Whether to enter all predictors at once or perform a hierarchical regression?

Question

Firstly, excuse my naivity but I am just starting out in research.

Overview of study

I am doing a project looking at Social anxiety in adolescence and using social network analysis (SNA). I argue that negative peer relations accounts for variance in social anxiety above and beyond individual level characteristics (in this case personality variables).

I have the following variables:

• Dependent Variable: Social anxiety score

• Independent Variables:

  • Demographics: Ethnicity, SES from fathers income, SES from mothers income
  • Personality variables (Big 5): Neuroticism, Openness, Conscientiousness, Extroversion, Agreeableness
  • Network variables: Unilateral rejection (indegree of a dislike network), Mutual antipathy (sum of reciprocated dislike ties); relational dissonance (sum of dislike tie received with a like tie sent).

My total number of participants was 94.

From past research and as expected Social anxiety is predicted by Neuro and extroversion. Past research indicated that unilateral rejection should be associated with Social anxiety. In my study none of the network variables have an expected association with Social anxiety, none of them are significant predictors of Social anxiety. In fact it was only Neuroticism and extroversion that came anywhere close to significant. All other bivariate correlations were extremely low.

I believe the non significant results is largely due to methodological issues.

As regression assumes independent observations but SNA assumes interdependent then the analysis may not be able to pick up on the associations. Also with a low sample size there is not enough power.

OK. That is my story in a nutshell. I am not looking to find significant results I just want to know the best way to do a regression, so I at least know I am doing that correctly.

I would like to enter them in blocks as this gives the R squared change but I do not want to make any false assumptions and do something that is inappropriate.

Questions

• Should I use the hierarchical method or not? My initial thought was to have demographics in block 1; personality variables in block 2 and network variables in block 3.
• Or should I just enter the predictors simultaneously and report the results as they were not significant anyway?

Answer 1

Whether to use hierarchical regression or enter all predictors at once

• As a starting point, the final block of a hierarchical regression is the same as if you had entered all predictors at once.
• If you have an hypothesis that is aligned with hierarchical regression, then you should perform a hierarchical regression. Your hypothesis is phrased in terms of one set of variables explaining variance over and above another set. Therefore, you have an hypothesis aligned with hierarchical regression.

Issues with non significant bivariate correlations

• If all correlations between each predictor and the dependent variable are non-significant, then it is quite likely, although as discussed here not necessarily the case, that your overall regression model, and the r-square changes in a hierarchical regression will all be non-significant. Thus, as you have gathered, a quick look at the correlations can give you a sense of what the answer is likely to be to your hierarchical regression question.
• Nonetheless, multiple regressions can vary in the degree to which they are performed for exploratory versus confirmatory purposes. Thus, if you are being confirmatory, then the fact that the predictors are not significantly correlated with the dependent variable should not stop you from performing the hierarchical regression.

Answer 2

The rule of thumb is 10 cases for each IV. You have (if I counted right) 11 IVs. Not too far over that. Surely the two SES variables are highly correlated? They could be combined and that gets you down to 10 IVs.

Regarding dependent vs. independent - you haven't said what your sampling plan is. You can do SNA and still get independent observations if the SNA aspect is only in the variables and not in the sample. But if all the students were from one or a few classes, then you probably do have dependent data.

Regarding your questions: You can do either. Each will be just as much a violation of assumptions as the other. This doesn't depend on significance or even effect size. Since you want to report change in R squared, I would go with your first option. However, this may cause other people (editors, professors, whoever) to look askance.