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For a study I am researching a quite simple research model (7 IVs - 1 DV), in which I am not interested in underlying relations between the IVs: the relation between the IVs and the DV is all that matters.

My sample size exists of n = 189. The data is non-normal distributed and the assumption of multivariate normality is not met. I have tried to transform the data in multiple ways (sqrt, log10, box-cox etc.) and to delete outliers to meet the assumptions, but this does not work. I also tested the assumptions of Homoscedasticity and Multicollinearity, and these are met.

I have measured the correlation coefficients with a non-parametric test, and the results show that the IVs and DV are very weak correlated (r2 < 0.2).

Now, I want to test my model. My professor tells me to test the model in AMOS with SEM, but, likely due to the small sample size, non-multivariate normality and the low correlations, the fit of the model (based on CFI/TLI/RMSEA/X2/df) is terrible. The coeficcient values are also close to zero. I could not improve the goodnes of fit by adjusting the model based on literature, by transforming variables, by enabling bootstrapping or by removing outliers. I have read multiple fora and papers, and come to the conclusion that the model fits poorly, and that the very low correlations between the IV's and DV lead to a poor model fit.

However, I still want to report something. In class we learned how to use MLR with block-regression in SPSS. In multiple papers I read that for MLR my sample size should not be a problem, and that with bootstrapping MLR should be more or less robust to non-multivariate normality.

My question: is it okay to report the results of the MLR (Multiple linear regression) if I report that I could not achieve a good model fit in AMOS? Or does MLR apply the same calculations as used in SEM, and is it of no use to also execute a MLR?

Thank you in advance, all answers or suggestions are welcome. I had to learn everything about statistic in less than a month, so my way of thinking or the formulation of this text may be poor, for which I apologize in advance.

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  • $\begingroup$ There are good reasons here to ignore the SEM goodness of fit tests in this situation. For your problem, both models are the same. But it's better to approach it as a basic regression problem, instead of as an SEM and unnecessary assumptions about multivariate normality. There is no assumption of multivariate normality with OLS. You can find a regression text to see how to conduct standard diagnostics for the regression model. Also, FWIW, it's not immediately obvious that MLR means multiple linear regression. $\endgroup$ – Heteroskedastic Jim Jul 3 '18 at 12:23
  • $\begingroup$ Also, your SEM models of 7 regressors to one response variable will give you the best fitting SEM model of any combination of those 8 variables. If relations are too weak in the data, there is good reason to believe most global goodness of fit statistics in the SEM literature are not useful in the ways intro courses lead us to believe. Even in models with strong relations, their utility is still questionable. Regression is a better studied problem, so work with that since it is an option. $\endgroup$ – Heteroskedastic Jim Jul 3 '18 at 12:28
  • $\begingroup$ Thank you for your response, this is exactly the information I needed. I have not yet looked into OLS, and will do so right now. And as you stated, I was taught that the goodnes of fit statistics should always be good, and that if this is not the case there must be something wrong with the model or the way you inserted it. And I did not know that it is not obvious that MLR stands for Multiple Linear Regression, good to know, helpfull information. $\endgroup$ – B. van der Wal Jul 3 '18 at 13:08
  • $\begingroup$ For your purposes, OLS is MLR, what you have already tried. $\endgroup$ – Heteroskedastic Jim Jul 3 '18 at 13:16
  • $\begingroup$ How are you test the model? The models can't be the same. $\endgroup$ – Jeremy Miles Jul 3 '18 at 17:27

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