If a variable is more meaningful in its quantitative form but does not fulfill the assumptions for linear regression, is it statistically commendable practice to categorize it and fit a logistic regression model?
By dichotomizing a continuous dependent variable you are getting rid of valuable information and losing statistical power.
Can you tell us about the nature of the dependent variable, how was it measured , and its distribution? Remember that the normality assumption concerns the residuals conditional on the predictor variables. Unless there are outliers, it is not a particularly important assumption in comparison to non-independence and heteroscedasticity. Moreover, the generalized model is designed to deal with different distributions. Thus Gamma regression, is useful for highly positively skewed data while Inverse-Gaussian regression is useful when the response is strictly positive and skewed to the right.
Thanks Kelvyn Jones, the variable under consideration is physical activity among school adolescents. The questionnaire used is the physical activity questionaire for adolescents(PAQ_A). The developers recommended mean score from 8 items in a likert scale. The finding among adolescents in my setting inclined consistently to the lower scores with a significant number of outliers breaking the assumptions of linear regression. What if I categorize it as " higher physical activity" for those who scored above the mean and " lower..." for the reverse.