MATLAB: F-Test for difference between coefficients

coefficientsf-testMATLABregression

Hi there,

I need to conduct F-Tests for differences in estimated regression coefficients. That is, to say: "Yes, the one coefficient is really lower/higher than the other" or "No, they are not statistically significantly different".

I believe, the equivalent stata command would be -test-. However, I can't seem to find how to do it matlab.

Any help is greatly appreciated!

Christian

Best Answer

help coefTest

and use a contrast H that compares the two desired coefficients (e.g. [0 1 -1] compares the second and third regression coefficients in your linear model).

Generally, for a linear model of the form:

 Y = X*B + noise

coeffTest will test any hypothesis of the form:

 H*B = 0

(where H can be a vector or a matrix)

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MATLAB: Compare 2 regression models

One way is to use likelihood ratio test (similar to R anova function). For more information see here.

y = randn(200, 1); % test response
x = randn(200, 1); % test predictor
model1 = fitlm(x, y)
model2 = fitlm([x, x.^2], y);
LR = 2*(model2.LogLikelihood - model1.LogLikelihood); % has a X2 distribution with a df equals to number of constrained parameters, here: 1
pval = 1 - chi2cdf(LR, 1);

MATLAB: CoefTest and one tailed T-test

You are right that the result from coefTest is an F-test. There is no built-in way to carry out a one-sided t test.

Here are some commands to reproduce the calculations for the t statistic and its p-value as they appear int the coefficient table:

load carsmall
d = dataset(MPG,Weight);
d.Year = ordinal(Model_Year);
glm = GeneralizedLinearModel.fit(d,'MPG ~ Year + Weight + Weight^2')
glm.Coefficients.Estimate(3)
glm.Coefficients.Estimate(3)/sqrt(glm.CoefficientCovariance(3,3))
2*(1 - tcdf(glm.Coefficients.Estimate(3)/sqrt(glm.CoefficientCovariance(3,3)),glm.DFE))

You could compute a contrast among the coefficients (instead of just taking the third one as I did), use the covariance matrix to compute the variance of this contrast, and so on. Then you could pick the desired tail of the t distribution.

Best Answer

Related Solutions

MATLAB: Compare 2 regression models

MATLAB: CoefTest and one tailed T-test

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