Multiple regression V.S. Bivariate regression

#1
Hi there,

I'm interested in the effect of several variables on severity of schizophrenia symptoms. I want to look at the effect of 9 predictor variables in a regression model. Severity of schizophrenia symptoms is the outcome variable.

My sample size is about 60. My 9 predictor variables include variables created from questionnaire data and cognitive task data. Questionnaire data look at quality of life, depression symptoms, anxiety symptoms, social support, and community support. Then there are scores from 4 cognitive tasks. I want to conduct a regression to examine the predictive value of each of these scores on schizophrenia symptom severity. I should also mention that only 45 out of the 60 completed the cognitive tasks.

My question is this: Should I conduct multiple regression or individual bivariate regressions? With multiple regression, I would be (from my understanding, correct me if I'm wrong) setting up a regression model where there are 9 predictor variables and 1 outcome variable all in one model. With bivariate regression, I would be setting up 9 independent models where there is just one of the predictor variables and then the outcome variable.

When I run independent bivariate regressions, 3 of the predictor variables come up significant. When I run the multiple regression with all 9 of the predictors in one model, none of the predictors have a significant effect. I'm also, unsure why there is this discrepancy.

I'm unsure which is the correct approach.

Any help would be greatly appreciated! :)
 

CB

Super Moderator
#2
Hi there :welcome:

My question is this: Should I conduct multiple regression or individual bivariate regressions?
These two alternatives allow you to study quite different things.

The sequence of 9 bivariate regression equations allows you to look at the simple relationship between each of the predictor variables and severity of schizophrenia systems. It's a lot like just looking at 9 different correlations.

The multiple regression allows you to look at:
  1. How accurately you can predict severity of schizophrenia symptoms when using all 9 predictors simultaneously
  2. The relationship between each of the individual predictor variables and severity of schizophrenia symptoms while holding all the other predictor variables constant.

So they're each giving you quite different information, and it really depends on which is the better match to your actual research questions and/or hypotheses.

When I run independent bivariate regressions, 3 of the predictor variables come up significant. When I run the multiple regression with all 9 of the predictors in one model, none of the predictors have a significant effect. I'm also, unsure why there is this discrepancy.
As above - it's because the analyses are looking at different things (the relationship between a predictor and the DV, vs the relationship between a predictor and the DV while holding all other predictors constant).
 

Karabiner

TS Contributor
#3
When I run independent bivariate regressions, 3 of the predictor variables come up significant. When I run the multiple regression with all 9 of the predictors in one model, none of the predictors have a significant effect.
Perhaps you compare analyses including n=60 subjects with analyses including n=45?

Moreover, a multiple regression with n=45 and 9 predictors looks underpowered. What exactely do you want to achieve with your multiple regression (see CowboyBears's post for possible goals of your analyses)?

With kind regards

K.
 

rogojel

TS Contributor
#4
Besides with 9 tests you have a 37% probability of having at least one false positive so 3 significant results is not really impressive.

regards