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I'm running a logistic regression in R. The data for the model comes from survey responses. The response variable is 'change in wellbeing' and the predictor variables are derived from several other questions from the survey. The main goal of this analysis is to identify good predictors of wellbeing increase.

We have a total of 720 responses to the survey. We have fitted 20 covariates in the model. Almost all of these covariates are categorical, and some of them are ordered categorical variables (e.g. likert scale: strongly agree, agree, neutral, disagree, strongly disagree).

The coefficients for levels of some of the covariates don’t make sense to me. For example, one of our covariates is ‘do you receive enough support in your activities’, in the R code this variable is named ‘support.enough’. Respondents answered this question on a likert scale. Please note - for the analysis we merged the 'disagree' and 'strongly disagree' categories.

This variable plotted against the response variables is presented below. People who agree and agree strongly that they receive enough support are more likely to report an increase in wellbeing than those who are neutral or disagree. enter image description here

Strongly agree is the reference level. Based on this I would expect the coefficients for each level of this covariate to all be negative. However the coefficients and standard errors are as follows:

                                                                 Estimate Std. Error 
    support.enoughAgree                                         0.5040895  0.2954718 
    support.enoughNeutral                                      -0.1778296  0.4380676   
    support.enoughDisagree.AND.Disagree.Strongly               -0.6018862  0.6103662    

My understanding is that this output is suggesting that those who 'agree' that they receive enough support are more likely to report an increase in wellbeing than those who 'strongly agree'.

I’ve been trying to understand why there is an obvious discrepancy between the data and the coefficients. From doing some reading around, I believe that multicollinearity could be causing issues, however, my understanding is that this would inflate the standard error around the coefficient rather than the estimate itself. VIF=3.58 of the variable shown above. I’m also thinking that I could be using too many covariates, given the size of the dataset.

There are four other covariates in the model where a similar thing is happening.

My questions are:

  • Why are the coefficients disagreeing with the data?
  • Is this a cause for concern?
  • Am I interpreting this incorrectly?

I’ve seen a few other questions about logistic regression coefficients, but I didn’t think any of them quite matched what is going on with this model.

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  • $\begingroup$ The standard errors are very high so the true parameter values could very well be negative. $\endgroup$ – Robert Long Jan 28 at 12:10
  • $\begingroup$ You are adding a lot of "one hot encoded" variables to your model which complicates optimization and like you said, probably causes high multicollinearity which will inflate SEs. Reduce the number of IVs or think whether or not you can consider any of them linearly (e.g., not making them factors or ordered factors). $\endgroup$ – John Stud Jan 28 at 14:19
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This is because the estimated coefficients are in a model controlling for other variables, whereas the plot you made does not control for other variables. If you were to make a simple model just of the outcome regressed on the single scale you are looking at, the model coefficients would reproduce the marginal plot exactly.

There are many reasons why this can happen that depend on the (unknown) causal structure of the variables in your model. The other variables in the model could be confounders of the relationship between the scale and the outcome, or mediators, or colliders; controlling for any of these types of variables can change the direction of estimated coefficients compared to a model that doesn't include them. A clear example of this is Simpson's paradox, where conditioning on a variable (i.e., including it as a covariate in a regression model) changes the sign of the effect of one variable on the outcome. The causes of Simpson's paradox may not be exactly what is going on in your data, but it's an illustrative example of how coefficients in an adjusted model could fail to match up with an observed pattern of marginal relationships.

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