How to obtain p-values from a multivariable regression using the mvregress function?

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Brett Erickson 2022-7-18

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https://ww2.mathworks.cn/matlabcentral/answers/1763105-how-to-obtain-p-values-from-a-multivariable-regression-using-the-mvregress-function

回答： Rangesh 2023-10-13

I have a multivariable regression model I fit using mvregress. There are 6 response variables and 9 predictor variables, which gives me a total of 60 regression coefficients (1 intercept + 9 variables). The code I have runs without error, I just want to make sure I am calculating my p-values correctly given what MATLAB spits out for results. Here is what I have:

[beta, sigma, E, V] = mvregress(Xcell,doseDifferences); %Fitting the regression model
beta %Spitting out my regression coefficients
se = sqrt(diag(V)) %standard error calculation, V is the covariance matrix
dof = n-9-1; %degrees of freedom calculation (n observations, 9 predictor variables)
tRatio = beta./se; %Calculating t-statistic
pVals = 2*(1-tcdf(abs(tRatio),dof)); %Calculating my p-values

When I run this, my p-values make sense for the most part but some of the p-values don't seem correct. Am I calcualting the p-values correctly? Are my degrees of freedom calculated correctly?

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Star Strider 2022-7-18

The mvregress documentation links to manova1, so that would be where I would begin to find the relevant statistics. (I’m not posting this as an answer because I don’t have any recent experience with either function.) I’m surprised that something similar to fitlm (not applicable here) that produces nice summary statistics tables doesn’t exist for mvregress.

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Answer 1

Rangesh 2023-10-13

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Hi Brett,

I see that you are working on calculating p-values for multivariate linear regression. In your scenario, you have 6 response variables and 9 predictor variables, which leads to a total of 60 regression coefficients. To accurately calculate the degrees of freedom, you should use the formula dof = n - p - 1, where p represents the total number of coefficients (60 in your case). This discrepancy in calculating the degrees of freedom could have caused the discrepancy in the p-values.

I hope this resolves your query.

With regards,

Rangesh P