Hi, I am trying to find the relationship between physical activity and glucose levels using multivariate linear regression. Glucose levels is the dependent variable and physical activity measuere (Met.minutes per week) is the independent variable (covariates: age, gender and ethnicity). I have two questions please:
1) Is it essential for my dependent variable to have normal distribution for linear regression (both glucose and physical activity have skewed distribution). I used log and inverse transformation to achieve a normal distribution, but the result is still slightly skewed, although the inverse transformation shows less skewness (-1.29) than the log transformed glucose (2.6).
2) How can I carry out sensitivity analysis. Kindly let me know if a detailed article/notes available for the method?
( I hope the questions make sense)
Thank you.
Saima
Hi Saima
The correct assumption is that the residuals (observed - predicted values) are Normally distributed rather than the dependent variable. There is no distributional assumption made about the predictors variables. Sometimes the residuals can be approximately Normally distributed when the dependent variable is not.
One quite good method of analysis is quantile regression. which models the median rather than the mean. Unfortunately, it is not available in SPSS. Another alternative is to dichotomise your glucose levels, then use logistic regression.
Adrian
[EDITED; part of my original answer wasn't correct, so in the interest of keeping things "clean", I've taken out that part]
Hi Saima,
1) Try looking into generalized linear models that can be used when the assumptions of linear regression aren't met. This wiki page gives a pretty good overview: https://en.wikipedia.org/wiki/Generalized_linear_model. In Stata there's a ladder command that tests for normality with different transformations; the corresponding gladder yields histograms with the same distributions. As far as I know, there's not a similar function in R, and I'm not familiar with SAS and SPSS.
2) To dive into sensitivity analysis, I'd read this wiki page: https://en.wikipedia.org/wiki/Sensitivity_analysis. It's pretty thorough and quite well-referenced, so you can follow the references and find more information.
Hope it's useful!
Cheers,
Ben
Dear Ben,
Thanks a lot, I am just going through the wiki pages. they are really helpful.
My sample size is 683. I am using SPSS and there is no such optiion as far as I know, however I can perform the transformations individually and go through them.
Regards
Saima
Hi Saima
The correct assumption is that the residuals (observed - predicted values) are Normally distributed rather than the dependent variable. There is no distributional assumption made about the predictors variables. Sometimes the residuals can be approximately Normally distributed when the dependent variable is not.
One quite good method of analysis is quantile regression. which models the median rather than the mean. Unfortunately, it is not available in SPSS. Another alternative is to dichotomise your glucose levels, then use logistic regression.
Adrian
Hi Saima,
Another thread on non-normal distributions may be of interest.
Bryce
https://www.researchgate.net/post/What_to_do_when_normality_is_violated_in_multiple_regression_n157
Hi Saima,
I suggest you to take on board the Adrian`s answer on the assumptions and method of analysis. On my side, I can suggest a link for the sensitivity analysis.
Best regards,
Roberto
https://ec.europa.eu/jrc/en/samo
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