- sponding model that was presented in table 2 and that provided an acceptable fit.

model with four latent classes for women's promotion prospects now has a likelihood-ratio chi-square value of 2.55 (on 4 df), the model with three latent classes for men's job autonomy now has a likelihood-ratio chi-square value of 51.62 (on 47 df), and the model with four latent classes for women's job autonomy now has a likelihood-ratio chi-square value of 48.58 (on 41 df).ls

We have shown here that the various items pertaining to the different aspects of the respondents' job characteristics (the three manifest items on payment conditions, the four manifest items on promotion prospects, the six manifest items on job autonomy) can be reduced to three latent dimensions, one related to the payment conditions, one to promotion

'5F~reach of these more parsimonious models in table 3, there are more constraints that are imposed on the parameters in the model (when compared to the number of constraints-if any-that are imposed on the parameters in the corresponding model in table 2), with one or more of the parameters in the model in table 3 (one or more of the conditional probabilities) set equal to zero or to one. For example, with respect to the model with two latent classes for men's payment conditions (with 3 df in table 3 and 2 df in table 2), one of the conditional probabilities in the model in table 3 was set equal to zero, as can be seen from the corresponding entry in table 4. A similar kind of comment applies with respect to each of the more parsimonious models in table 3.

prospects, and one to job autonomy;16 and the three latent dimensions for the men's data differ in some respects from the three latent dimensions for the women's data. We shall next provide a somewhat more detailed description of the latent dimensions for the men's data and for the women's data, and we shall also see whether the latent dimensions turn out to be meaningful in terms pertaining to social class. We consider now the interpretation of these dimensions.

The maximum-likelihood estimates of some of the parameters in the latent class models in table 3 are reported in table 4. With the two-class model applied to the data on the payment conditions, is it possible that the two latent classes can be described in terms that are related to a labor contract and a service contract? The estimated parameters show that the modal categories for the men in latent class 1 describe employees on a typical salaried contract; those who receive a basic salary (74%), those who do not have to clock on (93%), and those who are not paid for overtime (69%). And the modal categories for the men in latent class 2 are those who receive hourly pay (57%), those who must clock on (61%), and those who receive payment for overtime work (92%). Thus, for men, the modal categories for latent class 2 describe employees on a typical wage-earner contract. Since latent class 1 here tends to consist of more salaried employees, and latent class 2 here tends to consist of respondents who are not, we shall call these two latent classes the salariat-type (or salariat) latent class and the non-salariat-type (or non-salariat) latent class, respectively.

For women's payment conditions, we see from table 4 that the modal categories for the women in latent class 1 are the same as those obtained for the men in latent class 1; namely, the modal categories that describe employees on a typical salaried contract. It is also worth noting that only 39% of men compared to 64% of women are in latent class 1 (see table 5).17

'"hen the relationships among the items in the set of manifest items on payment conditions, the relationships among the items in the set of manifest items on promotion prospects, and the relationships among the items in the set of manifest items on job autonomy, can be explained by the corresponding latent variables pertaining to pay- ment conditions, promotion prospects, and job autonomy, respectively, and the rela- tionships among the items in any one of the three sets of manifest items (say, set A) are conditionally independent of the latent variables pertaining to the other two sets of manifest items (say, set B and set C), given the level of the latent variable pertaining to set A (with this conditional independence holding true when "set A" refers in turn to payment conditions, promotion prospects, and job autonomy), then the relation- ships among all of the manifest items (i.e., the items in sets A, B, and C) can be explained by the three latent variables and the joint distribution of these latent vari- ables. (For further details, see, e.g., Goodman 1974a, 19746.).

"This gender difference and other gender differences noted in this section will be considered further in the next section using homogeneous and heterogeneous latent structure models.

TABLE 4

Payment conditions: Men:

Form of remuneration ...................... Hourly pay Basic salary Other

Clock on .......................................Yes No Paid overtime ................................. Yes No Women:

Form of remuneration ...................... Hourly pay Basic salary Other

Clock on ................................... Yes No Paid overtime ................................. Yes No Promotion prospects:

Men: High chance of internal promotion ...... Promotion most likely immediate way

to pay raise ................................ Promotion most likely long-term way to pay raise ...................................

On career ladder .............................

Women: High chance of internal promotion ...... Promotion most likely immediate way

to pay raise ................................ Promotion most likely long-term way to pay raise ................................... On career ladder ........................... Job autonomy:

Men: Design own work ............................ Decide day-to-day tasks .................... Decide amount or pace ..................... Decide start and quit times ............... Reduce work pace ......................... Initiate new tasks on job ..................

