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Are there methodological problems with using percentage outcome?
I was wondering, since a linear regression assume that the outcome is a continuous distribution, are there methodological problems in applying such model to percentages, which are limited between 0 and 100? I’ll address the issues relevant to either discrete or continuous possibility:
Why do we model counts rather than ratios?
That’s the linear predictor. The primary reason to model counts directly rather than proportions or ratios is that you don’t lose information. Intuitively you’d be a lot more confident about inferences from an observed ratio of 1 (boys to girls) if it came from seeing 100 boys and 100 girls than from seeing 2 and 2.
When to use logistic regression for percentages and counts?
One key consideration is the dependent variable. For linear models, the dependent variable doesn’t have to be normally distributed, but it does have to be continuous, unbounded, and measured on an interval or ratio scale. Percentages don’t fit these criteria. Yes, they’re continuous and ratio scale.
How to transform percentage scores into logits in regression?
You can transform the percentage scores into logits and use them as outcome for the linear regression. Here ist the transformation formula: ln (p/ (1-p)) By doing that, you adapt the link-function of logistic regression to the linear regression.
What are the problems with ordinary linear regression?
The big problem with ordinary linear regression is that the model can predict values that aren’t possible–values below 0 or above 1. But the other problem is that the relationship isn’t linear–it’s sigmoidal. A sigmoidal curve looks like a flattened S–linear in the middle, but flattened on the ends. So now what?
Why is linear regression invalid when the outcome is binary?
The linear regression model is based on an assumption that the outcome is continuous, with errors (after removing systematic variation in mean due to covariates ) which are normally distributed. If the outcome variable is binary this assumption is clearly violated, and so in general we might expect our inferences to be invalid.