Hi there,

When I run a random intercept + random slope model, I get exactly the same
result as when running a model where there is no random intercept. I can't
figure out why this is.

Model 1:

*m1 <- lmer(rt ~ treatment + (1+treatment|subject),data=df)*
*m1*
*Linear mixed model fit by REML ['lmerMod']*
*Formula: rt ~ treatment + (1 + treatment | subject)*
*   Data: df*
*REML criterion at convergence: 32558.52*
*Random effects:*
* Groups   Name        Std.Dev. Corr       *
* subject  (Intercept) 71.64               *
*          treatment2  54.55    -0.31      *
*          treatment3  54.79    -0.34  0.89*
* Residual             97.38               *
*Number of obs: 2700, groups: subject, 30*
*Fixed Effects:*
*(Intercept)   treatment2   treatment3  *
*   598.6675      -0.9037      50.9770  *

Model 2:

*m2 <- lmer(rt ~ treatment + (0+treatment|subject) ,data=df)*
*m2*
*Linear mixed model fit by REML ['lmerMod']*
*Formula: rt ~ treatment + (0 + treatment | subject)*
*   Data: df*
*REML criterion at convergence: 32558.52*
*Random effects:*
* Groups   Name       Std.Dev. Corr     *
* subject  treatment1 71.64             *
*          treatment2 75.18    0.72     *
*          treatment3 74.03    0.72 0.94*
* Residual            97.38             *
*Number of obs: 2700, groups: subject, 30*
*Fixed Effects:*
*(Intercept)   treatment2   treatment3  *
*   598.6675      -0.9037      50.9770  *

Compare both models:

*anova(m1,m2)*
*refitting model(s) with ML (instead of REML)*
*Data: df*
*Models:*
*m1: rt ~ treatment + (1 + treatment | subject)*
*m2: rt ~ treatment + (0 + treatment | subject)*
*    Df   AIC   BIC logLik deviance Chisq Chi Df Pr(>Chisq)*
*m1 10 32598 32657 -16289    32578                        *
*m2 10 32598 32657 -16289    32578     0      0          1*

Thanks in advance

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