TABLE 4 (Continued)

Women: | |||||||
---|---|---|---|---|---|---|---|

Design own work ............................ | 1 | .85 | .52 | .16 | .12 | ||

Decide day-to-day tasks .................... | 1 | 1.00 | 1.00 | .20 | .13 | ||

Decide amount or pace ..................... | 1 | .95 | 1.00 | .73 | .18 | ||

Decide start and quit times | ............... | 1 | .83 | .OO | .23 | .04 | |

Reduce work pace ........................... | 1 | .87 | .33 | .90 | .OO | ||

Initiate new tasks on job | .................. | 1 | .77 | .87 | .39 | .06 |

NOTE.-This table presents the estimated conditional probability that a response is in a specified response category on a specified manifest variable, given that the respondent is in a specified latent class, for each of the models in table 3. Since each manifest variable pertaining to promotion prospects and each manifest variable pertaining to job autonomy is dichotomous, the corresponding estimated conditional probability is presented in this table only for the first response category on each of the specified dichotomous variables. (The corresponding estimate for the second response category is simply one minus the estimate for the first response category.)

TABLE 5

Payment conditions: | |||||||||
---|---|---|---|---|---|---|---|---|---|

Men | ...........................................................39 | .61 | |||||||

Women | ................................................... .64 | .36 | |||||||

Promotion prospects: | |||||||||

Men | .......................................................28 | .72 | |||||||

Women | .......................................................05 | .23 | .09 | .63 | |||||

Job autonomy: | |||||||||

Men | ...................................................... | .2 7 | .48 | .25 | |||||

Women | ................................................. | .2 1 | .19 | .34 | .26 |

NOTE.-This table presents the estimated probability that a respondent is in a specified latent class, for each of the models in table 3.

For women's payment conditions, we also see from table 4 that the modal categories for women in latent class 2 include those who must clock on (7 1%)and those who receive payment for overtime work (89%). And, with respect to the form in which remuneration is received by the women in latent class 2, we see that 48% receive hourly pay and 37% are on basic salaries. (Note that 52% of the women in this latent class do not receive hourly pay but 48% do.)

As was the case for men's payment conditions, we shall call the two latent classes (latent classes 1 and 2) for women's payment conditions the salariat-type (or salariat) latent class and the non-salariat-type (or non-salariat) latent class, respectively. We also see from table 5 that the salariat latent class is the modal latent class for women (64%), and the non-salariat latent class is the modal latent class for men (61%).

With respect to the latent classes pertaining to promotion prospects for men, from table 4 we see that the modal categories for the first latent class include those who think they have high chances of internal promo- tion (54%), those who regard promotion as the most likely immediate way to a pay raise (65%), those who regard promotion as the most likely long-term way to a pay raise (71%), and those who are on a career ladder (84%). The modal categories for the second latent class include those who do not think they have high chances of internal promotion (96%), those who do not regard promotion as the most likely immediate way to a pay raise (loo%), those who do not regard promotion as the most likely long-term way to a pay raise (93%), and those who report that they are not on a career ladder (60%).

We found four latent classes pertaining to women's promotion pros- pects. This suggests that the latent structure of women's promotion pros- pects is more complex than men's. As can be seen from table 4, the modal categories for the first latent class for women include all the catego- ries that indicate good promotion prospects, and the modal categories for the fourth latent class for women include all the categories that indicate poor promotion prospects. The other two latent classes consist mainly of women with less clearcut responses. The modal categories for the second latent class include those women who are on a career ladder (loo%), those who do not think they have a high chance of internal promotion (69%), those who do not regard promotion as the most likely immediate way to a pay raise (7 I%), and those who do not regard promotion as the most likely long-term way to a pay raise (60%). (Thus, this latent class consists of women who are on a career ladder, but otherwise they are more likely than not to regard their promotion prospects as uncertain.) And the modal categories for the third latent class include those women who are not on a career ladder (77%), those who do not think they have high chances of internal promotion (83%), those who regard promotion as the most likely long-term way to a pay raise (82%), and those who regard promotion as the most likely immediate way to a pay raise (55%). (Thus, these women are more likely than not to not be on a career ladder, and they are more likely than not to not regard themselves as having high chances of being promoted, but they are also more likely than not to regard promotion as the most likely way to a pay raise.)

Since the first latent class pertaining to men's promotion prospects consists of employees who are more likely than not to view their jobs as having good prospects, and the second latent class pertaining to men's promotion prospects consists of employees who are more likely than not to view their jobs as having poor prospects, we shall call these two latent classes the good-prospects latent class, and the poor-prospects latent class, respectively. For women's promotion prospects, there is also a good-prospects latent class (women's latent class 1) and a poor-prospects latent class (women's latent class 4); in addition, the latent structure of women's promotion prospects also includes another two latent classes: one of these can be called the mixed-I-prospects latent class (women's latent class 2), and the other can be called the mixed-11-prospects latent class (women's latent class 3).

