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The Standardization of Linear and Nonlinear Effects in Direct and Indirect Applications of Structural Equation Mixture Models for Normal and Nonnormal Data.

Brandt H, Umbach N, Kelava A - Front Psychol (2015)

Bottom Line: The application of mixture models to flexibly estimate linear and nonlinear effects in the SEM framework has received increasing attention (e.g., Jedidi et al., 1997b; Bauer, 2005; Muthén and Asparouhov, 2009; Wall et al., 2012; Kelava and Brandt, 2014; Muthén and Asparouhov, 2014).Here, we provide a general standardization procedure for linear and nonlinear interaction and quadratic effects in mixture models.The procedure can also be applied to multiple group models or to single class models with nonlinear effects like LMS (Klein and Moosbrugger, 2000).

View Article: PubMed Central - PubMed

Affiliation: Hector Research Institute of Education Sciences and Psychology, Eberhard Karls Universität Tübingen Tübingen, Germany.

ABSTRACT
The application of mixture models to flexibly estimate linear and nonlinear effects in the SEM framework has received increasing attention (e.g., Jedidi et al., 1997b; Bauer, 2005; Muthén and Asparouhov, 2009; Wall et al., 2012; Kelava and Brandt, 2014; Muthén and Asparouhov, 2014). The advantage of mixture models is that unobserved subgroups with class-specific relationships can be extracted (direct application), or that the mixtures can be used as a statistical tool to approximate nonnormal (latent) distributions (indirect application). Here, we provide a general standardization procedure for linear and nonlinear interaction and quadratic effects in mixture models. The procedure can also be applied to multiple group models or to single class models with nonlinear effects like LMS (Klein and Moosbrugger, 2000). We show that it is necessary to take nonnormality of the data into account for a correct standardization. We present an empirical example from education science applying the proposed procedure.

No MeSH data available.


Scatter plots of the estimated factor scores based on the two class solutions of Model (a) (left panels) and Model (b) (right panels) for reading attitude and reading skills (upper panels) and online activities and reading skills (lower panels). The model based relationships between the variables are indicated with solid lines, class membership is indicated by black or gray dots.
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Figure 1: Scatter plots of the estimated factor scores based on the two class solutions of Model (a) (left panels) and Model (b) (right panels) for reading attitude and reading skills (upper panels) and online activities and reading skills (lower panels). The model based relationships between the variables are indicated with solid lines, class membership is indicated by black or gray dots.

Mentions: In this analysis, we did not evaluate whether the direct or the indirect application [Model (a) or Model (b)] was more appropriate because the application of either model should be based on theory. While Model (a) aims to extract subgroups with homogeneous patterns, Model (b) fits a model for all subjects and only accounts for nonnormality by the latent class model. Thus, the latent classes are not interpreted as subgroups. Figure 1 illustrates the differences between Model (a) and (b). The subgroups in Model (a) were distinguished especially by their reading skills and attitudes. The second class consisted of a very homogeneous group of subjects with high reading skills and attitudes (see estimates in Table 3, C = 2). In Model (b) differences in the subgroups were related only to high or low reading attitudes. This implies that the better model fit for the two class solution compared to the single class solution was caused by the nonnormality of the reading attitudes in this example.


The Standardization of Linear and Nonlinear Effects in Direct and Indirect Applications of Structural Equation Mixture Models for Normal and Nonnormal Data.

Brandt H, Umbach N, Kelava A - Front Psychol (2015)

Scatter plots of the estimated factor scores based on the two class solutions of Model (a) (left panels) and Model (b) (right panels) for reading attitude and reading skills (upper panels) and online activities and reading skills (lower panels). The model based relationships between the variables are indicated with solid lines, class membership is indicated by black or gray dots.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4663265&req=5

Figure 1: Scatter plots of the estimated factor scores based on the two class solutions of Model (a) (left panels) and Model (b) (right panels) for reading attitude and reading skills (upper panels) and online activities and reading skills (lower panels). The model based relationships between the variables are indicated with solid lines, class membership is indicated by black or gray dots.
Mentions: In this analysis, we did not evaluate whether the direct or the indirect application [Model (a) or Model (b)] was more appropriate because the application of either model should be based on theory. While Model (a) aims to extract subgroups with homogeneous patterns, Model (b) fits a model for all subjects and only accounts for nonnormality by the latent class model. Thus, the latent classes are not interpreted as subgroups. Figure 1 illustrates the differences between Model (a) and (b). The subgroups in Model (a) were distinguished especially by their reading skills and attitudes. The second class consisted of a very homogeneous group of subjects with high reading skills and attitudes (see estimates in Table 3, C = 2). In Model (b) differences in the subgroups were related only to high or low reading attitudes. This implies that the better model fit for the two class solution compared to the single class solution was caused by the nonnormality of the reading attitudes in this example.

Bottom Line: The application of mixture models to flexibly estimate linear and nonlinear effects in the SEM framework has received increasing attention (e.g., Jedidi et al., 1997b; Bauer, 2005; Muthén and Asparouhov, 2009; Wall et al., 2012; Kelava and Brandt, 2014; Muthén and Asparouhov, 2014).Here, we provide a general standardization procedure for linear and nonlinear interaction and quadratic effects in mixture models.The procedure can also be applied to multiple group models or to single class models with nonlinear effects like LMS (Klein and Moosbrugger, 2000).

View Article: PubMed Central - PubMed

Affiliation: Hector Research Institute of Education Sciences and Psychology, Eberhard Karls Universität Tübingen Tübingen, Germany.

ABSTRACT
The application of mixture models to flexibly estimate linear and nonlinear effects in the SEM framework has received increasing attention (e.g., Jedidi et al., 1997b; Bauer, 2005; Muthén and Asparouhov, 2009; Wall et al., 2012; Kelava and Brandt, 2014; Muthén and Asparouhov, 2014). The advantage of mixture models is that unobserved subgroups with class-specific relationships can be extracted (direct application), or that the mixtures can be used as a statistical tool to approximate nonnormal (latent) distributions (indirect application). Here, we provide a general standardization procedure for linear and nonlinear interaction and quadratic effects in mixture models. The procedure can also be applied to multiple group models or to single class models with nonlinear effects like LMS (Klein and Moosbrugger, 2000). We show that it is necessary to take nonnormality of the data into account for a correct standardization. We present an empirical example from education science applying the proposed procedure.

No MeSH data available.