Does acquiescence disagree with Measurement Invariance testing?

Measurement invariance (MI) is required for validly comparing latent constructs measured by multiple ordinal self-report items. Non-invariances may occur when disregarding(group differences in) an acquiescence response style (ARS; an agreeing tendency regardless of item content). If non-invariance results solely from neglecting ARS, one should not worry about scale inequivalences but model the ARS instead. In a simulation study, we investigated the effect of ARS on MI testing, both when including ARS as a factor in the measurement model or not. For (semi-) balanced scales, disregarding a large ARS resulted in non-invariance already at the configural level. This was resolved by including an ARS factor for all groups. For unbalanced scales, disregarding ARS did not affect testing, and including an ARS factor often resulted in non-convergence. Implications and recommendations for applied research are discussed

Scale length does matter:Recommendations for measurement invariance testing with categorical factor analysis and item response theory approaches

In social sciences, the study of group differences concerning latent constructs is ubiquitous. These constructs are generally measured by means of scales composed of ordinal items. In order to compare these constructs across groups, one crucial requirement is that they are measured equivalently or, in technical jargon, that measurement invariance (MI) holds across the groups. This study compared the performance of scale- and item-level approaches based on multiple group categorical confirmatory factor analysis (MG-CCFA) and multiple group item response theory (MG-IRT) in testing MI with ordinal data. In general, the results of the simulation studies showed that, MG-CCFA-based approaches outperformed MG-IRT-based approaches when testing MI at the scale level, whereas, at the item level, the best performing approach depends on the tested parameter (i.e., loadings or thresholds). That is, when testing loadings equivalence, the likelihood ratio test provided the best trade-off between true positive rate and false positve rate, whereas, when testing thresholds equivalence, the chi-square test outperformed the other testing strategies. In addition, the performance of MG-CCFA's fit measures, such as RMSEA and CFI, seemed to depend largely on the length of the scale, especially when MI was tested at the item level. General caution is recommended when using these measures, especially when MI is tested for each item individually

Awareness is bliss:How acquiescence affects exploratory factor analysis

Assessing the measurement model (MM) of self-report scales is crucial to obtain valid measurement of individuals' latent psychological constructs. This entails evaluating the number of measured constructs and determining which construct is measured by which item. Exploratory factor analysis (EFA) is the most-used method to evaluate these psychometric properties, where the number of measured constructs (i.e., factors) is assessed, and, afterwards, rotational freedom is resolved to interpret these factors. This study assessed the effects of an acquiescence response style (ARS) on EFA for unidimensional and multidimensional (un)balanced scales. Specifically, we evaluated (i) whether ARS is captured as an additional factor, (ii) the effect of different rotation approaches on the recovery of the content and ARS factors, and (iii) the effect of extracting the additional ARS factor on the recovery of factor loadings. ARS was often captured as an additional factor in balanced scales when it was strong. For these scales, ignoring (i.e., not extracting) this additional ARS factor, or rotating to simple structure when extracting it, harmed the recovery of the original MM by introducing bias in loadings and cross-loadings. These issues were avoided by using informed rotation approaches (i.e., target rotation), where (part of) the MM is specified a priori. Not extracting the additional ARS factor did not affect the loading recovery in unbalanced scales. Researchers should consider the potential presence of an additional ARS factor when assessing the psychometric properties of balanced scales, and use informed rotation approaches when suspecting that an additional factor is an ARS factor

The dire disregard of measurement invariance testing in psychological science

In psychological science, self-report scales are widely used to compare means in targeted latent constructs across time points, groups, or experimental conditions. For these scale mean comparisons (SMC) to be meaningful and unbiased, the scales should be measurement invariant across the compared time points or (experimental) groups. Measurement invariance (MI) testing checks whether the latent constructs are measured equivalently across groups or time points. Since MI is essential for meaningful comparisons, we conducted a systematic review to check whether MI is taken seriously in psychological research. Specifically, we sampled 426 psychology articles with openly available data that involved a total of 918 SMCs to (1) investigate common practices in conducting and reporting of MI testing, (2) check whether reported MI test results can be reproduced, and (3) conduct MI tests for the SMCs that enabled sufficiently powerful MI testing with the shared data. Our results indicate that (1) 4% of the 918 scales underwent MI testing across groups or time and that these tests were generally poorly reported, (2) none of the reported MI tests could be successfully reproduced, and (3) of 161 newly performed MI tests, a mere 46 (29%) reached sufficient MI (scalar invariance), and MI often failed completely (89; 55%). Thus, MI tests were rarely done and poorly reported in psychological studies, and the frequent violations of MI indicate that reported group differences cannot be solely attributed to group differences in the latent constructs. We offer recommendations on reporting MI tests and improving computational reproducibility practices

A many-analysts approach to the relation between religiosity and well-being

The relation between religiosity and well-being is one of the most researched topics in the psychology of religion, yet the directionality and robustness of the effect remains debated. Here, we adopted a many-analysts approach to assess the robustness of this relation based on a new cross-cultural dataset (N=10,535 participants from 24 countries). We recruited 120 analysis teams to investigate (1) whether religious people self-report higher well-being, and (2) whether the relation between religiosity and self-reported well-being depends on perceived cultural norms of religion (i.e., whether it is considered normal and desirable to be religious in a given country). In a two-stage procedure, the teams first created an analysis plan and then executed their planned analysis on the data. For the first research question, all but 3 teams reported positive effect sizes with credible/confidence intervals excluding zero (median reported β=0.120). For the second research question, this was the case for 65% of the teams (median reported β=0.039). While most teams applied (multilevel) linear regression models, there was considerable variability in the choice of items used to construct the independent variables, the dependent variable, and the included covariates

Does acquiescence disagree with Measurement Invariance testing?

