Degrees of Freedom in Multigroup Confirmatory Factor Analyses

2020 ◽  
Vol 36 (1) ◽  
pp. 105-113 ◽  
Author(s):  
Ulrich Schroeders ◽  
Timo Gnambs
Keyword(s):  
Measurement Invariance ◽  
Psychological Assessment ◽  
Latent Variables ◽  
Degrees Of Freedom ◽  
Measurement Model ◽  
Psychological Research ◽  
Confirmatory Factor Analyses ◽  
Invariance Testing ◽  
Testing Procedures ◽  
Confirmatory Factor

Abstract. Measurement invaraiance is a key concept in psychological assessment and a fundamental prerequisite for meaningful comparisons across groups. In the prevalent approach, multigroup confirmatory factor analysis (MGCFA), specific measurement parameters are constrained to equality across groups. The degrees of freedom ( df) for these models readily follow from the hypothesized measurement model and the invariance constraints. In light of research questioning the soundness of statistical reporting in psychology, we examined how often reported df match with the df recalcualted based on information given in the publications. More specifically, we reviewed 128 studies from six leading peer-reviewed journals focusing on psychological assessment and recalculated the df for 302 measurement invariance testing procedures. Overall, about a quarter of all articles included at least one discrepancy with metric and scalar invariance being more frequently affected. We discuss moderators of these discrepancies and identify typical pitfalls in measurement invariance testing. Moreover, we provide example syntax for different methods of scaling latent variables and introduce a tool that allows for the recalculation of df in common MGCFA models to improve the statistical soundness of invariance testing in psychological research.

Scale Development and Factor Analysis

2018 ◽  
pp. 159-183
Author(s):  
Lihua Xu
Keyword(s):  
Scale Development ◽  
Stereotype Threat ◽  
Measurement Invariance ◽  
Leadership Style ◽  
Analytical Methods ◽  
The United States ◽  
Invariance Testing ◽  
Testing Procedures ◽  
Confirmatory Factor ◽  
The Common

Scale development is an important step in empirical research. This chapter describes the common procedures to follow in scale development with essential factor analytical methods. The concept of measurement invariance, the importance of its testing prior to group comparisons, and testing procedures are discussed. Single-group, multi-group, and hierarchical confirmatory factor analytical methods and associated decision making are described. Procedural steps in scale development and measurement invariance testing are illustrated at length using a real dataset in stereotype threat and principals' leadership style in the United States.

scholarly journals Forgiveness in the Context of Divorce: A Cross-Cultural Measurement Invariance Study via Multiple-Group Factor Analysis (CFA) across Chile and Spain

2021 ◽  
Vol 18 (16) ◽  
pp. 8236
Author(s):  
Diana Rivera-Ottenberger ◽  
Mónica Guzmán-González ◽  
Carlos Calderón ◽  
Sagrario Yárnoz-Yaben ◽  
Priscila Comino
Keyword(s):  
Measurement Invariance ◽  
Initial Step ◽  
Cross Cultural ◽  
Confirmatory Factor Analyses ◽  
Invariance Testing ◽  
Cross Cultural Differences ◽  
Multiple Group ◽  
Cultural Field ◽  
Confirmatory Factor ◽  
The Cross

(1) Background: Current research on the factors involved in the adaptation process to divorce or separation has explored cross-cultural differences. An initial step in the cross-cultural field is to investigate whether the measurements applied are comparable in different cultural contexts. The aim of the present study is to test the measurement invariance of the Questionnaire of Forgiveness in Divorce-Separation (CPD-S); (2) Methods: The CPD-S was completed by 556 (M = 44.52, SD = 10.18) and 240 (M = 41.44, SD = 7.87) Chilean and Spanish divorced individuals, respectively. Confirmatory factor analyses in single samples and measurement invariance testing in a multi-group framework were conducted to test the cross-group equivalence; (3) Results: The single-factor structure of the CPD-S was supported in both countries. Measurement invariance analysis demonstrated that the CPD-S had partial scalar measurement invariance; (4) Conclusions: The evidence supports the conclusion that CPD-S operates similarly across both countries. Findings are discussed from a cross-cultural and methodological perspective.

