Parametric statistics and levels of measurement.

If Y is a continuous, ordinal measure of latent variable θ and Y has a normal distribution with equal variances in several groups, then t tests and one-way analyses of variance on Y can be used to test hypotheses about population mean differences on θ in the corresponding groups. If X and Y are continuous, ordinal measures of latent variables θ and φ, and if X and Y have a bivariate normal distribution, then a test of the null hypothesis that the population correlation between X and Y is zero is also a test of the hypothesis that θ and φ are independent. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Analysis of multivariate frequency data by graphical models and generalizations of the multidimensional row-column association model.

Models used to analyze cross-classifications of counts from psychological experiments must represent associations between multiple discrete variables and take into account attributes of stimuli, experimental conditions, or characteristics of subjects. The models must also lend themselves to psychological interpretations about underlying structures mediating the relationship between stimuli and responses. To meet these needs, the author extends the graphical latent variable models for nominal and/or ordinal data proposed by C. J. Anderson and J. K. Vermunt (2000) to situations in which dependencies between observed variables are not fully accounted for by the latent variables. The graphical models provide a unified framework for studying multivariate associations that include log-linear models and log-multiplicative association models as special cases. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

The Integration of Continuous and Discrete Latent Variable Models: Potential Problems and Promising Opportunities.

Structural equation mixture modeling (SEMM) integrates continuous and discrete latent variable models. Drawing on prior research on the relationships between continuous and discrete latent variable models, the authors identify 3 conditions that may lead to the estimation of spurious latent classes in SEMM: misspecification of the structural model, nonnormal continuous measures, and nonlinear relationships among observed and/or latent variables. When the objective of a SEMM analysis is the identification of latent classes, these conditions should be considered as alternative hypotheses and results should be interpreted cautiously. However, armed with greater knowledge about the estimation of SEMMs in practice, researchers can exploit the flexibility of the model to gain a fuller understanding of the phenomenon under study. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Structural-equation models of current drug use: Are appropriate models so simple(x)?

The simplex and common-factor models of drug use were compared using maximum-likelihood estimation of latent variable structural models in two samples: a sample of 226 high school students, using ratio-scale measures of current drug use, and a sample of 310 industrial workers and 811 college students, using ordinal-scale measures of current drug use. Latent variables of alcohol, marihuana, enhancer hard drugs, and dampener hard drugs were specified in a series of structural models. Contrary to previous findings with cumulative drug-use data, the common-factor model provided a more acceptable representation of the observed current-use data than did the simplex model in both samples. In addition, the similarity of results across both of these samples supports recent contentions by Huba and Bentler (1982) that quantitatively measured variables are not necessarily superior to qualitative, ordinal indicators in latent variable models of drug use. (49 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Response variable hypotheses in the multivariate analysis of variance.

Es using multivariate analysis of variance (MANOVA) usually want to analyze effects separately for each response variable after rejecting a null hypothesis of multivariate dispersion. From the standpoint of the multivariate general linear model, 4 measures of importance for response variables are discussed: univariate F statistic for each response, standardized canonical coefficient for each response, contribution to the MANOVA test criterion by each response, and simultaneous confidence intervals on estimates of treatment effects on each response. Artificial data are presented to illustrate problems in using these measures. (17 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Criteria for criteria.

"When one selects a criterion to evaluate the effectiveness of some independent variable, the choice is frequently made… . [on the basis of] relevance, expedience, or precedence." Among the criterion dimensions which might be studied are: (a) Time. (When is the measurement taken?) (b) Type. (What performance measure is selected and why that one?) (c) Level. (What level of performance is considered success or failure?) "If we knew more about the functioning of criterional variables, we should be able to predict which criteria are relevant for assessing effects of independent variables and with this knowledge, be able to state more concerning the operations of the independent and the intervening variables." From Psyc Abstracts 36:02:2AF28W. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Sampling variance in the correlation coefficient under indirect range restriction: Implications for validity generalization.

The authors conducted Monte Carlo simulations to investigate whether indirect range restriction (IRR) on 2 variables X and Y increases the sampling error variability in the correlation coefficient between them. The manipulated parameters were (a) IRR on X and Y (i.e., direct restriction on a third variable Z), (b) population correlations ρxy, ρxz, and ρyz and (c) sample size. IRR increased the sampling error variance in rxy to values as high as 8.50% larger than the analytically derived expected values. Thus, in the presence of IRR, validity generalization users need to make theory-based decisions to ascertain whether the effects of IRR are artifactual or caused by situational-specific moderating effects. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Effect of personal characteristics on relationships between attitudes and job performance.

