Partial Invariance and Problems with Free Boundaries

Author(s):  
V. V. Pukhnachev
Methodology ◽  
2013 ◽  
Vol 9 (1) ◽  
pp. 1-12 ◽  
Author(s):  
Holger Steinmetz

Although the use of structural equation modeling has increased during the last decades, the typical procedure to investigate mean differences across groups is still to create an observed composite score from several indicators and to compare the composite’s mean across the groups. Whereas the structural equation modeling literature has emphasized that a comparison of latent means presupposes equal factor loadings and indicator intercepts for most of the indicators (i.e., partial invariance), it is still unknown if partial invariance is sufficient when relying on observed composites. This Monte-Carlo study investigated whether one or two unequal factor loadings and indicator intercepts in a composite can lead to wrong conclusions regarding latent mean differences. Results show that unequal indicator intercepts substantially affect the composite mean difference and the probability of a significant composite difference. In contrast, unequal factor loadings demonstrate only small effects. It is concluded that analyses of composite differences are only warranted in conditions of full measurement invariance, and the author recommends the analyses of latent mean differences with structural equation modeling instead.


2021 ◽  
pp. 0192513X2110300
Author(s):  
Anne Shaffer ◽  
Violeta J. Rodriguez ◽  
David J. Kolko ◽  
Paul A. Pilkonis ◽  
Oliver Lindhiem

Questions persist in the parenting literature regarding how best to define positive and negative parenting behaviors. Are there optimal parenting behaviors shared by mothers and fathers, or among different racial and ethnic groups? This study draws from a nationally representative sample of US parents of school-age children, testing aspects of measurement invariance in the Alabama Parenting Questionnaire (APQ) full and short forms. Our goal was to highlight psychometric approaches to enhancing cultural sensitivity and inclusivity in parenting research, by assessing whether self-reported parenting behaviors have similar conceptual structure across groups. Tests of measurement invariance revealed that the factor structure of the APQ was the same across parent gender, race, and ethnicity. While partial invariance was found in some instances, we did not find metric and scalar invariance in comparisons among these groups. We conclude with research- and practice-based implications, and provide recommendations for future measurement development and use.


2017 ◽  
Vol 37 (1) ◽  
pp. 55-68 ◽  
Author(s):  
Kathan D. Shukla ◽  
Tracy E. Waasdorp ◽  
Sarah Lindstrom Johnson ◽  
Mercedes Gabriela Orozco Solis ◽  
Amanda J. Nguyen ◽  
...  

School climate is an important construct for guiding violence prevention efforts in U.S. schools, but there has been less consideration of this concept in its neighboring country Mexico, which has a higher prevalence of violence. The U.S. Department of Education outlined a three-domain conceptualization of school climate (i.e., safe and supportive schools model) that includes engagement, safety, and the school environment. To examine the applicability of this school climate model in Mexico, the present study tested its measurement invariance across middle school students in the United States ( n = 15,099) and Mexico ( n = 2,211). Findings supported full invariance for engagement and modified-safety scales indicating that factor loadings and intercepts contributed almost equally to factor means, and scale scores were comparable across groups. Partial invariance was found for the environment scales. Results of a multigroup confirmatory factor analysis (MGCFA) consisting of all 13 school climate scales indicated significantly positive associations among all scales in the U.S. sample and among most scales in the Mexico sample. Implications of these findings are discussed.


2004 ◽  
Vol 41 (3) ◽  
pp. 413-420 ◽  
Author(s):  
S. Conti ◽  
U. Weikard
Keyword(s):  

1984 ◽  
Vol 282 (2) ◽  
pp. 431-431 ◽  
Author(s):  
Hans Wilhelm Alt ◽  
Luis A. Caffarelli ◽  
Avner Friedman

1952 ◽  
Vol 3 (1) ◽  
pp. 34-42 ◽  
Author(s):  
David Gilbarg

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