Roger E. Millsap

Assessing Factorial Invariance in Ordered-Categorical Measures.

The factor analysis of ordered-categorical measures has been described in the literature on factor analysis, but the extension of the analysis to the multiple-population case is less well-known. For example, a comprehensive statement of identification conditions for the multiplepopulation case seems absent in the literature. We review this multiple-population extension here, with an emphasis on model specification and identification. The use of the method in the study of factorial invariance is described. New results on identification are given for a variety of factor structures and types of measures. Two widely-available software packages, LISREL 8.52 (Joreskog & Sorbom, 1996) and Mplus 2.12 (Muthen & Muthen, 1998), are applied in simulated data to illustrate the method. The two programs are shown to have different model specifications for this method, leading to different fit results in some cases. The final section discusses some remaining problems facing researchers who wish to study factorial invariance in ordered-categorical data.

Methodology review: Statistical approaches for assessing measurement bias

Statistical methods developed over the last decade for detecting measurement bias in psycho logical and educational tests are reviewed. Earlier methods for assessing measurement bias generally have been replaced by more sophisticated statistical techniques, such as the Mantel-Haenszel procedure, the standardization approach, logistic regression models, and item response theory approaches. The review employs a conceptual framework that distin guishes methods of detecting measurement bias based on either observed or unobserved conditional invariance models. Although progress has been made in the development of statistical methods for detecting measurement bias, issues related to the choice of matching variable, the nonuniform nature of measurement bias, the suitability of cur rent approaches for new and emerging perform ance assessment methods, and insights into the causes of measurement bias remain elusive. Clearly, psychometric solutions to the problems of measurement bias will further understanding of the more central issue of construct validity. The con tinuing development of statistical methods for detecting and understanding the causes of mea surement bias will continue to be an important scientific challenge.

Evaluating the impact of partial factorial invariance on selection in two populations.

Studies of factorial invariance examine whether a common factor model holds across multiple populations with identical parameter values. Partial factorial invariance exists when some, but not all, parameters are invariant. The literature on factorial invariance is unclear about what should be done if partial invariance is found. One approach to this problem evaluates the impact of partial invariance on accuracy of selection on the basis of a composite of the measures whose factor structure is being studied. Assuming a single-factor model holds, accuracy of selection using the composite is evaluated under varying degrees of partial invariance. A variety of examples are presented with discussion of extensions and limitations.

Doing the Four-Step Right

Our response to Hayduk and Glaser will principally focus on their critique of the four-step procedure. Hayduk and Glaser project things into the four-step procedure that are not part of its conception. They fail to see the implicit context in which those who use this particular four-step procedure operate, which qualifies its application. They also have misunderstandings about the rationale for the procedure and read too much of exploratory factor analysis into its use. Hayduk (1996) proposed a method for doing structural equation modeling with as few as one or two indicators per latent variable, which he feels is incompatible with the factor-analytic underpinnings of the four-step procedure and which motivates him further to seek its overthrow. He did not clarify this sufficiently on SEMNET, so we have been compelled to read Hayduk (1996) to better understand his position, and we will point out some limitations of it from our own point of view. We further argue that Hayduk’s (1996) advocacy of the use of fixed parameters in sparse measurement models is not a viable general alternative to the use of multiple indicators. Hayduk also believed the usual .05 level of significance in testing the exact fit of models favors the null hypothesis. He recommended that the significance level for a chi-square test be set at .75. We show this recommendation to be incoherent with the idea of a significance test and further show it to be unnecessary because, on the contrary, in most studies the null hypothesis is likely to be rejected. STRUCTURAL EQUATION MODELING,7(1), 36–73 Copyright

On the misuse of manifest variables in the detection of measurement bias

Measurement invariance (lack of bias) of a manifest variableY with respect to a latent variableW is defined as invariance of the conditional distribution ofY givenW over selected subpopulations. Invariance is commonly assessed by studying subpopulation differences in the conditional distribution ofY given a manifest variableZ, chosen to substitute forW. A unified treatment of conditions that may allow the detection of measurement bias using statistical procedures involving only observed or manifest variables is presented. Theorems are provided that give conditions for measurement invariance, and for invariance of the conditional distribution ofY givenZ. Additional theorems and examples explore the Bayes sufficiency ofZ, stochastic ordering inW, local independence ofY andZ, exponential families, and the reliability ofZ. It is shown that when Bayes sufficiency ofZ fails, the two forms of invariance will often not be equivalent in practice. Bayes sufficiency holds under Rasch model assumptions, and in long tests under certain conditions. It is concluded that bias detection procedures that rely strictly on observed variables are not in general diagnostic of measurement bias, or the lack of bias.

