# ANOVA or Multiple Regression for Big 5 predicting criteria instead of SEM

I am working on a project where I am studying the relationship between personality and certain economic outcomes. Direct measures for the economics outcome is available, while for personality I am using a Big Five Inventory from here In many studies, I have seen SEM being used when such questions are asked, but there we need an a-priori structure. But I have no such apriori structure in mind. I wish to find if the economic outcome is different for different people based on their personalities.

I want to ask if alternative strategies can be used such as one way ANOVA or multiple linear regression.

1. Is it possible to use ANOVA for example, dividing people into extraverted vs non-extraverted, neurotic vs non-neurotic etc. by first calculating for each person the score for each factor by taking the arithmetic mean and then dividing the sample into two groups by median? So for example, each person would be in a category like Open-Conscientious-Non Extravert-Agreeable-Non Neurotic or Non Open-Conscientious-Extravert-Agreeable-Non Neurotic etc. And then use 2x2x2x2x2 ANOVA to see if there are statistically significant differences. Is it possible? Are there examples in the literature where psychometric scales like the Big 5 have been used in this manner?

2. Or can multiple linear regression be used by deriving the scores of each factor by simple arithmetic mean? I understand SEM also includes path analysis which is based on regression, but I am talking about the usual Multiple Regression, such as $$Y = \beta_0 + \beta_1 Openness + \beta_2 Conscientiousness + .... + \beta_5 Neuroticism$$.

You should not do median splits on continuous measures of the Big Five. Personality traits are continuous variables and generally approximately normally distributed. If you convert into categorical variables, you will throw out a lot of meaningful information and reduce your ability to predict criteria of interest. So in short, you should not adopt the "ANOVA" approach.

It is quite normal to estimate bivariate correlations with the criteria and combine this with a regression model with the Big Five as predictors of your criteria.

Of course, you could also do SEM and this is basically equivalent to multiple regression albeit it involves specifying a measurement model for the Big Five and it seeks to give you regression coefficients and variance explained of the underlying latent variables. Regarding your point about a priori structure, you do have that: the scoring key for the Big five specifies which items should load on which factors.

I generally prefer multiple regression, because it rests on fewer assumptions than SEM, and is in some senses more reproducible.