Keith F. Widaman

To Parcel or Not to Parcel: Exploring the Question, Weighing the Merits

We examine the controversial practice of using parcels of items as manifest variables in structural equation modeling (SEM) procedures. After detailing arguments pro and con, we conclude that the unconsidered use of parcels is never warranted, while, at the same time, the considered use of parcels cannot be dismissed out of hand. In large part, the decision to parcel or not depends on ones philosophical stance regarding scientific inquiry (e.g., empiricist vs. pragmatist) and the substantive goal of a study (e.g., to understand the structure of a set of items or to examine the nature of a set of constructs). Prior to creating parcels, however, we recommend strongly that investigators acquire a thorough understanding of the nature and dimensionality of the items to be parceled. With this knowledge in hand, various techniques for creating parcels can be utilized to minimize potential pitfalls and to optimize the measurement structure of constructs in SEM procedures. A number of parceling techniques are described, noting their strengths and weaknesses.

Factor Analysis in the Development and Refinement of Clinical Assessment Instruments

The goals of both exploratory and confirmatory factor analysis are described and procedural guidelines for each approach are summarized, emphasizing the use of factor analysis in developing and refining clinical measures. For exploratory factor analysis, a rationale is presented for selecting between principal components analysis and common factor analysis depending on whether the research goal involves either identification of latent constructs or data reduction. Confirmatory factor analysis using structural equation modeling is described for use in validating the dimensional structure of a measure. Additionally, the uses of confirmatory factor analysis for assessing the invariance of measures across samples and for evaluating multitrait-multimethod data are also briefly described. Suggestions are offered for handling common problems with item-level data, and examples illustrating potential difficulties with confirming dimensional structures from initial exploratory analyses are reviewed.

Sample size in factor analysis.

The factor analysis literature includes a range of recommendations regarding the minimum sample size necessary to obtain factor solutions that are adequately stable and that correspond closely to population factors. A fundamental misconception about this issue is that the minimum sample size, or the

Confirmatory Factor Analysis and Item Response Theory: Two Approaches for Exploring Measurement Invariance

This study investigated the utility of confirmatory factor analysis (CFA) and item response theory (IRT) models for testing the comparability of psychological measurements. Both procedures were used to investigate whether mood ratings collected in Minnesota and China were comparable. Several issues were addressed. The first issue was that of establishing a common measurement scale across groups, which involves full or partial measurement invariance of trait indicators. It is shown that using CFA or IRT models, test items that function differentially as trait indicators across groups need not interfere with comparing examinees on the same trait dimension. Second, the issue of model fit was addressed. It is proposed that person-fit statistics be used to judge the practical fit of IRT models. Finally, topics for future research are suggested.

Hierarchically Nested Covariance Structure Models for Multitrait-Multimethod Data:

A taxonomy of covariance structure models for rep resenting multitrait-multimethod data is presented. Us ing this taxonomy, it is possible to formulate alternate series of hierarchically ordered, or nested, models for such data. By specifying hierarchically nested models, significance tests of differences between competing models are available. Within the proposed framework, specific model comparisons may be formulated to test the significance of the convergent and the discriminant validity shown by a set of measures as well as the ex tent of method variance. Application of the proposed framework to three multitrait-multimethod matrices al lowed resolution of contradictory conclusions drawn in previously published work, demonstrating the utility of the present approach.

Unidimensional Versus Domain Representative Parceling of Questionnaire Items: An Empirical Example

Two alternative methods for parceling questionnaire items for use in confirmatory analyses are presented. The first method requires that parcels must (a) pass a minimum standard of reliability and (b) provide indications of unidimensionality to be retained for analysis. The second method requires that parcels be equally representative of the multiple aspects of a domain. The parcels may then serve as adequate indicators for the general construct. The latter method is consistent with the rationale underlying aggregation of measures, a procedure currently recommended for improving the psychometric properties of behavioral measures of personality. The two methods for parceling and a comparison are illustrated with an empirical example.

HIV-related stigma and knowledge in the United States: prevalence and trends, 1991-1999.

OBJECTIVES This study assessed the prevalence of AIDS stigma and misinformation about HIV transmission in 1997 and 1999 and examined trends in stigma in the United States during the 1990s. METHODS Telephone surveys with national probability samples of English-speaking adults were conducted in the period 1996 to 1997 (n = 1309) and in 1998 to 1999 (n = 669). Findings were compared with results from a similar 1991 survey. RESULTS Overt expressions of stigma declined throughout the 1990s, with support for its most extreme and coercive forms (e.g., quarantine) at very low levels by 1999. However, inaccurate beliefs about the risks posed by casual social contact increased, as did the belief that people with AIDS (PWAs) deserve their illness. In 1999, approximately one third of respondents expressed discomfort and negative feelings toward PWAs. CONCLUSION Although support for extremely punitive policies toward PWAs has declined, AIDS remains a stigmatized condition in the United States. The persistence of discomfort with PWAs, blame directed at PWAs for their condition, and misapprehensions about casual social contact are cause for continuing concern and should be addressed in HIV prevention and education programs.

Sample size in factor analysis: The role of model error

This article examines effects of sample size and other design features on correspondence between factors obtained from analysis of sample data and those present in the population from which the samples were drawn. We extend earlier work on this question by examining these phenomena in the situation in which the common factor model does not hold exactly in the population. We present a theoretical framework for representing such lack of fit and examine its implications in the population and sample. Based on this approach we hypothesize that lack of fit of the model in the population will not, on the average, influence recovery of population factors in analysis of sample data, regardless of degree of model error and regardless of sample size. Rather, such recovery will be affected only by phenomena related to sampling error which have been studied previously. These hypotheses are investigated and verified in two sampling studies, one using artificial data and one using empirical data.

Effects of extensive temporal lobe damage or mild hypoxia on recollection and familiarity

Memory for past events can be based on recollection or on assessments of familiarity. These two forms of human memory have been studied extensively by philosophers and psychologists, but their neuroanatomical substrates are largely unknown. Here we examined the brain regions that are involved in these two forms of memory by studying patients with damage to different temporal lobe regions. Our results come from (i) structural covariance modeling of recall and recognition, (ii) introspective reports during recognition and (iii) analysis of receiver operating characteristics. In sum, we found that the regions disrupted in mild hypoxia, such as the hippocampus, are centrally involved in conscious recollection, whereas the surrounding temporal lobe supports familiarity-based memory discrimination.

On the Merits of Orthogonalizing Powered and Product Terms: Implications for Modeling Interactions Among Latent Variables

The goals of this article are twofold: (a) briefly highlight the merits of residual centering for representing interaction and powered terms in standard regression contexts (e.g., Lance, 1988), and (b) extend the residual centering procedure to represent latent variable interactions. The proposed method for representing latent variable interactions has potential advantages over extant procedures. First, the latent variable interaction is derived from the observed covariation pattern among all possible indicators of the interaction. Second, no constraints on particular estimated parameters need to be placed. Third, no recalculations of parameters are required. Fourth, model estimates are stable and interpretable. In our view, the orthogonalizing approach is technically and conceptually straightforward, can be estimated using any structural equation modeling software package, and has direct practical interpretation of parameter estimates. Its behavior in terms of model fit and estimated standard errors is very reasonable, and it can be readily generalized to other types of latent variables where nonlinearity or collinearity are involved (e.g., powered variables).