If we now compare the latent class probabilities for men's and women's promotion prospects (see table 5), we see that, while 72% of the men are in the poor-prospects latent class, 63% of the women are in that kind of latent class; and, while 28% of the men are in the good-prospects latent class, only 5% of the women are in that kind of latent class. In addition, with respect to the two mixed-prospects latent classes, we see that 23% of the women are in the mixed-I-prospects latent class, 9% of the women are in the mixed-11-prospects latent class, and no men are in these mixed-prospects latent classes. It is interesting that these gender differences are not detectable in table 1, where we look at the bivariate relationship between gender and each manifest variable per- taining to promotion prospects. It is when the manifest variables per- taining to promotion prospects are cross-classi&ed, and the latent pattern is extracted separately for the men's data and for the women's data, that we are able to detect these gender differences in promotion pr~spects.'~

When we look at the latent classes pertaining to job autonomy, there were three for men and four for women. The first latent class for men consists mainly of men with a high degree of autonomy and control over their work situation (see table 4); 27% of the men are in this class (see table 5). The third latent class consists mainly of men with a low degree of autonomy and control over their work situation; 25% of the men are in this class. The second latent class is the largest; 48% of the men are in this latent class. This latent class consists mainly of men with less clear-cut responses in terms of autonomy and control. The modal catego- ries for this latent class include those who cannot design their own work (61%), those who cannot decide their day-to-day tasks (62%), those who

''As we noted earlier, the gender differences described in this section will be consid- ered further in the next section.

cannot decide when to start and finish their work (70%), and those who cannot initiate new tasks (54%); but the modal categories also include those who can decide the amount or pace of their work (7 I%), and also those who can reduce their work pace if they want to (71%).

For women, there is one additional latent class, which suggests that the latent structure of women's autonomy and control over their work situation is also somewhat more complex than men's. As was the case for the men, one latent class consists mainly of women with a high degree of autonomy and control over their work situation (see table 4); 21% of the women are in to this class (see table 5). Another latent class consists mainly of women with a low degree of autonomy and control; 26% of the women are in this class.

The other two latent classes pertaining to women's job autonomy con- tain 19% and 34% of the female employees in our sample. Both of these latent classes consist mainly of women with less clear-cut responses. The modal categories for one of these latent classes include those women who design their own work (52%), those who can decide day-to-day tasks (loo%), those who can initiate new tasks (87%), and those who can decide the amount or pace of their work (100%); but the modal catego- ries also include those who cannot decide when to start and finish their work (loo%), and those who cannot reduce their work pace (67%). These women are more likely than not to be relatively autono- mous at their work insofar as they are in control of their work tasks, but they are not in control of the time factor related to their work, and they are more likely than not to be unable to reduce the pace of their work.

In the other latent class pertaining to women's job autonomy, the pattern of modal categories is reversed to some extent. The modal catego- ries include those who can control the amount or pace of their work (73%), and those who can reduce the work pace if they want to (90%); but the modal categories also include those who are not able to control the work tasks they are given, that is, they cannot design they own work (84%), they cannot decide day-to-day tasks (go%), they cannot decide when to start and finish their work (77%), and they cannot initiate new tasks (61%). These women are more likely than not to be in control of the amount or pace of their work, but they are also more likely than not to be unable to be in control over their work tasks and their work situation.

Thus, while 27% of the men are in the high-autonomy latent class, 21% of the women are in that kind of class; and, while 25% of the men are in the low-autonomy latent class, 26% of the women are in that kind of class. In addition, 48% of the men are in the mixed-autonomy latent class, while 19% plus 34% of the women are in the latent classes of that kind (i.e., the mixed-I-autonomylatent class and the mixed-11-autonomy latent class).

The analysis reported in this section clearly shows that meaningful distinctions can be extracted from the pattern of answers respondents have given to the questions considered here. The latent structure analysis is not only a helpful tool to enable us to understand and explain better the relationship among the manifest variables corresponding to these questions (or to understand and explain better the data in the cross-classification tables that describe the pattern of answers respondents have given to the questions), the technique also yields a smaller set of latent variables that provides a more concise way to summarize the information that is contained in the original tables. In the next section, we shall apply the methods of latent structure analysis in a different way in order to obtain some additional information pertaining to the gender differences in the underlying pattern of the latent variables associated with the job characteristics of men and women.

ADDITIONAL GENDER COMPARISONS USING HETEROGENEOUS

AND HOMOGENEOUS LATENT STRUCTURE MODELS

In the preceding section, the parameters in the latent structure models for the men's data were estimated separately from the corresponding parameters in the models for the women's data, and the gender differ- ences in the corresponding estimated parameters obtained in this way were as large or as small as was indicated in the analysis of the data. The size of the gender differences was not restricted except to the extent that the gender differences in the estimated parameters reflected what- ever were the corresponding gender differences in the data analyzed. We shall next consider latent structure models that iestrict the size of the gender differences in the estimated parameters, and we shall see whether these models are congruent with the data.

In the analysis of the men's and women's data, the "fully homogeneous model" applies the same latent structure model to these data restricting the estimated parameters for the men to be equal to the corresponding esti- mated parameters for the women. The "homogeneous-conditionalprobabilities model" applies the same latent structure model to these data restricting the estimated conditional-probabilities for the men to be equal to the corresponding estimated conditional-probabilities for the women. The "fully heterogeneous model" considered here applies the same latent structure model to these data without restricting any of the estimated pa- rameters for the men to be equal to the corresponding estimated parameters

for the women.19 Table 6 reports results obtained when the men's and

women's data are analyzed using these models (i.e., the fully heterogeneous

model, the homogeneous-conditional-probabilities model, and the fully ho-

mogeneous model).

From the results in table 6 pertaining to payment conditions, we see that the two-class fully heterogeneous model is congruent with the data, and that neither the corresponding homogeneous-conditionalprobabilities model is congruent with the data, nor is the corresponding fully homogeneous model.20 Note that the results presented in table 6 (see, e.g., the likelihood-ratio chi-square gender components) for the two- class fully heterogeneous model are in agreement with the corresponding results in table 2.21

From the results presented in table 6 pertaining to promotion pros- pects, we see that the three-class fully heterogeneous model is not congru- ent with the data, and neither is the corresponding homogeneous- conditional-probabilities The results in table 2 and the above results from table 6 indicate that the three-class model is not satisfactory as a model that could describe both the men's data and women's data.23 As we had noted earlier, the three-class model is satisfactory for the men's data, but it is not satisfactory for the women's data.24 Also, while

19A "still more fully heterogeneous model" would not restrict the latent structure model applied to the men's data to be the same as the corresponding latent structure model applied to the women's data. The results reported in the preceding section can be viewed as results obtained when the men's and women's data are analyzed using this kind of still more fully heterogeneous model. (For more details on homogeneous and heterogeneous models, see, e.g.,Goodman [1973], and Clogg and ~oodman [1985].)

''For the homogeneous-conditional-probabilities model, the likelihood-ratio chi-square value of 29.38 (on 12 df) is statistically significant at the .O1 level; and for the fully homogeneous model, the likelihood-ratio chi-square value of 47.47 (on 13 df) is statistically significant at the .00001 level.

"For each of the fully heterogeneous models in table 6, the chi-square values (and the degrees of freedom) presented in the table can be obtained simply by adding the corresponding chi-square values (and the corresponding degrees of freedom) for the corresponding two models in table 2 (namely, the corresponding model for men and the corresponding model for women).

l2For the fully heterogeneous model, the likelihood-ratio chi-square value of 14.87 (on 7 df) is statistically significant at the .05 level; and for the homogeneous-conditional- probabilities model, the likelihood-ratio chi-square value of 26.61 (on 16 df) is also statistically significant at the .05 level.

23Note that here too the likelihood-ratio chi-square gender components presented in table 6 for the three-class fully heterogeneous model are in agreement with the corre- sponding results for the three-class model in table 2.

14The table 6 chi-square value of 14.87 (on 7 df), which is statistically significant at the .05 level, pertains to the three-class model as a model that would describe both

the three-class model is satisfactory for the men's data, this is also true for the two-class model applied to the men's data (see table 2); and so our attention earlier herein was focused more on the two-class model (than on the three-class model) for the men's data because this is the more parsimonious model (see tables 2 and 3).

The chi-square values presented in table 6 for the three-class fully homogeneous model for promotion prospects might appear, at first sight, to weaken to some extent the related conclusion presented in the preced- ing paragraph.25 However, when the chi-square values are viewed in terms of their gender components for the three-class fully homogeneous model, the relatively small gender component for men and the relatively large gender component for women presented in table 6 draws attention to the fact that the three-class model fit the men's data well but it did not provide a satisfactory fit for the women's data.26

If the three-class fully homogeneous model for promotion prospects is assumed to be true as a model that could describe both the men's data and the women's data, then the usual latent class model with three latent classes would also be true for the data on promotion prospects for the total sample.27 However, when the usual latent class model with three

the men's data and women's data; and the table 2 chi-square value of 11.29 (on 3 df), which is statistically significant at nearly the .O1 level (actually at the ,0103 level), pertains to the three-class model as a description of the women's data.

"For the fully homogeneous model, with a likelihood-ratio chi-square value of 27.12

(on 19 df), the corresponding P-value is ,102. 16With a corresponding comparison of the likelihood-ratio chi-square value and its gender components for the three-class fully heterogeneous model, we noted in n. 24 that the level of statistical significance moved from being at nearly the .01 level (actually at the ,0103 level) for the gender component for the women's data to being at the .05 level when the gender component for the women's data was combined with the gender component for the men's data. Even if the level of statistical significance had moved from being at nearly the .O1 level for the gender component for the women's data to being at, say, the .I02 level when the gender component for the women's data was combined with the gender component for the men's data (which would have occurred if the gender component for the men's data had been small enough), we would not conclude in this case that the three-class model is satisfactory as a model that would describe both the men's data and the women's data.

"With respect to the cross-classification table for the data on promotion prospects for the total sample (a 2 x 2 x 2 x 2 table), each frequency in the table is the sum of the corresponding frequencies in the 2 x 2 x 2 x 2 table for men and the 2 x 2 x 2 x 2 table for women. (For the sake of completeness, we also note here that, if the three-class homogeneous-conditional-probabilities model for promotion prospects is assumed to be true as a model that could describe both the men's data and the women's data, then the usual latent class model with three latent classes would also be true for the data on promotion prospects for the total sample.)

###### TABLE 6

LIKELIHOOD-RATIO

GENDERCOMPONENTS

LIKELIHOOD | GOODNESS | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

df | Ratio xi | of-Fit X' | Men | Women | |||||||||

Payment conditions: | |||||||||||||

Models with two latent classes: | |||||||||||||

Fully heterogeneous model | ...................................................... | ||||||||||||

Homogeneous-cp model | .......................................................... | ||||||||||||

Fully homogeneous model | .................................................... .. | ||||||||||||

Promotion prospects: | |||||||||||||

Models with three latent classes: | |||||||||||||

Fully heterogeneous model | ...................................................... | ||||||||||||

Homogeneous-cp model | ........................................................ | ||||||||||||

Fully homogeneous model | ....................................................... | ||||||||||||

Job autonomy: | |||||||||||||

Models with four latent classes: | |||||||||||||

Fully heterogeneous model | ...................................................... | ||||||||||||

Homogeneous-cp model | .......................................................... | ||||||||||||

Fully homogeneous model | ....................................................... |

NOTE.-Fully heterogeneous model = model in which the conditional probabilities may be heterogeneous for men and women, and the latent class probabilities may be heterogeneous for men and women. Homogeneous-cp model = model in which the conditional probabilities are homogeneous for men and women, and the latent class probabilities may be heterogeneous for men and women. Fully homogeneous model = model in which the conditional probabilities are homogeneous for men and women, and the latent class probabilities are homogeneous for men and women.

latent classes is applied to the data on promotion prospects for the total

sample, we find that this model does not provide an acceptable fit for

these data.28

Having drawn attention to the need for caution when interpreting the chi-square values for the three-class fully homogeneous model applied to the data on promotion prospects, it should nevertheless be noted that the level of the statistical significance obtained for these data is not as small (i.e., not as statistically significant) as the corresponding level obtained for the data on payment conditions, nor is the level of the statistical significance for the data on promotion prospects as small as the corre- sponding level obtained for the data on job autonomy.29

From the results presented in table 6 pertaining to job autonomy, we see that the four-class fully heterogeneous model is congruent with the data; however, neither the corresponding homogeneous-conditional- probabilities model is congruent with the data, nor is the corresponding fully homogeneous model.30 As we noted earlier (see table 2), the four- class model is satisfactory for the men's data, and it is also satisfactory for the women's data. Also, while the four-class model is satisfactory for the men's data, this is also true for the three-class model for the men's data (see table 2); and so our attention earlier herein was focused more

"When the usual latent class model with three latent classes is applied to the data for the total sample, the likelihood-ratio chi-square value is 9.50 (on 4 df), which is statistically significant at the .05 level. When the three-class fully homogeneous model is applied to the cross-classification table for the data on promotion prospects (a 2 x 2 x 2 x 2 table for men and a corresponding 2 x 2 x 2 x 2 table for women), the likelihood-ratio chi-square value obtained (namely, 27.12 on 19 df) can be seen to be equal to the sum of the following two likelihood-ratio chi-square values: (1) the value obtained when testing the simple model of independence between gender and the response on the joint variable formed by the four manifest variables pertaining to promotion prospects (i.e., the model of independence between the row and column variables in a 2 x 16 table that has gender cross-classified with the 16 possible responses on the joint variable), and (2) the value obtained when the usual latent class model with three latent classes is applied to the cross-classification table for the data on promotion prospects for the total sample. The two chi-square values are as follows:

(1) 17.62 on 15 df, and (2) 9.50 on 4 df. This result sheds further light on the meaning of the fully homogeneous model. The result will hold true more generally when the fully homogeneous model is applied to other sets of data, e.g., the data considered here on payment conditions and the corresponding data on job autonomy.

29Compare the results presented in table 6 for the fully homogeneous models applied to the data on payment conditions, the data on promotion prospects, and the data on job autonomy.

