# [R] Interpreting factor*numeric interaction coefficients

Matthew Carroll mjc510 at york.ac.uk
Mon Apr 12 11:15:58 CEST 2010

```Dear all,
I am a relative novice with R, so please forgive any terrible errors...

I am working with a GLM that describes a response variable as a function of
a categorical variable with three levels and a continuous variable. These
two predictor variables are believed to interact.
An example of such a model follows at the bottom of this message, but here
is a section of its summary table:

Estimate	Std. Error z value Pr(>|z|)
(Intercept)        1.220186  	0.539475   2.262   0.0237 *
var1               0.028182  	0.050850   0.554   0.5794
cat2               -0.112454  0.781137  -0.144   0.8855
cat3               0.339589   0.672828   0.505   0.6138
var1:cat2          0.007091   0.068072   0.104   0.9170
var1:cat3          -0.027248  0.064468  -0.423   0.6725

I am having trouble interpreting this output.
I think I understand that:

# the 'var1' value refers to the slope of the relationship within the first
factor level

# the 'cat2' and 'cat3' values refer to the difference in intercept from
'cat1'

# the interaction terms describe the difference in slope between the
relationship in 'cat1' and that in 'cat2' and 'cat3' respectively

Therefore, if I wanted a single value to describe the slope in either cat2
or cat3, I would sum the interaction value with that of var1.

However, if I wanted to report a standard error for the slope in 'cat2', how
would I go about doing this? Is the reported standard error that for the
overall slope for that factor level, or is the actual standard error a
function of the standard error of var1 and that of the interaction?

Any help with this would be much appreciated,

Matthew Carroll

### example code

resp <- rpois(30, 5)
cat <- factor(rep(c(1:3), 10))
var1 <- rnorm(30, 10, 3)

mod <- glm(resp ~ var1 * cat, family="poisson")
summary(mod)

Call:
glm(formula = resp ~ var1 * cat, family = "poisson")

Deviance Residuals:
Min        1Q    Median        3Q       Max
-1.80269  -0.54107  -0.06169   0.51819   1.58169

Coefficients:
Estimate	Std. Error z value Pr(>|z|)
(Intercept)        1.220186  	0.539475   2.262   0.0237 *
var1               0.028182  	0.050850   0.554   0.5794
cat2               -0.112454  0.781137  -0.144   0.8855
cat3               0.339589   0.672828   0.505   0.6138
var1:cat2          0.007091   0.068072   0.104   0.9170
var1:cat3          -0.027248  0.064468  -0.423   0.6725
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for poisson family taken to be 1)

Null deviance: 23.222  on 29  degrees of freedom Residual deviance:
22.192  on 24  degrees of freedom
AIC: 133.75

Number of Fisher Scoring iterations: 5

--
Matthew Carroll
E-mail: mjc510 at york.ac.uk

```