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I have a question in mixed models. I'm quite new at this field and I'm trying to calculate a model in which "y" is predicted according to multiple covariates (Age,gender,BMI) and the random variable "randX". randX has two different unique values and I have 150 repeats with each of the values. I want the var-cov matrix to be a diagonal matrix with the same variance for both of randX types (but zero variance between the types). I read a lot about this subject and this is what I did so far. I have no idea if this is the right model.

model <- lme(y ~ Age+gender+BMI, data = df, random=list(randX = pdIdent(~Age+gender+BMI)), method = "REML")

please help me with that. Thanks.

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  • $\begingroup$ If randX has only two possible values, it cannot be a random effect. $\endgroup$
    – amoeba
    Commented Aug 22, 2018 at 11:17

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Considering randX as a random effect means that the observed values of randX are viewed as one possible sample from a broader population of values. And these values are assumed to follow a $\text{N}(0, \sigma^2_{\text{randX}})$ distribution. In R, the syntax 1 | randX is used to specify a random effect on the intercept at the randX level.

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  • $\begingroup$ Thank you for your answer. I know that this is the way to do it for a General symmetric positive-definite var-cov (default). I use this code in this case: model <- lme(y ~ Age+gender+BMI, data = df, random=~1|randX, method = "REML"). However, I want to apply a Multiple of an identity var-cov matrix and I don't know how. $\endgroup$
    – Amit
    Commented Aug 22, 2018 at 10:49
  • $\begingroup$ In this case, you do not have a covariance matrix, only a variance... $\endgroup$
    – ocram
    Commented Aug 22, 2018 at 11:02
  • $\begingroup$ That is true. So how do I implement it using lme? $\endgroup$
    – Amit
    Commented Aug 22, 2018 at 12:23

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