scholarly journals Measurement Invariance Testing Using Confirmatory Factor Analysis and Alignment Optimization: A Tutorial for Transparent Analysis Planning and Reporting

2021 ◽  
Author(s):  
Jessica Kay Flake ◽  
Raymond Luong
Keyword(s):  
Measurement Invariance ◽  
Traditional Approach ◽  
Research Question ◽  
Measurement Properties ◽  
Confirmatory Factor Analyses ◽  
Invariance Testing ◽  
Measurement Models ◽  
Multiple Group ◽  
Confirmatory Factor ◽  
Traditional Approaches

Measurement invariance—the notion that the measurement properties of a scale are equalacross groups, contexts, or time—is an important assumption underlying much of psychology research. The traditional approach for evaluating measurement invariance is to fit a series of nested measurement models using multiple-group confirmatory factor analyses. However, traditional approaches are strict, vary across the field in implementation, and present multiplicity challenges, even in the simplest case of two groups under study. The alignment method was recently proposed as an alternative approach. This method is more automated, requires fewer decisions from researchers, and accommodates two or more groups. However, it has different assumptions, estimation techniques, and limitations from traditional approaches. To address the lack of accessible resources that explain the methodological differences and complexities between the two approaches, we introduce and illustrate both, comparing them side by side. First, we overview the concepts, assumptions, advantages, and limitations of each approach. Based on this overview, we propose a list of four key considerations to help researchers decide which approach to choose and how to document their analytical decisions in a preregistration or analysis plan. We then demonstrate our key considerations on an illustrative research question using an open dataset and provide an example of a completed preregistration. Our illustrative example is accompanied by an annotated analysis report that shows readers, step-by-step, how to conduct measurement invariance tests using R and Mplus. Finally, we provide recommendations for how to decide between and use each approach and next steps for methodological research.

scholarly journals Testing measurement invariance across groups: applications in cross-cultural research.

2010 ◽  
Vol 3 (1) ◽  
pp. 111-130 ◽  
Author(s):  
Taciano L. Milfont ◽  
Ronald Fischer
Keyword(s):  
Factor Analysis ◽  
Measurement Invariance ◽  
Psychological Research ◽  
Cross Cultural ◽  
Methodological Issues ◽  
Psychological Variables ◽  
Invariance Testing ◽  
Cultural Research ◽  
Confirmatory Factor ◽  
Cross Cultural Research

Researchers often compare groups of individuals on psychological variables. When comparing groups an assumption is made that the instrument measures the same psychological construct in all groups. If this assumption holds, the comparisons are valid and differences/similarities between groups can be meaningfully interpreted. If this assumption does not hold, comparisons and interpretations are not fully meaningful. The establishment of measurement invariance is a prerequisite for meaningful comparisons across groups. This paper first reviews the importance of equivalence in psychological research, and then the main theoretical and methodological issues regarding measurement invariance within the framework of confirmatory factor analysis. A step-by-step empirical example of measurement invariance testing is provided along with syntax examples for fitting such models in LISREL.

Measurement Invariance Analysis of the Parental Stress Index

2019 ◽  
Vol 35 (6) ◽  
pp. 771-778 ◽  
Author(s):  
Bernhard Piskernik ◽  
Barbara Supper ◽  
Lieselotte Ahnert
Keyword(s):  
Measurement Invariance ◽  
Parental Stress ◽  
Stress Index ◽  
Factor Analyses ◽  
Confirmatory Factor Analyses ◽  
Mean Values ◽  
Confirmatory Factor ◽  
Structural Invariance ◽  
Parent Domain ◽  
Structural Levels

Abstract. While parenting research continues to compare similarities and differences in mothers’ and fathers’ behaviors based on mean values on the respective dimensions, measurement invariance as a prerequisite for these comparisons has seldom been assured. The present study thus subjected the well-known Parenting Stress Index (PSI), widely used in models of family functioning, to a rigorous measurement invariance analysis based on ( N = 214) Austrian couples with children younger than 3 years of age. We evaluated configural, metric, scalar, and uniqueness invariance on item and subscale levels, and tested for structural invariance of means and variances of the PSI parent and child domain by second-order confirmatory factor analyses. As a result, only measurement differences on the scalar levels affected the factor scores, though negligibly. On the structural levels, no differences were found on the PSI child domain across parents, but on the PSI parent domain, mothers reported more stress.

