Multivariate Regression Test Statistics

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Kevin Willeford 2021-2-12

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https://ww2.mathworks.cn/matlabcentral/answers/744067-multivariate-regression-test-statistics

评论： Kevin Willeford 2021-2-15

I have designed a multivariate regression with two response (Y) and three predictor (X) variables using mvregress. The response variables are horizontal and vertical eye position (h, v) and the predictor variables are a constant term with horizontal and vertical gaze position (x, y). How do I compute a p-value for each of my coefficients given what the function returns?

    % multivariate regression
    n = numX * numY; % number of gaze positions
    d = 2; % number of response variables
    numCoeffs = d * 2 + d;
    X0 = ones(n, 1);
    X1 = XX(:); 
    X2 = YY(:); 
    X = [X0, X1, X2]
    Y1 = H;
    Y2 = V;
    Y = [Y1, Y2]; 
    % coefficients, covariance matrix, residuals, variance of parameters, loglikelihood value, correlation matrix
    [B, S, R, V, L] = mvregress(X, Y);
    predY = X * B; 
    C = corrcov(S);
    E = sqrt(diag(V));

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dpb 2021-2-13

在 MATLAB Online 中打开

Yeah, same as for OLS, if you ran a separate OLS regression for each outcome variable you would get the same coefficients, standard errors, t- and p-values, and confidence intervals.

So, for each b,

t=b/SE;
p>|t| --> 2*(1-tcdf(t,dof))

Kevin Willeford 2021-2-15

在 MATLAB Online 中打开

I have two response variables, three predictor variables, and thus a total of six coefficients returned. I believe the DOF = 3 in this case because there are three predictor variables for each response variable. When I followed the above procedure, I got p values greater than 1.00 which cannot be correct?

    [B, S, R, V, L] = mvregress(X, Y);
    predY = X * B; 
    C = corrcov(S);
    SE = sqrt(diag(V));
    T = B(:) ./ SE;
    P = 2 * (1 - tcdf(T, DOF));
    
    
B =
   1.496605020258772  -0.000313029492716
   0.000389624484379  -0.004938677958117
  -0.053311651917679   0.000022111435119
  
SE =
   0.011649490387665
   0.000658994692039
   0.000658994692039
   0.000807196421197
   0.000045661925054
   0.000045661925054
   
T =
   1.0e+02 *
   1.284695699516166
   0.005912407020668
  -0.808984542087009
  -0.003877984149776
  -1.081574627492846
   0.004842422892381
   
P =
   0.000001039860816
   0.595950373533595
   1.999995836953775
   1.275955907490467
   1.999998257520655
   0.661365573305742