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I have a data of around 100 observation with two dependent variables--one is ordered attitude (values encoded as '1','2', and '3') and the other is binary requirement (values encoded as '0', '1'). I have multiple predictors including binary like gender, interval like age, and 2 multinomial style (6 values) and degree (3 values) and I don't care interactions.

A category of attitude has only 5 observations which means some cell value between predictor style and response attitude is very small and even 0. The other dependent variable requirement has similar issue. My major question: is this (rare event or small cell) a big problem for both of ordinal logistic and logistic regression models? If so, does it help to remove some predictors and/or combine categories in the predictors? Any other suggestions?

My other minor questions: can someone help clarify whether below issues in R output are related to the small cells?

  1. When running a Pulkstenis-Robinson goodness of fit test, a warning message shows up with large p-value Warning: Less than 80% of the estimated frequencies are greater than 1, test results may be inaccurate.
  2. Coefficients for some levels of multinomial predictors (style or degree) in the ordinal logistic model have very small standard error (e.g., 2e^-10) which leads to very small CI of the OR.
  3. This may be related to bullet 2, the coefficient of some level of style has significant p-value but the ANOVA type III shows that overall style is not significant. Which one should I adopt as the conclusion?

Thank you and any help is appreciated.

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1 Answer 1

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Is it a big problem to have such small cell sizes? Yes, it is. It can lead to overfitting. If one level of your dependent variable has only 5 people (or even fewer) in it, then even a model with just one independent variable can be problematic. This is true for ordinal or binomial logistic regression.

For the ordinal model, it may be possible to combine two levels of the dependent variable.

But, if you have a lot of independent variables, you will need more data.

For 1 and 2, yes, those are consequences of small cell sizes (at least, that's one possible cause, and a likely one in your case).

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  • $\begingroup$ Thank you for your input. Is there any other solution to this issue? $\endgroup$
    – ksing
    Commented Mar 27 at 22:32
  • $\begingroup$ Not really. To make models, you need data. For more complex models, you need more data. $\endgroup$
    – Peter Flom
    Commented Mar 27 at 22:40
  • $\begingroup$ Thank you @Peter Flom I just thought people who analyze data in epidemiology, especially when they analyze risk factors for rare disease (small cell even for big sample) would have ways to make complex model on data with small cell. $\endgroup$
    – ksing
    Commented Mar 27 at 23:23

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