I am struggling with what analysis to use for my data, I am currently looking at the effect of the 5 different personality traits (independents) on overall psychological well-being (dependent) with both being continuous variables. My sample size is quite small at 73. I have looked at normality, with neuroticism and overall psychological well not being not normally distributed.
I have done a pearsons correlation test finding every personality trait apart from conscientiousness to have a significant correlation with PWB (p
Tayla-Jade -
First you might plot each independent variable separately against the dependent variable. You could form an idea of the relationships involved. But note that when 'independent' variables are used together, they may impact each other. One such case is collinearity, where part of the information in one or more variables is contained within one or more others. People use "principal components regression," but that makes interpretation even harder, I'd say, and I suspect that random 'error' and any omitted variable problems might be more convoluted. At any rate, you want the best combination of independent variables, no more, no less. You could research "model selection." Whatever you do, you could have spurious results due to your specific sample.
If you try multiple regression, or even if you had just one regressor, you may or may not want an intercept term. If you expect zero for the dependent variable when all independent variables are zero, then do not use an intercept term. You should have a plausible reason for everything you use. Having subject matter expertise, you could use that to justify each alternative model you want to explore.
You can check for model fit by using "graphical residual analyses," and check for overfitting to your particular sample by using some kind of "cross-validation."
If you have a good combination of regressors, and no real data issues, you can expect a degree of heteroscedasticity which is discussed in here:
https://www.researchgate.net/publication/320853387_Essential_Heteroscedasticity
Examples showing how to handle heteroscedasticity are here:
https://www.researchgate.net/publication/333642828_Estimating_the_Coefficient_of_Heteroscedasticity
and a tool for doing this with your data is here:
https://www.researchgate.net/publication/333659087_Tool_for_estimating_coefficient_of_heteroscedasticityxlsx
More information is found here, for regressions of form y = y* + e, which are most useful for finite population predictions:
https://www.researchgate.net/project/OLS-Regression-Should-Not-Be-a-Default-for-WLS-Regression, and the project updates.
By the way, 'normality' is not needed at all here for the x or y data, though it is somewhat desirable for the estimated residuals, or (better) for the random factors of the estimated residuals in weighted least squares regression.
Also, you are correct that you do not want to make too much of a moderate sample size.
Cheers - Jim
The significance of regression coefficients can be very different from the significance of particular correlations with dependent variable. This is usually due to the substantial correlations between independents (multicollinearity). In regression analysis, the influence of predictors is partialized, so the effect of each predictor variable is genuine with taking away the effects of other predictors in the model. For the predicting purposes, only regression coefficient should be considered. The small sample size is certainly affecting the generalizability of your results.
Regards,
Janek Musek
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