Binary variable shows twice in random effects when random intercept excluded [R, lme4]

Question

When I use lmer of lme4 to fit a random one-variable slope model with random intercept excluded, both levels of the one-variable slope are reported with random variances, as if the slope had two variables (i.e., as if it were a three-level treatment effect). How should I interpret this?

Detailed Example:

Scenario 1
Here is what the model looks like with both random slope and intercept included. Everything works as expected: in line 7, the binary variable Cond1 shows up with just one effect (Cond1hetero, the upper level of the two-level categorical)...

> RT_log.CVquestA.lmer=lmer(RT_log~Cond1+(1+Cond1|Subject),data=basedata)
> summary(RT_log.CVquestA.lmer)
...
Random effects:
 Groups   Name        Variance Std.Dev. Corr 
 Subject  (Intercept) 0.026121 0.16162       
          Cond1hetero 0.001366 0.03696  -0.47
 Residual             0.028667 0.16931       
Number of obs: 3321, groups:  Subject, 19

Fixed effects:
            Estimate Std. Error t value
(Intercept)  6.57461    0.03725  176.49
Cond1hetero  0.02815    0.01052    2.68

Correlation of Fixed Effects:
            (Intr)
Cond1hetero -0.412

Scenario 2
Here is what the model looks like when I remove the random intercept. Note the extra variance term on line 6 of the block below (i.e., we now see an effect for Cond1non-hetero, the reference level of the Cond1 categorical variable, in addition to the upper level Cond1hetero). I don't know how to interpret or use this output!

> RT_log.CVquestB.lmer=lmer(RT_log~Cond1+(0+Cond1|Subject),data=basedata)
> summary(RT_log.CVquestB.lmer)
...
Random effects:
 Groups   Name            Variance Std.Dev. Corr
 Subject  Cond1non-hetero 0.02612  0.1616       
          Cond1hetero     0.02184  0.1478   0.98
 Residual                 0.02867  0.1693       
Number of obs: 3321, groups:  Subject, 19

Fixed effects:
            Estimate Std. Error t value
(Intercept)  6.57461    0.03725  176.49
Cond1hetero  0.02815    0.01052    2.68

Correlation of Fixed Effects:
            (Intr)
Cond1hetero -0.412

Answer 1

You got exactly what you asked for. If you compute models such as ANOVA, regression etc. they by default contain intercept and in vast majority of cases you should not drop the intercept from your model. In models with intercept included, it is a "starting point" (see e.g. here), where all the other parameters describe how the dependent variable behaves given the parameters. If you have categorical variable among the independent variables in your model, then you can estimate effects for $k-1$ out of $k$ levels of such variable, because otherwise your model won't be identifable. If you drop intercept, you estimate effects for $k$ levels since there is no other baseline.

To make the example simpler, I'm going to use as an example mtcars dataset and simple linear regression. As you can see below, model with intercept shows how manual transmission (am=1) influences car's miles per gallon, while model without intercept shows different behavior of cars with automatic or with manual transmission. As there are only two levels in am variable and the model is very simple, there is no substantial difference in both models.

> lm(mpg ~ as.factor(am), data = mtcars)

Call:
lm(formula = mpg ~ as.factor(am), data = mtcars)

Coefficients:
   (Intercept)  as.factor(am)1  
        17.147           7.245  

> lm(mpg ~ 0 + as.factor(am), data = mtcars)

Call:
lm(formula = mpg ~ 0 + as.factor(am), data = mtcars)

Coefficients:
as.factor(am)0  as.factor(am)1  
         17.15           24.39