30For the fully heterogeneous model, with a likelihood-ratio chi-square value of 85.47 (on 76 df), the corresponding P-value is .21. For the homogeneous-conditional- probabilities model, the likelihood-ratio chi-square value of 123.47 (on 98 df) is statisti- cally significant at the .05 level; and for the fully homogeneous model, the likelihood- ratio chi-square value of 144.48 (on 99 df) is statistically significant at the ,002 level.

on the three-class model (than on the four-class model) for the men's data because this is the more parsimonious model (see tables 2 and 3).

CONCLUSIONS

This article illustrates how latent structure analysis can serve as a powerful technique for analyzing cross-classifications of certain kinds of categorical variables. By replacing the cross-classifications pertaining to the manifest variables by one or a few latent variables, the latent structure analysis yields a more parsimonious model that facilitates interpretation of the cross-classifications, and it also provides meaningful distinctions among the respondents. The latent structure analysis allows us to discover and see empirical distinctions that are in the data (distinctions that may not be readily discoverable or visible using the more usual methods of analysis). With the empirical results, we can address theoretical expectations, and thus contribute to the development of possibly better theories.

The results reported here show that, for both men and women employ- ees, the various items measuring job characteristics can be reduced to three latent dimensions, one pertaining to payment conditions, one per- taining to promotion prospects, and one pertaining to job autonomy. The pattern of the latent structures that describe the three dimensions for men's job characteristics is different in various respects from the corre- sponding pattern of the latent structures that describe the three dimen- sions for women's job characteristics. There are two latent classes (a salariat-type latent class and a non-salariat-type latent class) pertaining to the latent structure of payment conditions for both men and women, and the gender differences in these latent classes are described in detail. There are also two latent classes pertaining to the latent structure of men's promotion prospects, but there are four latent classes pertaining to the corresponding structure of women's promotion prospects. There are three latent classes pertaining to the latent structure of men's job autonomy, but there are four latent classes pertaining to the correspond- ing structure of women's job autonomy. The latent structure of women's job characteristics pertaining to promotion prospects, and the latent structure of women's job characteristics pertaining to job autonomy, are more complex than the corresponding latent structures of men's job characteristics, and the results reported in this article describe in more detail the gender differences and why the women's job characteristics have a more complex latent structure.

Since the latent structures described in this article were based on an analysis of data on job characteristics obtained using the kinds of items that are relevant in studies that pertain to the Erikson-Goldthorpe class schema, the results reported here demonstrate that the underlying indica- tors of location in the class schema will be different for women than for men. The latent structure results presented in this article are new; and they serve to illustrate the merits of the application of latent structure analysis in the present context with a set of job characteristics that is of interest in connection with the E-G class schema and also of interest in its own right. These results may also help to encourage additional re- search that applies the general approach used here in the study of other sets of job characteristics that may be of interest in connection with other conceptualizations of social class and/or that may be of interest in their own right. Even more generally, these results may encourage the further application of latent structure analysis in the study of various research topics in sociology and in the social sciences more generally, where the observed relationships among a set of manifest qualitative/categorical variables are of interest and where the possible underlying latent struc- ture that might be able to explain the observed relationships is also of interest.

APPENDIX A

The Latent Class Model

This appendix presents a brief description of the latent class model ex- pressed in mathematical terms. For expository purposes, we shall begin by focusing our attention on the case where there are, say, three manifest dichotomous variables, and the latent variable in the latent class model is also dichotomous. (For a description of the more general case, see, e.g., Goodman 1974a.)

Let A, B, and C denote the three manifest dichotomous variables, and let X denote the dichotomous latent variable. Let denote the proba- bility that an individual's response on variables A, B, and C takes on the value i, j, and k, respectively (i = 1, 2; j = 1, 2; k = 1, 2); let IIf denote the probability that an individual on latent variable X is in latent class t (t = 1, 2); let II$::x denote the probability that an individual's response on variables A, B, and C takes on the value i, j, and k, respectively, and that the individual is in latent class t on latent variable X; let II{lxdenote the conditional probability that an individual's response will take on the value i on variable A, given that the individual's latent class is t on latent variable X; and let IIjIxand n$be similarly defined. The latent class model states that

ABCX = nX ,AlX nBlX nClX

nijkt t t~t jlt k~t,

Formula (1) states that, given that an individual is in latent class t on

latent variable X, the individual's responses on the manifest variables

(A, B, C) will be mutually independent. (In other words, when the latent

class t on latent variable X is held constant, the relationships among the

manifest variables [A, B, C] disappear; i.e., the latent variable explains

the relationships among the manifest variables.) Formula (2) describes

the fact that each individual is in one (and only one) of the two latent

classes. The parameters in the latent class model (namely, nf, nilx,

IIljx, n$) can be estimated using the maximum-likelihood estimates

introduced in Goodman (1974a, 19743).

