Solved – Interpretation of Baseline Reference Group

categorical datamultiple regression

I have more of a theoretical question regarding the use of dummy regression. I know that one level of a categorical variable is used as a reference group, and the means of all subsequent levels are compared to the mean of the reference group, and that these differences give different p-values.

I understand how each level in a categorical variable is interpreted for a categorical variable, but I am not sure how the p-value in the reference group should be interpreted. This may be too simplistic, but I thought the interpretation of a reference group was not meaningful because I believe the mean is being compared with itself, and thus not useful. Is this an inappropriate way of conceptually understanding my question?

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You can think of the coefficient for the reference group as comparing the reference group mean to 0. So the t-statistic and p-value for that coefficient reflect the null hypothesis that the mean of the reference group = 0.

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Solved – Interpretation of logistic regression intercept with one dumthe coded categorical variable

I think you are making this hard on yourself. Make sure race is a factor variable so that the software provides the overall $\chi^2$ of association with $k-1$ d.f. for $k$ categories. Coding doesn't affect the value of $\chi^2$. Don't use a stepwise process for making inference about the importance of race. Use the overall "chunk" test as described above, which has a built-in perfect multiplicity adjustment besides being invariant to coding. In R this would look like (for a binary or ordinal logistic model predicting $Y$):

require(rms)
f <- lrm(Y ~ rcs(age, 4) + race)
anova(f)   # 3 d.f. test for age, k-1 for race
# also prints 2 d.f. test of linearity in age
# age fit is restricted cubic spline with 4 default knots

When doing multiple imputation with the Hmisc package aregImpute function or with the mice package, you would substitute the following for the 2nd line above:

f <- fit.mult.impute(Y ~ rcs(age, 4) + race, lrm, impute_object, n.impute=20)

which would adjust the covariance matrix for multiple imputation [n.impute recommended to be the percent of observations that have any variable missing].

Categorical Encoding – Coding Categorical Variables for Regression

Here is an example using the employee data.sav data, which comes with standard installation. Suppose salary is the dependent variable, job category, jobcat, is the categorical independent variable, and beginning salary, salbegin, is the continuous independent variable. Using GLM, you can perform pairwise comparisons between each pair of job categories. The steps are as follow:

With the data set open, go to Analyze > General Linear Model > Univariate.
Put the dependent variable and independent variable into the correct slots. Categorical independent variables go to "Fixed Factor(s)" and continuous ones go to "Covariate(s)." Do not worry about the Random Factors. When it's all set, click the "Model" button.
In the Model panel, highlight the two independent variables, then change the build term to "Main effects," and then click the arrow button (indicated by the red circle) to bring the two variables over. When all set, click "Continue."
Now, click the "Option" button.
In the Option panel, do the followings: 1) Highlight jobcat, 2) bring it over to the right by clicking the arrow button, 3) Check "Compare Main Effects", 4) Specify the adjustment you'd like to make for the multiple pairwise comparisons. I left it as LSD which does not adjust for multiple tests, 5) Check "Parameter Estimates" so that you'll also get the regression coefficients. When it's all done, click Continue and then OK to submit the test.
Here is the regression coefficient table:
Scroll down a bit and you'll find the pairwise comparisons table:

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Solved – Interpretation of logistic regression intercept with one dumthe coded categorical variable

Categorical Encoding – Coding Categorical Variables for Regression

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