The outcome variable is continuous and predictors are categorical (both binary and nominal). Small sample size, negatively skewed histogram. Which regression analysis should I use?
The fact that your outcome measure is skewed may not be important. A major assumption of linear regression, is that the residuals are normally distributed, not the outcome measure. So, in the first instance, try standard linear regression. If the residuals look horribly skewed, you can try quantile (median) regression.
How small is your sample size? Hypothesis testing could be executed at univariate level according to relevant parametric or non-parametric tests. You may then pull these variables together to undergo multivariate.
Skewed residuals are often a consequence of the boundaries of the outcome variable. Is your outcome a count variable, perhaps? Then you better go with Poisson regression. For temporal outcomes Gamma regression sometimes works. However, not so for reaction times, as these are not bounded at zero. Log transforming temporal outcomes sometimes reduces skew and establishes homogeneity of variance, making them amenable for linear regression.
The problem normaly with categorical variables in small samples is a normality hypothese.
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