The latent class model described above can be generalized directly to the case where there are more than three manifest variables, where the manifest variables are polytomous (not necessarily dichotomous), where the latent variable is polytomous (not necessarily dichotomous), and where the latent variable is multivariate (not necessarily univariate); see, e.g., Goodman (1974~). We shall next describe briefly the case where the latent variable is, say, bivariate (rather than univariate), and where there are, say, four manifest variables (rather than three).

Let A, B, C, and D denote the four manifest variables, and let U and V denote the two dimensions of the bivariate latent variable. (In other words, we let U and V denote latent variables that have a joint bivariate distribution.) We shall now consider the case where the relationships among the manifest variables A and B are explainable in terms of the latent variable U, the relationships among the manifest variables C and D are explainable in terms of the latent variable V, and the relationships among the manifest variables A, B, C, and D are explainable in terms of the latent variables U and V. This latent class model states that

ABCDUV = nUV A nBU nclv nDlV

~ U

ijklrs 7s tlr jlr kls 11s ,

and

where II:vdenotes the probability that an individual is in latent class r on latent variable U and in latent class s on latent variable V, and where the other symbols in (3)-(4) are defined in a similar way to the correspond- ing symbols in formulas (1)-(2). Formula (3) states that, given that an individual is in latent class r on latent variable U and in latent class s on latent variable V, the individual's responses on the manifest variables (A, B, C, D) will be mutually independent; and, given that the individual is in latent class r on latent variable U, the individual's responses on the manifest variables A and B will be mutually independent; and, given that the individual is in latent class s on latent variable V, the responses on the manifest variables C and D will be mutually independent. The parameters in this latent class model (namely, IIEv, II4LU, IIjJu, II$', II$lv) can also be estimated using the maximum-likelihood estimates in- troduced in Goodman (1974a, 19743).

The statistical methods that are usually used in latent structure analysis can be justified when the number of manifest variables (and the corre- sponding number of latent variables that are needed) is not too large relative to the size of the sample. In the case considered here, we have 13 manifest variables (see table 1, where the 13 variables include one manifest trichotomous variable and 12 manifest dichotomous variables), and there are three latent variables that are used here (namely, a payment conditions latent variable, a promotion prospects latent variable, and a job autonomy latent variable) to explain relationships among manifest variables. With the 13 manifest variables, the corresponding 13-way cross-classification table has 3 X 2 l2 = 12,288 cells, but the sample size was only from 542 to 566 men and from 275 to 288 women (depending on the difference in the nonresponse rate on the different manifest vari- ables), and there were only 525 men and 265 women who responded on all of the manifest variables3' Considering those who responded on all of the manifest variables, the number of men per cell in the cross-classification is .04, and the corresponding number of women per cell is .02.

For the analysis presented in the present article, the 13-way cross- classification table was replaced by a three-way table (on payment condi- tions), a four-way table (on promotion prospects), and a six-way table (on job autonomy), and the number of cells in the tables was thereby reduced from 12,288 cells (for the 13-way table) to 12 cells (for the three- way table), 16 cells (for the four-way table), and 64 cells (for the six-way table). The number of men per cell in the latter three tables is approxi- mately 43.75, 32.81, and 8.20, respectively; and the corresponding num- ber of women per cell is approximately 22.08, 16.56, and 4.14, respec- tively.

Together with the analysis presented here, we might also have consid- ered the following modification: the 13-way table could have been re-

31There were 580 men and 289 women who responded on at least one of the manifest variables.

placed by a seven-way table (on payment conditions and promotion pros- pects), a nine-way table (on payment conditions and job autonomy), and a 10-way table (on promotion prospects and job autonomy), and each of the latter three tables could have been analyzed using the techniques of latent structure analysis introduced in Goodman (1974~) for the case when two latent variables are needed to explain the relationships among the manifest variables. For the seven-way table, the nine-way table, and the lo-way table, the number of cells in the tables would be 192 cells, 768 cells, and 1,024 cells, respectively. And so the number of men per cell in these tables would be approximately 2.73, 0.68, and 0.52, respec- tively; and the corresponding number of women per cell would be ap- proximately 1.38, 0.35, and 0.26, respectively.

