About when to drop correlation between random intercept and slope

[David Sidhu]

I am estimating the following model:

exp1<-brm (DV ~ IV1*IV2+(1+IV1+IV2|Subject) + (1|Item), data=data1, family="bernoulli", prior = prior, warmup = 1500, iter = 3000, chains = 30)

All of the output in the resulting model looks good, except for the correlation between the subject intercept and IV1, which has an Rhat of 1.03.

I believe this means that the analysis has not converged on a value for this correlation.

However, the value of this correlation per se is not of interest to me, I only have the random effects in the model to increase accuracy with regards to the fixed effects. Thus, I'm wondering if it is necessary to have the model converge on a value for this correlation when my interest is solely in the fixed effects?

I've tried increasing the number of iterations and chains however this hasn't worked. I thought to try a model that doesn't estimate this correlation, but it doesn't seem like that's possible while still estimating the IV2 random slope, and its correlation with the subject intercept?

Thanks, as always.

[Paul Buerkner]

You can drop correlation by replacing "|" with "||" in random effects terms.

That said, I would rather include the correlation even if convergence is not optimal.

You may try setting a stronger prior on it. For instance

set_prior("lkj(2)", class = "cor", group = "Subject")

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[David Sidhu]

Thanks Paul! I will try changing the prior.

Out of interest, am I right that (1+IV1+IV2||Subject) will not model ANY correlations between slopes and intercepts?

I'm curious if there is a way to still model the intercept/IV2 correlation, and only not model the intercept/IV1 correlation?

On Tuesday, 17 April 2018 01:14:49 UTC-6, Paul Buerkner wrote:

You can drop correlation by replacing "|" with "||" in random effects terms.

That said, I would rather include the correlation even if convergence is not optimal.

You may try setting a stronger prior on it. For instance

set_prior("lkj(2)", class = "cor", group = "Subject")

2018-04-16 22:25 GMT+02:00 David Sidhu <dms...@gmail.com>:

I am estimating the following model:

exp1<-brm (DV ~ IV1*IV2+(1+IV1+IV2|Subject) + (1|Item), data=data1, family="bernoulli", prior = prior, warmup = 1500, iter = 3000, chains = 30)

All of the output in the resulting model looks good, except for the correlation between the subject intercept and IV1, which has an Rhat of 1.03.

I believe this means that the analysis has not converged on a value for this correlation.

However, the value of this correlation per se is not of interest to me, I only have the random effects in the model to increase accuracy with regards to the fixed effects. Thus, I'm wondering if it is necessary to have the model converge on a value for this correlation when my interest is solely in the fixed effects?

I've tried increasing the number of iterations and chains however this hasn't worked. I thought to try a model that doesn't estimate this correlation, but it doesn't seem like that's possible while still estimating the IV2 random slope, and its correlation with the subject intercept?

Thanks, as always.

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[Paul Buerkner]

You can specify

(1+IV2|Subject) + (0+IV1|Subject)

so that Intercept and IV2 will be modeled as correlated, but IV1 will not be modeled as correlated with the other two. Only works if IV1 is numeric (not a factor).

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