scholarly journals A two-stage estimation procedure for non-linear structural equation models

Biostatistics ◽  
2019 ◽  
Vol 21 (4) ◽  
pp. 676-691
Author(s):  
Klaus Kähler Holst ◽  
Esben Budtz-Jørgensen

Summary Applications of structural equation models (SEMs) are often restricted to linear associations between variables. Maximum likelihood (ML) estimation in non-linear models may be complex and require numerical integration. Furthermore, ML inference is sensitive to distributional assumptions. In this article, we introduce a simple two-stage estimation technique for estimation of non-linear associations between latent variables. Here both steps are based on fitting linear SEMs: first a linear model is fitted to data on the latent predictor and terms describing the non-linear effect are predicted by their conditional means. In the second step, the predictions are included in a linear model for the latent outcome variable. We show that this procedure is consistent and identifies its asymptotic distribution. We also illustrate how this framework easily allows the association between latent variables to be modeled using restricted cubic splines, and we develop a modified estimator which is robust to non-normality of the latent predictor. In a simulation study, we compare the proposed method to MLE and alternative two-stage estimation techniques.

Methodology ◽  
2019 ◽  
Vol 15 (4) ◽  
pp. 137-146 ◽  
Author(s):  
Milica Miočević

Abstract. Maximum Likelihood (ML) estimation is a common estimation method in Structural Equation Modeling (SEM), and parameters in such analyses are interpreted using frequentist terms and definition of probability. It is also possible, and sometimes more advantageous ( Lee & Song, 2004 ; Rindskopf, 2012 ), to fit structural equation models in the Bayesian framework ( Kaplan & Depaoli, 2012 ; Levy & Choi, 2013 ; Scheines, Hoijtink, & Boomsma, 1999 ). Bayesian mediation analysis has been described for manifest variable models ( Enders, Fairchild, & MacKinnon, 2013 ; Yuan & MacKinnon, 2009 ). This tutorial outlines considerations in the analysis and interpretation of results for the single mediator model with latent variables. The reader is guided through model specification, estimation, and the interpretations of results obtained using two kinds of diffuse priors and one set of informative priors. Recommendations are made for applied researchers and annotated syntax is provided in R2OpenBUGS and Mplus. The target audience for this article are researchers wanting to learn how to fit the single mediator model as a Bayesian SEM.


2021 ◽  
Author(s):  
Kenneth A. Bollen ◽  
Zachary F. Fisher ◽  
Michael L. Giordano ◽  
Adam G. Lilly ◽  
Lan Luo ◽  
...  

Author(s):  
Noelle J. Strickland ◽  
Raquel Nogueira-Arjona ◽  
Sean Mackinnon ◽  
Christine Wekerle ◽  
Sherry H. Stewart

Abstract. Self-compassion is associated with greater well-being and lower psychopathology. There are mixed findings regarding the factor structure and scoring of the Self-Compassion Scale (SCS). Using confirmatory factor analysis, we tested and conducted nested comparisons of six previously posited factor structures of the SCS. Participants were N = 1,158 Canadian undergraduates (72.8% women, 26.6% men, 0.6% non-binary; Mage = 19.0 years, SD = 2.3). Results best supported a two-factor hierarchical model with six lower-order factors. A general self-compassion factor was not supported at the higher- or lower-order levels; thus, a single total score is not recommended. Given the hierarchical structure, researchers are encouraged to use structural equation models of the SCS with two latent variables: self-caring and self-coldness. A strength of this study is the large sample, while the undergraduate sample may limit generalizability.


2019 ◽  
Vol 37 (2) ◽  
pp. 471-485 ◽  
Author(s):  
José-Manuel Tomás ◽  
Melchor Gutiérrez

La literatura especializada ofrece evidencias de que en todo el mundo las tasas de deserción universitaria son elevadas, generando inconvenientes para los propios estudiantes, para la institución a la que pertenecen y para la sociedad en general. Los determinantes del abandono de los estudios son diversos, considerando uno de los más importantes la satisfacción de los estudiantes con su entorno educativo. La satisfacción académica de los estudiantes depende en gran medida del clima motivacional del aula y de la satisfacción de las necesidades psicológicas básicas, fundamento de la teoría de la autodeterminación. En el marco teórico de la motivación autodeterminada y de la psicología positiva, el objetivo de este trabajo es analizar la capacidad predictiva del apoyo a la autonomía por los profesores sobre la satisfacción académica de los alumnos, mediado por la satisfacción de las necesidades psicológicas básicas de los estudiantes. Los participantes son 752 estudiantes universitarios dominicanos. Instrumentos: Percepción de Apoyo a la Autonomía por los Profesores, Satisfacción Necesidades de las Psicológicas Básicas de los Estudiantes, y Conectividad Académica. Los datos se analizan a través de dos Modelos de Ecuaciones Estructurales con variables latentes, uno con mediación total y otro con mediación parcial. Los resultados muestran que el apoyo a la autonomía se relaciona positivamente con la satisfacción de las necesidades psicológicas básicas; las necesidades básicas se relacionan positivamente con la satisfacción académica; y también aparece un efecto positivo y directo del apoyo a la autonomía por los profesores sobre la satisfacción académica de los estudiantes universitarios. The specialized literature offers evidence that university dropout rates are high throughout the world, creating problems for the students themselves, for the institution to which they belong, and for society in general. The determining factors of dropout are diverse, considering the student satisfaction with their educational environment as one of the most important ones. There is also evidence that the students’ satisfaction with their academic environment depends to a large extent on the classroom motivational climate and the satisfaction of basic psychological needs, main elements of the self-determination theory. In the theoretical framework of self-determined motivation and positive psychology, the objective of this paper is to analyze the predictive capacity of teachers’ autonomy support on students’ academic satisfaction, mediated by the satisfaction of the students’ basic psychological needs. Participants are 752 Dominican university students. Instruments: Perceived Teachers’ Autonomy Support, Students’ Basic Psychological Needs Scale, and Academic Connectedness Scale. The data has been analyzed through two Structural Equation Models with latent variables, a total mediational model and a partial mediational model. The results show that support for autonomy is positively related to the satisfaction of basic psychological needs; that basic needs are positively related to academic satisfaction; and that there is also a positive and direct effect of autonomy support by teachers on university students’ academic satisfaction.


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