As time goes by: change and stability in personality over fifty years.

Dimensions of personality, based on Q-sorted descriptions at seven points in time over a 50-year period and derived from a three-way component analysis, are described for a core sample of 118 subjects and two additional childhood samples of 99 and 108 subjects that partially overlap with the core sample. Stability and change in personality are described between adjacent periods and across a substantial segment of the life span from early childhood to late adulthood. These descriptions do not seem consistent with various explanations that personality develops either by stages or by steady gradual accumulation, or that it results from early effects. Instead, some aspects of personality shifted in level and correlational stability at particular intervals in time and according to sex of participants; other aspects were comparatively stable, irrespective of time interval and sex of participants. We suggest that the development of personality and achievement-based variables is not alike. Instead, personality development appears to be considerably more innovative and responsive-that is, more adaptive.

Early Puberty and Adolescent Pregnancy: The Influence of Alcohol Use

Objective. Early pubertal timing predicts deleterious outcomes for young girls, including substance use, risky sexual behavior, and pregnancy. In turn, adolescent pregnancy predicts long-term negative consequences such as reduced educational attainment and income-earning potential. Despite evidence of the direct links between early puberty and negative outcomes, this study is the first to examine the role that alcohol plays in the timing of sexual intercourse and pregnancy among early-maturing females. Design. Participants were 666 females, aged 18 to 22 years, from 4 major ethnic groups in Arizona (non-Hispanic white, black, Latino, and Native American). All women included in the sample had experienced a pregnancy in their teens or early 20s. Participants completed a self-administered questionnaire that inquired about their timing of menarche, sexual initiation, first alcohol use, and age at first pregnancy. A mediating model predicting age at pregnancy was tested by using path modeling. Results. Early puberty was found to be associated with earlier age of alcohol use and sexual initiation, which in turn predicted early pregnancy. Age at first sexual intercourse and age at first substance use significantly mediated the relation between age at menarche and age at first pregnancy. The results did not vary by ethnic group. Conclusions. Girls who mature early are more likely to engage in early substance use and sexual intercourse, which in turn puts them at greater risk for adolescent pregnancy. It is important that health care providers are sensitive to the risks associated with early maturation among young girls and provide preventive screening, education, and counseling related to alcohol use and sexual initiation for this group.

Rationale and Construct Validity Evidence for the Job Search Behavior Index: Because Intentions (and New Year's Resolutions) Often Come to Naught.

Abstract A conceptual framework for the determinants of organizational turnover which identifies five panels of variables—job properties, affective/attitudinal reactions, intentions to leave/stay, job search behavior, and turnover occurrences—is advanced. Accordingly, it is reasoned that job search behavior (e.g., revising ones resume) is a more immediate precursor of voluntary turnover than are antecedent variables, such as intentions. Further, it is argued that behavior is required to translate intentions into results. Data from three samples indicate that the Job Search Behavior Index (JSBI) is psychometrically sound and construct valid. Evidence also indicates that the JSBI is a superior predictor of organizational turnover (and intraorganizational job change) in comparison to attitudinal and intention measures. Moreover, stepwise multiple regression and discriminant analyses indicate that the JSBI explains significant incremental variance in turnover, over and beyond the variance explained by perceptual, affective, attitudinal, and intention measures combined.

Detecting Violations of Factorial Invariance Using Data-Based Specification Searches: A Monte Carlo Study.

In testing factorial invariance, researchers have often used a reference variable strategy in which the factor loading for a variable (i.e., reference variable) is fixed to 1 for identification. This commonly used method can be misleading if the chosen reference variable is actually a noninvariant item. This simulation study suggests an alternative method for testing factorial invariance and evaluates the performance of the method in specification searches based on the modification index. The results of the study showed that the proposed specification searches performed well when the number of noninvariant variables was relatively small and this performance improved as sample size increased and the size of group differences increased. When the number of noninvariant variables was relatively large, however, the method rarely succeeded in detecting the noninvariant items in the specification searches. Implications of the findings are discussed along with the limitations of the study.

Component analysis in cross-sectional and longitudinal data

An extension of component analysis to longitudinal or cross-sectional data is presented. In this method, components are derived under the restriction of invariant and/or stationary compositing weights. Optimal compositing weights are found numerically. The method can be generalized to allow differential weighting of the observed variables in deriving the component solution. Some choices of weightings are discussed. An illustration of the method using real data is presented.