topic Please help me explain why you can't put cluster level variable in a person level model in Statistical Procedures

Please help me explain why you can't put cluster level variable in a person level model

proctice — Tue, 10 May 2016 18:06:01 GMT

An example would be a putting a school level variable like public/priviate into a student level model without a random or fixed effect for school.

I believe this is wrong but I'm having trouble explaining it.

The person I am trying to explain it to understands the need to control for correlations with a cluster/school, but wants to skip that step because "that is how they did it in olden days".

If I am wrong and this is ok, please let me know. Thanks.

Re: Please help me explain why you can't put cluster level variable in a person level model

Rick_SAS — Tue, 10 May 2016 18:20:39 GMT

Can you provide example syntax? For example, are you saying that client wants to use a model that looks something like:

model RESPONSE = student student*school;

Often the "student effect" is associated with a random intercept term, so the previous fixed-effect model would be strange indeed.

In general terms, random effects are used when the levels in the study are randomly chosen from the population. In most studies, the five schools in your study are merely representative of the schools in the district/region/state. You can treat the schools as random effects if you want to make inferences to other schools that were not in the study.

Fixed effects are used when the levels in the study represent all the levels that you care about. If you only care about the five schools in your study, and you don't want to make inferences beyond these five schools, then you could treat them as fixed effects.

Re: Please help me explain why you can't put cluster level variable in a person level model

proctice — Tue, 10 May 2016 18:44:38 GMT

The person is suggesting a model like this:

Model student_response= age sex race private_school_dummy ;

There is no variable for school id in the random statement or in the model statement and I think if they are going to have the school level dummy code they need school id in the model.

*************Separate question**************************;

I understand the random effect vs. fixed effect issue, but I think you still need to be concerned about clusters and significant intraclass correlation and cluster level predictors in the fixed effect situation, correct? Thanks.

Re: Please help me explain why you can't put cluster level variable in a person level model

Rick_SAS — Tue, 10 May 2016 19:34:27 GMT

What is the goal of your analysis? What questions are you trying to answer.

Seeing the proposed model does not immediately cause me to shudder. You are interested in two particular levels of private/public. You want to know if the response differs between these two groups. If you did the study again, you would have the same private/public levels. All these are classic reasons to treat the dummy variable as a fixed effect.

Is there likely to be school-level correlations/clusters? Maybe. But rather than fight with your client, would it make sense to do the following?

1. Run the fixed effects model he proposed.

2. Graph the predicted values versus the continuous explanatory variables and color the residuals by the School_ID.

The model diagnostic plots might show evidence that the model is inadequate. For example, if you see evidence that certain schools are systematically high or low, that gives you evidence to suggest that the data are clustered in a way that is not being modeled. If you show him evidence in the data, you will probably get less resistance.