# Interpreting intercepts in mixed effect model with categorical predictors

Trying to fit a linear mixed effects model with 2 categorical predictors (group & worker) where worker is a random effect and group a fixed effect. I'm trying to figure out 1) whether I should specify intercept=0 and 2) why these 2 model results seem to give different conclusions about the effect of group.

Model1: tps ~ group + (1 | worker)

Model2: tps ~ group + (1 | worker) + 0

summary(Model1):
Linear mixed model fit by REML ['merModLmerTest']
Formula: tps ~ group + (1 | worker)
Data: mydata

REML criterion at convergence: 3489.872

Random effects:
Groups   Name        Variance Std.Dev.
worker   (Intercept) 1866     43.20
Residual             3165     56.26
Number of obs: 318, groups: worker, 18

Fixed effects:
Estimate Std. Error     df t value Pr(>|t|)
(Intercept)    70.15      15.59  11.27   4.501 0.000848 ***
group phone   -20.85      21.75  10.83  -0.959 0.358586
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Correlation of Fixed Effects:
(Intr)
group phone -0.717

summary(Model2):
Linear mixed model fit by REML ['merModLmerTest']
Formula: tps ~ group + (1 | worker) + 0
Data: mydata

REML criterion at convergence: 3489.872

Random effects:
Groups   Name        Variance Std.Dev.
worker   (Intercept) 1866     43.20
Residual             3165     56.26
Number of obs: 318, groups: worker, 18

Fixed effects:
Estimate Std. Error    df t value Pr(>|t|)
group computer    70.15      15.59 11.27   4.501 0.000848 ***
group phone       49.30      15.17 10.40   3.251 0.008291 **
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Correlation of Fixed Effects:
grpcmp
group phone 0.000


In the first model the 'phone' effect is the same as the difference between the two groups' effects in model 2 (this makes sense because in model1 the 'computer' group is the baseline). In model2, both groups' effects are significant, whereas in model1 only the intercept is significant.

Which is the "right" model for a situation where the group predictor is binary? It must be only one or the other (seems to indicate that model1 is correct, because there the intercept "is the same as" the computer group, right? Model2 allows a "zero" value for group which doesn't make sense). Am I right about this?

And how to interpret the fact that in model1 the intercept is significant but 'phone' is not?

• I don't use R. I assume model2 = intercept through the origin. Why would you do this? I'm sure there are situations where this might make sense, but I don't think they are commonly encountered. I think your reasoning sounds solid in that model1 makes sense. – charles Dec 14 '13 at 21:02
• thanks charles. would it also be correct to interpret the fact that in model1, the intercept coefficient is significant but not the "phone group" coefficient to mean that there is no significant difference between the groups, while the intercept coefficient being significant doesn't have a physical interpretation (other than: "yes, you do indeed have data")? – andy Dec 14 '13 at 21:44
• Yes. That is how I would interpret it. – charles Dec 14 '13 at 21:50
• @charles i think you've answered my question but i can't give you credit unless you post it as an answer... – andy Dec 14 '13 at 22:45