In structural Equation Modelling, researcher use amos in measurement model and path model. Some time researcher prefer second order anlysis in amos. why do the researcher use second order, when & where it need?
The Second Order model is not the preference of any researcher, rather it is due to the items measuring a particular construct loads into several distinct components in the EFA. And this is supported by theory. Thus, the researcher needs to treat the components as the sub-constructs, and that particular construct has become a second order construct. Therefore, the researcher needs to carry out second order CFA instesd of the usual first order.
The second order CFA is a statistical method to confirm that the theorized construct in a study loads into certain number of underlying sub-constructs. E.g: service quality (main construct) consists of five constructs (sub-construct) based on theory posited..so, the five constructs were considered as sub-construct and each sub-constructs is measured using certain number of items.
The Second Order model is not the preference of any researcher, rather it is due to the items measuring a particular construct loads into several distinct components in the EFA. And this is supported by theory. Thus, the researcher needs to treat the components as the sub-constructs, and that particular construct has become a second order construct. Therefore, the researcher needs to carry out second order CFA instesd of the usual first order.
The second-order model represents the hypothesis that these seemingly distinct, but related constructs can be accounted for by one or more common underlying higher order constructs.
2. Implications of second-order factor models and measurement invariance in psychological research were discussed in the Article
Testing Measurement Invariance of Second-Order Factor Models
Fang Fang Chen, Karen H. Sousa, and Stephen G. West
Arizona State University
Second-order models are most typically applicable in research contexts in which measurement instruments assess several related constructs, each of which is measured by multiple items. The second-order model represents the hypothesis that these seemingly distinct, but related constructs can be accounted for by one or more common underlying higher order constructs. For example, in a recent application in personality research, evidence suggests that measures of self-esteem, neuroticism, locus of control, and generalized self-efficacy may all be accounted for by a common higher order general factor, and after controlling for the general factor, each trait has little additional ability to predict external criteria (Judge, Erez, Bono,& Thoresen, 2002). In comparison to first-order models with correlated factors,second-order factor models can provide a more parsimonious and interpretable model when researchers hypothesize that higher order factors underlie their data.
> Anyone knows why fit indices of first order model and second order model are identical ? (using Amos)
If you have 3 first order latent variables and one higher order latent variable this second order model is equivalent to a correlated first order mode. You are simple replacing three second-order factor loadings for three first-order correlations.
You'll need some constraints on the second-order loadings (2 or more being equal) to compare the fit.