In addition to the consideration here of the number of cells in the cross-classification of the manifest variables, we should also give some consideration to the number of cells in the complete cross-classification of both the manifest and latent variables. The set of three cross-classification tables of manifest variables considered in the preceding paragraph (the seven-way, nine-way, and 10-way tables) would be trans- lated into a corresponding set of three complete cross-classification tables of both manifest and latent variables (a nine-way, 11-way, and 12-way table, respectively). For the sake of simplicity, let us consider for a mo- ment the special case where the latent variables pertaining to payment conditions, promotion prospects, and job autonomy are all dichotomous latent variables3' In this special case, the number of cells in the complete tables would be 192 x 4 = 768 cells, 768 x 4 = 3,072 cells, and 1,024

x 4 = 4,096 cells, respectively. And each of the numbers of men per cell and women presented in the preceding paragraph would then need to be divided by

We would have analyzed the 13-way table of manifest variables using the maximum-likelihood techniques for the case where three

321n the latent class analysis presented earlier in this article, we found that the latent variable pertaining to payment conditions actually was dichotomous; but we also found that two or four latent classes (two for men and four for women) were needed for the latent variable pertaining to promotion prospects, and three or four latent classes (three for men and four for women) were needed for the latent variable per- taining to job autonomy.

331n the special case where, say, two latent classes are needed for the payment condi- tions latent variable, three latent classes are needed for the promotion prospects latent variable, and four latent classes are needed for the job autonomy latent variable, then the number of cells in the complete table would be 192 X 6 = 1,152 cells, 768 X 8 = 6,144 cells, and 1,024 X 12 = 12,288 cells, respectively; and the numbers of men per cell and women per cell presented in the preceding paragraph would then need to be divided by 6, 8, and 12, respectively, corresponding to the three tables under consideration here.

latent variables are needed, if the sample size had been large enough to justify doing so. We would have analyzed the set of three tables of manifest variables considered in the paragraph before the preceding one (the seven-way, nine-way, and 10-way tables) using the maximum- likelihood techniques for the case where two latent variables are needed for each table (see Goodman 1974a), if the sample size had been large enough to justify doing so. Other sets of tables could also have been used (e.g., the seven-way table referred to above, which pertains to payment conditions and promotion prospects, and the six-way table considered earlier, which pertains to job autonomy), if the sample size had been large enough to justify doing so with each of the tables in the set. With the data considered in the present article, the sample size was large enough to justify the use of the statistical methods applied here to the three-way table (pertaining to payment conditions), four-way table (pertaining to promotion prospects), and six-way table (pertaining to job autonomy).

APPENDIX B

Description of Manifest Variables

The manifest variables used in this article were based on the answers given by respondents to the questions presented below. For further details about the questionnaire from which these questions were selected, see Marshal et al. (1988). The questions presented below pertain to the payment conditions, prospects at work, and autonomy at work.

Form of remuneration.-"Which [one] of the ways on this [show card] best describes how you are paid in your present job?" The possible answers include "hourly paid," "performance," "piecework," "basic plus commission," "basic plus productivity," "basic only," "miscella- neous wage," and "no pay." We grouped the "hourly paid," "perfor- mance," "piecework" responses together in a single category (called "hourly paid" for short), we kept the "basic only" response as a separate category, and we grouped the rest of the responses together as "other responses."

Clock on.-"Are you required to clock or sign yourself on and off work?" (yestno) Paid overtime.-"Are you paid for any overtime you work?" (yes/ no)

All variables considered here under prospects were recoded as dichoto- mous variables.

Internal promotion.-"How high do you think your chances are of being given a significant promotion within your present organization?" (definite, high chance, fifty-fifty, low chance, no chance). We grouped those answering "definite" and "high chance" together; the others were placed in a second category.

Immediate way to pay raise.-"Thinking'about the immediate future, in which [one] of the ways on this [show card] are you most likely to increase your present level of pay?" (longer hours, more productivity, promotion, union pay raise, own pay raise, second job, higher job in new organization, same job in new organization, other, no way of getting a pay raise). We contrasted those answering "promotion" with all the others.

Long-term way to pay raise.-"Thinking ahead a few years, in which [one] of the ways on this [show card] are you most likely to increase your present level of pay?" (longer hours, more productivity, promotion, union pay raise, own pay raise, second job, higher job in new organiza- tion, same job in new organization, other, no way of getting a pay raise). Again, we contrasted those answering "promotion" with all the others.

On career ladder.-"Thinking about getting a promotion or going up a career ladder, is your present job a step on a recognized career or promotion ladder within your organization?" (yeslno)

All variables considered here under autonomy are dichotomous.

Design own work.-"Is yours a job which allows you to design and plan important aspects of your own work or is your work largely defined for you?" (job allows design, work largely defined)

Decide day-to-day tasks.-"Do you decide the specific tasks or jobs you carry out from day to day or does someone else?" (respondent de- cides, someone else decides)

Decide amount or pace.-"Does someone else decide how much work you do or how fast you work during the day [or do you decide]?" (respon- dent decides, someone else decides)

Decide start and quit times. "Can you decide, officially or unofficially, the time you arrive and leave work?" (yeslno)

Reduce work pace.-"Can you considerably slow down your pace of work for a day when you want to?" (yeslno)

Initiate new tasks on job.-"Can you decide on your own to introduce a new task or work assignment that you will do on your job? (yeslno)

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