Measurement Invariance of Divergent Thinking Across Gender, Age, and School Forms

2009 ◽  
Vol 25 (1) ◽  
pp. 1-7 ◽  
Author(s):  
Jörg-Tobias Kuhn ◽  
Heinz Holling
Keyword(s):  
Measurement Invariance ◽  
Divergent Thinking ◽  
Factor Model ◽  
Age Groups ◽  
Thinking Skills ◽  
Specific Model ◽  
Confirmatory Factor Analyses ◽  
Domain Specific ◽  
Gender And Age ◽  
Confirmatory Factor

The present study explores the factorial structure and the degree of measurement invariance of 12 divergent thinking tests. In a large sample of German students (N = 1328), a three-factor model representing verbal, figural, and numerical divergent thinking was supported. Multigroup confirmatory factor analyses revealed that partial strong measurement invariance was tenable across gender and age groups as well as school forms. Latent mean comparisons resulted in significantly higher divergent thinking skills for females and students in schools with higher mean IQ. Older students exhibited higher latent means on the verbal and figural factor, but not on the numerical factor. These results suggest that a domain-specific model of divergent thinking may be assumed, although further research is needed to elucidate the sources that negatively affect measurement invariance.

scholarly journals A Proposed Model of Jazz Theory Knowledge Acquisition

2014 ◽  
Vol 62 (3) ◽  
pp. 291-301 ◽  
Author(s):  
Charles R. Ciorba ◽  
Brian E. Russell
Keyword(s):  
Academic Achievement ◽  
Knowledge Acquisition ◽  
Latent Variables ◽  
Path Model ◽  
Confirmatory Factor Analyses ◽  
Root Mean Square Residual ◽  
Proposed Model ◽  
Confirmatory Factor ◽  
Predicted Model ◽  
Jazz Theory

The purpose of this study was to test a hypothesized model that proposes a causal relationship between motivation and academic achievement on the acquisition of jazz theory knowledge. A reliability analysis of the latent variables ranged from .92 to .94. Confirmatory factor analyses of the motivation (standardized root mean square residual [SRMR] = .067) and jazz theory (SRMR = .063) measures indicated a good fit of the predicted model to the observed data. Results of the latent path model indicated good fit (χ2 = 20.08, p = .692, df = 24, N = 102) and large, positive, and statistically significant direct effects of motivation (β = 0.65) and academic achievement (β = 0.56) on jazz theory knowledge acquisition. The successful identification of this proposed model lends enough support for continued investigation into the process surrounding the acquisition of jazz theory knowledge.

scholarly journals Assessment of Different Dimensions of Shame Proneness: Validation of the SHAME

Assessment ◽  
2018 ◽  
Vol 27 (8) ◽  
pp. 1699-1717 ◽  
Author(s):  
Corinna N. Scheel ◽  
Hedwig Eisenbarth ◽  
Katrin Rentzsch
Keyword(s):  
Clinical Sample ◽  
Large Body ◽  
Factor Analyses ◽  
Confirmatory Factor Analyses ◽  
Invariance Testing ◽  
Network Analyses ◽  
Shame Proneness ◽  
Confirmatory Factor ◽  
Different Dimensions

A large body of research revealed that shame is associated with adaptive and maladaptive correlates. The aim of this work was to validate a new dimensional instrument (SHAME), which was developed to disentangle adaptive and maladaptive dimensions of shame proneness. Confirmatory factor analyses supported the three-factorial structure (bodily, cognitive, and existential shame) in American ( n = 502) and German ( n = 496) community samples, using invariance testing. Bifactor model analyses exhibited distinct associations of adaptive (bodily and cognitive shame) and maladaptive (existential shame) dimensions of shame with psychopathology and social functioning. Network analyses highlighted the role of existential shame in psychopathology, especially for a clinical sample of patients with Borderline Personality Disorder ( n = 92). By placing shame pronenesss into a network of similar and dissimilar constructs, the current findings serve as a foundation for drawing conclusions about the adaptive and maladaptive nature of shame.

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