scholarly journals Are Items More Than Indicators? An examination of psychometric homogeneity, item-specific effects, and consequences for structural equation models

2021 ◽  
Author(s):  
Kenneth McClure ◽  
Ross Jacobucci

Concerns of measurement error often motivate researchers to aggregate item information, using simple heuristics (e.g., sum scores) or latent variable methods, to mitigate unwanted effects such as parameter bias and attenuation. These approaches are often invoked without acknowledging that many scales in practice likely fail to possess the necessary properties for these models to be sufficient (i.e., positive conditional association and vanishing conditional dependence). We argue that measures which are not psychometrically homogeneous likely contain item specific effects particularly when examined in conjunction with external variables. We demonstrate this using a clinical empirical example assessing risk factors for suicidal ideation and show that measures constructed in alignment with principles of psychometric homogeneity are most appropriately modeled at the scale (or subscale) level while other measures should be considered at the item level. As a result, latent variable applications to such instruments are susceptible to interpretational confounding. The effects of interpretational confounding on R2, root mean square error, and model parameters are evaluated in a small simulation study. We conclude that item specific effects are not uncommon in practice and impact both explanatory and predictive research. Our findings suggest that classical approaches to addressing measurement error are insufficient to fully capture the breadth of instruments implemented in practice. Careful consideration of both the scale construction process and roles of scale items in the broader psychological theory are necessary prior to the application of traditional measurement methods.

2014 ◽  
Vol 77 (4) ◽  
pp. 361-386 ◽  
Author(s):  
Cesar J. Rebellon ◽  
Michelle E. Manasse ◽  
Karen T. Van Gundy ◽  
Ellen S. Cohn

Multiple criminological theories predict that attitudes toward delinquency should affect an individual’s delinquent behavior. Criminological research, however, has not sufficiently incorporated social psychological theory predicting the reverse causal relationship, and tends to suffer from important methodological limitations. The present study addresses these issues using longitudinal data from the New Hampshire Youth Study (N = 626). After using latent variable models to demonstrate the discriminant validity of attitudinal and behavioral measures, it uses structural equation models to examine whether attitudes are stronger predictors of behavior or vice versa. Net of controls, results provide qualified support for a reciprocal relationship but suggest that behavior affects attitudes much more than attitudes affect behavior. We conclude by discussing the implications of these findings for future research and for interventions aimed at controlling delinquency.


1981 ◽  
Vol 18 (3) ◽  
pp. 382-388 ◽  
Author(s):  
Claes Fornell ◽  
David F. Larcker

Several issues relating to goodness of fit in structural equations are examined. The convergence and differentiation criteria, as applied by Bagozzi, are shown not to stand up under mathematical or statistical analysis. The authors argue that the choice of interpretative statistic must be based on the research objective. They demonstrate that when this is done the Fornell-Larcker testing system is internally consistent and that it conforms to the rules of correspondence for relating data to abstract variables.


2001 ◽  
Vol 20 (15) ◽  
pp. 2351-2368 ◽  
Author(s):  
J. M. Batista-Foguet ◽  
G. Coenders ◽  
M. Artés Ferragud

1981 ◽  
Vol 18 (1) ◽  
pp. 39-50 ◽  
Author(s):  
Claes Fornell ◽  
David F. Larcker

The statistical tests used in the analysis of structural equation models with unobservable variables and measurement error are examined. A drawback of the commonly applied chi square test, in addition to the known problems related to sample size and power, is that it may indicate an increasing correspondence between the hypothesized model and the observed data as both the measurement properties and the relationship between constructs decline. Further, and contrary to common assertion, the risk of making a Type II error can be substantial even when the sample size is large. Moreover, the present testing methods are unable to assess a model's explanatory power. To overcome these problems, the authors develop and apply a testing system based on measures of shared variance within the structural model, measurement model, and overall model.


2016 ◽  
Vol 51 (2-3) ◽  
pp. 257-258 ◽  
Author(s):  
Andrea Hildebrandt ◽  
Oliver Lüdtke ◽  
Alexander Robitzsch ◽  
Christopher Sommer ◽  
Oliver Wilhelm

2006 ◽  
Vol 3 (2) ◽  
Author(s):  
Josep Bisbe ◽  
Germà Coenders ◽  
Willem Saris ◽  
Joan Batista-Foguet

Several methods have been suggested to estimate non-linear models with interaction terms in the presence of measurement error. Structural equation models eliminate measurement error bias, but require large samples. Ordinary least squares regression on summated scales, regression on factor scores and partial least squares are appropriate for small samples but do not correct measurement error bias. Two stage least squares regression does correct measurement error bias but the results strongly depend on the instrumental variable choice. This article discusses the old disattenuated regression method as an alternative for correcting measurement error in small samples. The method is extended to the case of interaction terms and is illustrated on a model that examines the interaction effect of innovation and style of use of budgets on business performance. Alternative reliability estimates that can be used to disattenuate the estimates are discussed. A comparison is made with the alternative methods. Methods that do not correct for measurement error bias perform very similarly and considerably worse than disattenuated regression.


2019 ◽  
Author(s):  
Steven M. Boker ◽  
Timo von Oertzen ◽  
Andreas Markus Brandmaier

A general method is introduced in which variables that are products of other variables in the context of a structural equation model (SEM) can be decomposed into the sources of variance due to the multiplicands. The result is a new category of SEM which we call a Multiplicative Reticular Action Model (XRAM). XRAM can include interactions between latent variables, multilevel random coefficients, latent variable moderators, and novel constructs such as factors of paths and twin genetic decomposition of multilevel random coefficients. The method relies on an assumption that all variance sources in a model can be decomposed into linear combinations of independent normal standardized variables. Although the distribution of a variable that is an outcome of multiplication between other variables is not normal, the assumption is that it can be decomposed into sources that are normal if one takes into account the non-normality induced by the multiplication. The method is applied to an example to show how in a special case it is equivalent to known unbiased and efficient estimators in the statistical literature. Two simulations are presented that demonstrate the precision of the approximation and implement the method to estimate parameters in a multilevel autoregressive framework.


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