Using 376 airmen, Whitlock and Cureton (see 35: 7252) collected attitude score and biographical data, which is reanalysed in the present study, using multiple regression techniques. "… much of the criterion variance associated with attitude measures is also related to more easily obtained biographical characteristics of workers and biographical variables should be considered when relating attitudes to productivity." (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Global and specific ratings of teaching effectiveness and their relation to course objectives: Reply to Marsh (1994).

W E. Cashin and R. G. Downey (see record 1994-08141-001) studied global student rating items, plus some control variables, for summative evaluation using the Instructional Development and Effectiveness Assessment (IDEA) composite from 17,183 classes processed in 1989–1990 as the criterion variable. H. W. Marsh (see record 1995-08082-001), analyzing 29,543 classes processed in 1990–1991, raised some questions about the effectiveness of the IDEA composite as a criterion of effective teaching. Marsh generated four additional criterion variables from the IDEA data. However, examination of Marsh's data revealed only minor differences. When the original study was replicated with each of Marsh's four criterion variables, the results were essentially the same. Using Marsh's criterion variables supported the original conclusion that global items account for most of the variance in criterion measures of teaching effectiveness and may be used for summative evaluation. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Ramsay-curve item response theory (RC-IRT) to detect and correct for nonnormal latent variables.

Popular methods for fitting unidimensional item response theory (IRT) models to data assume that the latent variable is normally distributed in the population of respondents, but this can be unreasonable for some variables. Ramsay-curve IRT (RC-IRT) was developed to detect and correct for this nonnormality. The primary aims of this article are to introduce RC-IRT less technically than it has been described elsewhere; to evaluate RC-IRT for ordinal data via simulation, including new approaches for model selection; and to illustrate RC-IRT with empirical examples. The empirical examples demonstrate the utility of RC-IRT for real data, and the simulation study indicates that when the latent distribution is skewed, RC-IRT results can be more accurate than those based on the normal model. Along with a plot of candidate curves, the Hannan-Quinn criterion is recommended for model selection. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Information-theoretic latent distribution modeling: Distinguishing discrete and continuous latent variable models.

Distinguishing between discrete and continuous latent variable distributions has become increasingly important in numerous domains of behavioral science. Here, the authors explore an information-theoretic approach to latent distribution modeling, in which the ability of latent distribution models to represent statistical information in observed data is emphasized. The authors conclude that loss of statistical information with a decrease in the number of latent values provides an attractive basis for comparing discrete and continuous latent variable models. Theoretical considerations as well as the results of 2 Monte Carlo simulations indicate that information theory provides a sound basis for modeling latent distributions and distinguishing between discrete and continuous latent variable models in particular. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

A confirmatory test of a model of performance determinants.

The total variance in any observed measure of performance can be attributed to 3 sources: (1) the correlation of the measure with the latent variable of interest (i.e., true score variance), (2) reliable but irrelevant variance due to contamination, and (3) error. A model is proposed that specifies 3, and only 3, determinants of the relevant variance: declarative knowledge, procedural knowledge and skill, and volitional choice (motivation). The 3 determinants are defined, and their implications for performance measurement are discussed. Using data from the US Army Selection and Classification Project (Project A), it was found that the model fits a simplex pattern to the criterion data matrix. The predictor–determinant correlations are also estimated. Analyses of the data with LISREL provided strong confirmation of the model. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

The contribution of individual variables to Hotelling's T2, Wilks' lambda, and R2

We examine the effect of each variable on the following statistics: the one-sample and two-sample Hotelling's T2, Wilks' lambda for multivariate analysis of variance, and R2 in multiple regression. For T2, the net effect of each variable is an increase in the multivariate statistic, and the particular factors determining the amount of increase are (i) the multiple correlation of the variable with all other variables, and (ii) how well the variable's contribution to falsifying the hypothesis can be linearly predicted from the other variables. The effect of each predictor variable on R2 is similar to the effect of each variable on T2. For Wilks' lambda, each variable induces a decrease, due to (i) the F for that variable alone, and (ii) the change in multiple correlation from within-sample to total-sample.     

Between-subjects expectancy theory research: A statistical review of studies predicting effort and performance.

A large number of between-Ss expectancy theory studies have correlated measures of employee motivation (force) to perform with measures of effort and performance. The results of these studies vary considerably. A statistical review of the studies was conducted to determine the extent to which the variance explained (the dependent variable) was a function of various characteristics of the effort and performance and of the force-to-perform measures (the independent variables). There were 160 observations, derived from 32 studies. With the use of multiple regression analysis it was found that variance explained in these studies was greater when (a) self-report or quantitative measures of effort and performance were used rather than evaluations of these variables by someone other than the S; (b) 10–25 outcomes were included in the force measure rather than a greater or smaller number of outcomes; (c) outcome valence was numerically scaled with positive numbers only, and the scale values were described in terms of desirability rather than importance; and (d) the force measure contained either no assessment of expectancy or an assessment that confounded expectancy and instrumentality. These variables accounted for 42% of the variance in the results obtained in the studies reviewed. (31 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

An Empirical Evaluation of Alternative Methods of Estimation for Confirmatory Factor Analysis With Ordinal Data.

Confirmatory factor analysis (CFA) is widely used for examining hypothesized relations among ordinal variables (e.g., Likert-type items). A theoretically appropriate method fits the CFA model to polychoric correlations using either weighted least squares (WLS) or robust WLS. Importantly, this approach assumes that a continuous, normal latent process determines each observed variable. The extent to which violations of this assumption undermine CFA estimation is not well-known. In this article, the authors empirically study this issue using a computer simulation study. The results suggest that estimation of polychoric correlations is robust to modest violations of underlying normality. Further, WLS performed adequately only at the largest sample size but led to substantial estimation difficulties with smaller samples. Finally, robust WLS performed well across all conditions. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Identification and prediction of two training criterion factors.

12 examination scores from 6 courses given as part of the Naval Pre-Flight Training Program were factored into two interpretable criterion factors. The intercorrelations of 10 predictor (standard test) variables were then added to the correlation matrix, and loadings for them on the criterion factors were obtained. Using the factor loadings of the predictors as validity coefficients, regression weights were found for them on each of the two criterion factors, using a modified Doolittle method. "The principal advantage… derived from the initial factor analysis of the criterion variables is that the obtained criterion factors may be isolated free from the influence of the variance of the predictor variables." (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Does resting electroencephalograph asymmetry reflect a trait? An application of latent state-trait theory.

Recent research on brain asymmetry and emotion treated measures of resting electroencephalograph (EEG) asymmetry as genuine trait variables, but inconsistency in reported findings and modest retest correlations of baseline asymmetry are not consistent with this practice. The present study examined the alternative hypothesis that resting EEG asymmetry represents a superimposition of a trait like activation asymmetry with substantial state-dependent fluctuations. Resting EEG was collected from 59 participants on 4 occasions of measurement, and data were analyzed in terms of latent state-trait theory. For most scalp regions, about 60% of the variance of the asymmetry measure was due to individual differences on a temporally stable latent trait, and 40% of the variance was due to occasion-specific fluctuations, but measurement errors were negligible. Further analyses indicated that these fluctuations might be efficiently reduced by aggregation across several occasions. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Hierarchical organization of personality and prediction of behavior.

Two studies evaluated personality trait measures and Big Five factor measures for their accuracy in predicting important behavior criteria. The results of both studies showed that the narrower traits and the broader factors, thought to define 2 levels of a hierarchy of personality variables, separately predicted most criterion variables. However, the incremental validity of the personality trait measures (the degree to which the traits increased the criterion prediction achieved by the factors) was generally much larger than the incremental validity of the Big Five factor measures. It was concluded that aggregating personality traits into their underlying personality factors could result in decreased predictive accuracy due to the loss of trait-specific but criterion-valid variance. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Generalized linear item response theory.

Generalized linear item response theory is discussed, which is based on the following assumptions: (1) A distribution of the response occurs according to given item format; (2) the item responses are explained by 1 continuous or nominal latent variable and p latent as well as observed variables that are continuous or nominal; (3) the responses to the different items of a test are independently distributed given the values of the explanatory variables; and (4) a monotone differentiable function g of the expected item response τ is needed such that a linear combination of the explanatory variables is a predictor of g(τ). It is shown that most of the well-known psychometric models are special cases of the generalized theory and that concepts such as differential item functioning, specific objectivity, reliability, and information can be subsumed under the generalized theory. (PsycINFO Database Record (c) 2011 APA, all rights reserved)