Merging Multilevel and Structural Equation Models to Estimate Random Change Points in Multi-Phasic Growth Models

Hybrid autoregressive-latent growth structural equation models for longitudinal data represent a synthesis of the autoregressive and latent growth modeling frameworks. Although these models are conceptually powerful, in practice they may struggle to separate autoregressive and growth-related processes during estimation. This confounding of change processes may, in turn, increase the risk of the models producing deceptively compelling results (i.e., models that fit excellently by conventional standards despite highly biased parameter estimates). Including additional time points provides models with more raw information about change, which could help improve process separability and the accuracy of parameter estimates to a degree. This study thus used Monte Carlo simulation methods to examine associations between change process separability, the number of time points in a model, and the consequences of misspecification, across three prominent hybrid autoregressive-latent growth models: the Latent Change Score model (LCS), the Autoregressive Latent Trajectory Model (ALT), and the Latent Growth Model with Structured Residuals (LGM-SR). Results showed that including more time points increased process separability and robustness to misspecification in the LCS and ALT, but typically not at a rate that would be practically feasible for most developmental researchers. Alternatively, regardless of how many time points were in the model process separability was high in the LGM-SR, as was robustness to misspecification. Overall, results suggest that the LGM-SR is the most effective of the three hybrid autoregressive-latent growth models considered here.

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Measuring the Big Five in Self-Report and Other Ratings

European Journal of Psychological Assessment ◽

10.1027//1015-5759.16.1.31 ◽

2000 ◽

Vol 16 (1) ◽

pp. 31-43 ◽

Cited By ~ 24

Author(s):

Claudio Barbaranelli ◽

Gian Vittorio Caprara

Keyword(s):

Big Five ◽

Structural Equation ◽

Structural Equation Models ◽

Error Variance ◽

The Self ◽

Self Report ◽

Sources Of Information ◽

Third Person ◽

Fit Indexes ◽

Response Modes

Summary: The aim of the study is to assess the construct validity of two different measures of the Big Five, matching two “response modes” (phrase-questionnaire and list of adjectives) and two sources of information or raters (self-report and other ratings). Two-hundred subjects, equally divided in males and females, were administered the self-report versions of the Big Five Questionnaire (BFQ) and the Big Five Observer (BFO), a list of bipolar pairs of adjectives ( Caprara, Barbaranelli, & Borgogni, 1993 , 1994 ). Every subject was rated by six acquaintances, then aggregated by means of the same instruments used for the self-report, but worded in a third-person format. The multitrait-multimethod matrix derived from these measures was then analyzed via Structural Equation Models according to the criteria proposed by Widaman (1985) , Marsh (1989) , and Bagozzi (1994) . In particular, four different models were compared. While the global fit indexes of the models were only moderate, convergent and discriminant validities were clearly supported, and method and error variance were moderate or low.

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Collective Efficacy and Organizational Commitment in an Italian City Hall

European Psychologist ◽

10.1027/1016-9040.14.4.363 ◽

2009 ◽

Vol 14 (4) ◽

pp. 363-371 ◽

Cited By ~ 14

Author(s):

Laura Borgogni ◽

Silvia Dello Russo ◽

Laura Petitta ◽

Gary P. Latham

Keyword(s):

Organizational Commitment ◽

Collective Efficacy ◽

Structural Equation ◽

Structural Equation Models ◽

Practical Significance ◽

City Hall ◽

Italian City ◽

Public Sector Managers ◽

The Individual ◽

Level Group

Employees (N = 170) of a City Hall in Italy were administered a questionnaire measuring collective efficacy (CE), perceptions of context (PoC), and organizational commitment (OC). Two facets of collective efficacy were identified, namely group and organizational. Structural equation models revealed that perceptions of top management display a stronger relationship with organizational collective efficacy, whereas employees’ perceptions of their colleagues and their direct superior are related to collective efficacy at the group level. Group collective efficacy had a stronger relationship with affective organizational commitment than did organizational collective efficacy. The theoretical significance of this study is in showing that CE is two-dimensional rather than unidimensional. The practical significance of this finding is that the PoC model provides a framework that public sector managers can use to increase the efficacy of the organization as a whole as well as the individual groups that compose it.

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A Cautionary Note on Incremental Fit Indices Reported by LISREL

Methodology ◽

10.1027/1614-1881.1.2.81 ◽

2005 ◽

Vol 1 (2) ◽

pp. 81-85 ◽

Cited By ~ 5

Author(s):

Stefan C. Schmukle ◽

Jochen Hardt

Keyword(s):

Factor Analysis ◽

Maximum Likelihood ◽

Structural Equation ◽

Structural Equation Models ◽

Null Model ◽

Likelihood Estimation ◽

Parameter Estimates ◽

Fit Indices ◽

Cautionary Note ◽

Confirmatory Factor

Abstract. Incremental fit indices (IFIs) are regularly used when assessing the fit of structural equation models. IFIs are based on the comparison of the fit of a target model with that of a null model. For maximum-likelihood estimation, IFIs are usually computed by using the χ2 statistics of the maximum-likelihood fitting function (ML-χ2). However, LISREL recently changed the computation of IFIs. Since version 8.52, IFIs reported by LISREL are based on the χ2 statistics of the reweighted least squares fitting function (RLS-χ2). Although both functions lead to the same maximum-likelihood parameter estimates, the two χ2 statistics reach different values. Because these differences are especially large for null models, IFIs are affected in particular. Consequently, RLS-χ2 based IFIs in combination with conventional cut-off values explored for ML-χ2 based IFIs may lead to a wrong acceptance of models. We demonstrate this point by a confirmatory factor analysis in a sample of 2449 subjects.

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Forced Zero Cross-Loading Misspecifications in Measurement Component of Structural Equation Models

Methodology ◽

10.1027/1614-2241/a000084 ◽

2014 ◽

Vol 10 (4) ◽

pp. 138-152 ◽

Cited By ~ 5

Author(s):

Hsien-Yuan Hsu ◽

Susan Troncoso Skidmore ◽

Yan Li ◽

Bruce Thompson

Keyword(s):

Structural Equation ◽

Structural Model ◽

Structural Equation Models ◽

Equation Model ◽

Model Fit ◽

Model Specification ◽

Simulation Design ◽

Measurement Models ◽

Fit Statistics ◽

Path Coefficients

The purpose of the present paper was to evaluate the effect of constraining near-zero parameter cross-loadings to zero in the measurement component of a structural equation model. A Monte Carlo 3 × 5 × 2 simulation design was conducted (i.e., sample sizes of 200, 600, and 1,000; parameter cross-loadings of 0.07, 0.10, 0.13, 0.16, and 0.19 misspecified to be zero; and parameter path coefficients in the structural model of either 0.50 or 0.70). Results indicated that factor pattern coefficients and factor covariances were overestimated in measurement models when near-zero parameter cross-loadings constrained to zero were higher than 0.13 in the population. Moreover, the path coefficients between factors were misestimated when the near-zero parameter cross-loadings constrained to zero were noteworthy. Our results add to the literature detailing the importance of testing individual model specification decisions, and not simply evaluating omnibus model fit statistics.

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