# [R] Logistic regression: At times correlation matrix of coefficients gets messed up

Pankaj Choudhary pankaj at utdallas.edu
Tue Jan 21 03:29:03 CET 2003

Hi,

When I include a categorical variable (RACE with 3 levels - "white",
"black" and "other") in my logistic regression model, the correlation
matrix of the coefficients gets messed up. I get something like:

-----------------------------------------
Correlation of Coefficients:
( A L RACEb
AGE       , 1
LWT       ,   1
RACEblack       1
RACEother .     .
attr(,"legend")
[1] 0 ` ' 0.3 `.' 0.6 `,' 0.8 `+' 0.9 `*' 0.95 `B' 1
-------------------------------------

I couldn't figure out how to interpret it. Here is the sequence of
commands and the complete output. (I am using R 1.6.2)

-----------------------------------------

> lowbwt.alr <- glm(LOW~AGE+LWT+RACE, family=binomial, data=lowbwt)
> summary(lowbwt.alr, correlation=TRUE)

Call:
glm(formula = LOW ~ AGE + LWT + RACE, family = binomial, data = lowbwt)

Deviance Residuals:
Min       1Q   Median       3Q      Max
-1.4052  -0.8946  -0.7209   1.2484   2.0982

Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept)  1.306741   1.069558   1.222   0.2218
AGE         -0.025524   0.033244  -0.768   0.4426
LWT         -0.014353   0.006521  -2.201   0.0277 *
RACEblack    1.003821   0.497957   2.016   0.0438 *
RACEother    0.443460   0.360184   1.231   0.2182
---
Signif. codes:  0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1

(Dispersion parameter for binomial family taken to be 1)

Null deviance: 234.67  on 188  degrees of freedom
Residual deviance: 222.66  on 184  degrees of freedom
AIC: 232.66

Number of Fisher Scoring iterations: 3

Correlation of Coefficients:
( A L RACEb
AGE       , 1
LWT       ,   1
RACEblack       1
RACEother .     .
attr(,"legend")
[1] 0 ` ' 0.3 `.' 0.6 `,' 0.8 `+' 0.9 `*' 0.95 `B' 1

---------------------------------------------------------------------

Strangely enough, when I just use (AGE and RACE) or (LWT and RACE) or
(AGE and LWT) or just RACE as the explanatory variable(s), there is no
problem.

Am I doing something wrong? I will greatly appreciate any help.

With best wishes,

Pankaj Choudhary
U. of Texas at Dallas