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].
R uses dummy coding by default for categorical predictor variables which are declared as factors. The way R does this is it treats the first level of that categorical variable as the *reference level" and creates dummy variables that will enable the comparison of each subsequent level against that reference level. To see what level R treats as "first" for a factor, simply use the levels() command on that factor. However, you can reorder the levels of a factor to make your comparisons more meaningful if needed.
In the example below, am is a categorical predictor variable from the mtcars dataset which stands for type of transmission for a car (0 = automatic, 1 = manual). In this dataset, am is declared as numeric (num) but we can convert it to a factor named am1vs0:
str(mtcars$am)
mtcars$am1vs0 <- factor(mtcars$am, levels = c(0,1))
By listing the levels of this factor in the order seen above (i.e., 0, 1), we are forcing R to treat 0 as the reference level and compare the remaining level, 1, against 0.
We can then fit the model below, where mpg stands for miles per gallon and wt stands for weight of car:
M1 <- lm(mpg ~ wt + am1vs0, data = mtcars)
summary(M1)
The summary of the model fit you will include this portion of output:
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 37.32155 3.05464 12.218 5.84e-13 ***
wt -5.35281 0.78824 -6.791 1.87e-07 ***
am1vs01 -0.02362 1.54565 -0.015 0.988
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
In this model, the intercept denotes the mean value of mpg for cars for which am1vs0 is equal to the reference level 0 (i.e., cars with automated transmission) who have the same weight.
Now, let's say that you want 1 to be the reference level for am:
mtcars$am0vs1 <- factor(mtcars$am, levels = c(1,0))
By listing the levels of the factor am0vs1 in the order seen above (i.e., 1, 0) we are forcing R to treat 1 as the reference level and compare the remaining level, 0, against 1. The corresponding model would be:
M2 <- lm(mpg ~ wt + am0vs1, data = mtcars)
summary(M2)
The output for this second model is:
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 37.29794 2.08566 17.883 < 2e-16 ***
wt -5.35281 0.78824 -6.791 1.87e-07 ***
am0vs10 0.02362 1.54565 0.015 0.988
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
The intercept for this second model represents the mean value of mpg for cars for which am0vs1 is equal to the reference level 1 (i.e., cars with manual transmission) who have the same weight.
So the two models have intercepts with different interpretations, because each model uses a different reference level for the categorical predictor am.
Now, we don't know from your post whether both you and your colleague used the same reference level for your categorical predictor gender. If you are seeing different intercepts for your models, chances are that you used difference reference levels for gender. Of course, you didn't use a factor variable rather a numeric binary variable in your model. But that should still give you the same result as if you coded gender as a factor and treated the level denoted by 0 as the reference level.
Best Answer
This description:
Doesn't sound like a zero-intercept model.
What they are saying here is that they used a constant (1) for the intercept which R likely does by default.
A bit of explanation below.
If you have a model like so:
Here
biare coefficients.You can write it as:
Note the "1" before the 'b0'. That's the constant they were talking about. When they arrange their data into a matrix format, so that all x1 ... x8 form 8 columns - they add that constant column of 1s for the intercept.
R does this by default (at least the lm() function) but you can also specify it by explicitly adding it: