Hi all,
I am investigating the relationship between adipocytokines and markers of metabolism. As the assays have a lower limit of detection some of my independent data sets are clustered around this value, and my data is skewed to the right.
I am wanting to run multivariate linear regression (with confounding factors for adjustment) to explore this association, my data does have normal distribution of residuals and fulfils the other assumptions of regression analysis but I was wondering whether some of the independent variables having a skewed distribution is of serious concern (n=83).
Nicola -
I don't know the particulars of your subject matter and data, but I can tell you that skewed continuous data are no problem at all. For establishment survey data, highly skewed data are exactly what are expected.
Consider slides 21, 22, 48, 49, 51, and 55 in https://www.researchgate.net/publication/263927238_Cutoff_Sampling_and_Estimation_for_Establishment_Surveys where points near the origin are crowded together so they are hard to see. Consider the scatterplots in https://www.researchgate.net/publication/262066356_Quasi-Cutoff_Sampling_and_Simple_Small_Area_Estimation_with_Nonresponse, and the scatterplot on the last page of https://www.researchgate.net/publication/261947825_Projected_Variance_for_the_Model-based_Classical_Ratio_Estimator_Estimating_Sample_Size_Requirements
Skewed data are fine. Normality is not expected for populations in general, but say for large samples for estimation of means due to the central limit theorem.
Cheers - Jim
Presentation Cutoff Sampling and Estimation for Establishment Surveys
Article Quasi-Cutoff Sampling and Simple Small Area Estimation with ...
Conference Paper Projected Variance for the Model-based Classical Ratio Estim...
Nicola, linear regression models make no assumption about the distribution of predictor variables. Since your outcome variable is normally distributed using a linear model will be fine.
If the data has a normal then regression analysis is great. You may however look into what type of model best describes your data as a linear model may not be the best
To be clear, if independent variables are such that predicted y (say y*) is skewed, and y is similarly skewed so that y = y*+e, you are OK. If only one independent variable, x, then both y and x can be skewed, such that y = bx + e. Linear regression is then OK. Only for the estimated residuals (say the random factors of the estimated residuals when considering heteroscedasticity, as one should) is normality desirable. The central limit theorem can be helpful there.
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