Measurement invariance (MI) is required for validly comparing latent constructs measured by multiple ordinal self-report items. Non-invariances may occur when disregarding(group differences in) an acquiescence response style (ARS; an agreeing tendency regardless of item content). If non-invariance results solely from neglecting ARS, one should not worry about scale inequivalences but model the ARS instead. In a simulation study, we investigated the effect of ARS on MI testing, both when including ARS as a factor in the measurement model or not. For (semi-) balanced scales, disregarding a large ARS resulted in non-invariance already at the configural level. This was resolved by including an ARS factor for all groups. For unbalanced scales, disregarding ARS did not affect testing, and including an ARS factor often resulted in non-convergence. Implications and recommendations for applied research are discussed

Scale length does matter: Recommendations for measurement invariance testing with categorical factor analysis and item response theory approaches

In social sciences, the study of group differences concerning latent constructs is ubiquitous. These constructs are generally measured by means of scales composed of ordinal items. In order to compare these constructs across groups, one crucial requirement is that they are measured equivalently or, in technical jargon, that measurement invariance (MI) holds across the groups. This study compared the performance of scale- and item-level approaches based on multiple group categorical confirmatory factor analysis (MG-CCFA) and multiple group item response theory (MG-IRT) in testing MI with ordinal data. In general, the results of the simulation studies showed that, MG-CCFA-based approaches outperformed MG-IRT-based approaches when testing MI at the scale level, whereas, at the item level, the best performing approach depends on the tested parameter (i.e., loadings or thresholds). That is, when testing loadings equivalence, the likelihood ratio test provided the best trade-off between true positive rate and false positve rate, whereas, when testing thresholds equivalence, the chi-square test outperformed the other testing strategies. In addition, the performance of MG-CCFA's fit measures, such as RMSEA and CFI, seemed to depend largely on the length of the scale, especially when MI was tested at the item level. General caution is recommended when using these measures, especially when MI is tested for each item individually

Scale length does matter: Recommendations for measurement invariance testing with categorical factor analysis and item response theory approaches

In social sciences, the study of group differences concerning latent constructs is ubiquitous. These constructs are generally measured by means of scales composed of ordinal items. In order to compare these constructs across groups, one crucial requirement is that they are measured equivalently or, in technical jargon, that measurement invariance (MI) holds across the groups. This study compared the performance of scale- and item-level approaches based on multiple group categorical confirmatory factor analysis (MG-CCFA) and multiple group item response theory (MG-IRT) in testing MI with ordinal data. In general, the results of the simulation studies showed that, MG-CCFA-based approaches outperformed MG-IRT-based approaches when testing MI at the scale level, whereas, at the item level, the best performing approach depends on the tested parameter (i.e., loadings or thresholds). That is, when testing loadings equivalence, the likelihood ratio test provided the best trade-off between true positive rate and false positve rate, whereas, when testing thresholds equivalence, the chi-square test outperformed the other testing strategies. In addition, the performance of MG-CCFA's fit measures, such as RMSEA and CFI, seemed to depend largely on the length of the scale, especially when MI was tested at the item level. General caution is recommended when using these measures, especially when MI is tested for each item individually

Awareness is bliss: How acquiescence affects exploratory factor analysis

Assessing the measurement model (MM) of self-report scales is crucial to obtain valid measurement of individuals' latent psychological constructs. This entails evaluating the number of measured constructs and determining which construct is measured by which item. Exploratory factor analysis (EFA) is the most-used method to evaluate these psychometric properties, where the number of measured constructs (i.e., factors) is assessed, and, afterwards, rotational freedom is resolved to interpret these factors. This study assessed the effects of an acquiescence response style (ARS) on EFA for unidimensional and multidimensional (un)balanced scales. Specifically, we evaluated (i) whether ARS is captured as an additional factor, (ii) the effect of different rotation approaches on the recovery of the content and ARS factors, and (iii) the effect of extracting the additional ARS factor on the recovery of factor loadings. ARS was often captured as an additional factor in balanced scales when it was strong. For these scales, ignoring (i.e., not extracting) this additional ARS factor, or rotating to simple structure when extracting it, harmed the recovery of the original MM by introducing bias in loadings and cross-loadings. These issues were avoided by using informed rotation approaches (i.e., target rotation), where (part of) the MM is specified a priori. Not extracting the additional ARS factor did not affect the loading recovery in unbalanced scales. Researchers should consider the potential presence of an additional ARS factor when assessing the psychometric properties of balanced scales, and use informed rotation approaches when suspecting that an additional factor is an ARS factor

Scale length does matter:Recommendations for measurement invariance testing with categorical factor analysis and item response theory approaches

In social sciences, the study of group differences concerning latent constructs is ubiquitous. These constructs are generally measured by means of scales composed of ordinal items. In order to compare these constructs across groups, one crucial requirement is that they are measured equivalently or, in technical jargon, that measurement invariance (MI) holds across the groups. This study compared the performance of scale- and item-level approaches based on multiple group categorical confirmatory factor analysis (MG-CCFA) and multiple group item response theory (MG-IRT) in testing MI with ordinal data. In general, the results of the simulation studies showed that MG-CCFA-based approaches outperformed MG-IRT-based approaches when testing MI at the scale level, whereas, at the item level, the best performing approach depends on the tested parameter (i.e., loadings or thresholds). That is, when testing loadings equivalence, the likelihood ratio test provided the best trade-off between true-positive rate and false-positive rate, whereas, when testing thresholds equivalence, the χ(2) test outperformed the other testing strategies. In addition, the performance of MG-CCFA’s fit measures, such as RMSEA and CFI, seemed to depend largely on the length of the scale, especially when MI was tested at the item level. General caution is recommended when using these measures, especially when MI is tested for each item individually