The outer model algorithm

[Atefeh Talebnejad]

Hi everyone.

I am having problem with selecting the appropriate outer model algorithm. According to the Warp 7 user manual,

1.      CFM algorithms first employ a new “true composite” estimation sub-algorithm, which estimates composites based on mathematical equations that follow directly from the common factor model. Then it employs a new “variation sharing” sub-algorithm, which can be seen as a “soft” version of the classic expectation-maximization algorithm used in maximum likelihood estimation, with apparently faster convergence and nonparametric properties. To estimate measurement error and true composite weights:

·        CFM3 employs both loadings and reliabilities from Dijkstra's consistent PLS. it uses loadings to improve computation efficiency;

·        CFM2 algorithm employs reliabilities from Dijkstra's consistent PLS technique, but not loadings;

·        CFM1 does not employ Dijkstra's consistent PLS technique at all, instead using Cronbach’s alpha.

2.      REG algorithms first estimate composites via PLS Regression, and then estimate factors employing variation sharing. To estimate measurement error and true composite weights:

·        REG2 employs reliabilities from Dijkstra's consistent PLS.

·        REG1 employs Cronbach’s alpha.

3.      PTH algorithms first estimate composites via Robust Path Analysis, and then estimate factors employing variation sharing. To estimate measurement error and true composite weights:

·        PTH2 employs reliabilities from Dijkstra's consistent PLS.

·        PTH1 employs Cronbach’s alpha.

4.      CFM algorithms assume that all indicators errors are uncorrelated. REG and PTH algorithms do not impose certain common factor model assumptions such as the assumption that all indicator errors are uncorrelated.

5.      With CFM, REG and PTH algorithms the inner model does not influence the outer model.

6.      With PLS Mode algorithms (Ms, As, Bs) the inner model influences the outer model. These algorithms deal with Reflective and Formative latent variables.

It reads that “Wold’s original PLS algorithms do not deal with actual factors, but with composites, which are the exact linear combinations of their indicators. Factor-Based PLS algorithms provided by this software are developed to address this perceived limitation of Wold’s original PLS algorithms”. But it also says that “all of the above algorithms calculate latent variable scores as exact linear combinations of their indicators, or of their indicators and measurement errors”; i.e. they deal with composites, like Wold’s original PLS algorithm if I get it correctly.

I am really confused and need help.

Could you please advise me on how to choose the most appropriate outer model algorithm? I don’t know how should I select the outer algorithm. I tried different algorithms and they yield very different results in terms of loadings, model fit indices, P values, path coefficients, R2 values.

Many thanks.

Atefeh   

[Ned Kock]

> Could you please advise me on how to choose the most appropriate outer model algorithm?  

One good answer would be: the one with the best overall fit with the data (e.g., the one with the lowest SRMR). From the WarpPLS User Manual: The menu option “Explore additional coefficients and indices” allows you to obtain an extended set of model fit and quality indices (see Figure B.4.12). This extended set of model fit and quality indices includes the classic indices normally included in reports of SEM analyses employing this software, as well as new indices that allow investigators to assess the fit between the model-implied and empirical indicator correlation matrices. These new indices are the standardized root mean squared residual (SRMR), standardized mean absolute residual (SMAR), standardized chi-squared (SChS), standardized threshold difference count ratio (STDCR), and standardized threshold difference sum ratio (STDSR).    

[Ned Kock]

If two outer model algorithms yield the same SRMR, then I would recommend the APC, ARS and GoF.

[Atefeh Talebnejad]

Thank you prof. Kock. It helped a lot.