I fitted a linear mixed model as follows:

fit=lmer(Time.to.obtain.loan ~ borrower.Gender+ borrowing.Amount + (1|borrower.Country) + (1|borrowing.Sector)) 

The following was obtained with plot(fit). enter image description here

The following was obtained with -



enter image description here

  1. What do these two plots mean? Does the same set of assumptions (normality of residuals; homogenity of variance) apply for linear mixed effects model? Am I right in reading that this model is not properly specified as it violates normality assumptions?

  2. How should one go about fixing such violations?


1 Answer 1


The plots but also the name of your outcome variable, Time.to.obtain.loan, suggest that you have a bounded outcome. Do you perhaps have (many) zeros in the Time.to.obtain.loan? If this is the case, indeed assuming a normal distribution would not be optimal. You could give a try to a Beta mixed effects models.

However, again the name of your response variable suggests that you perhaps need to account for censoring occurring in the Time.to.obtain.loan, i.e., some people have not obtained a loan yet. Hence, their time to obtain a loan is right-censored. In this case you would need to go for a survival type of model. For example, you could have a look at the coxme package.

  • $\begingroup$ Thank you @dimitris-rizopoulos. My dataset consists of only those that have received loans. So I assume right censoring does not apply for Time.to.obtain.loan. Please correct me if I am wrong. I am not sure what you mean by outcome as bounded. Yes, it is bounded on lower end at 0 (Time.to.obtain.loan is not negative). But it has no limit on upper end. So what do I do? $\endgroup$
    – SanMelkote
    Sep 19, 2018 at 14:15
  • $\begingroup$ @BengaluruSun Do you have people who have 0 Time.to.obtain.loan? If not, then you could possibly consider working with the log-transformed Time.to.obtain.loan. If yes, then you may want to consider a type of a two-part model for semi-continuous data. For example, you can fit such a model with GLMMadaptive (drizopoulos.github.io/GLMMadaptive); for more info check: drizopoulos.github.io/GLMMadaptive/articles/… $\endgroup$ Sep 19, 2018 at 15:53
  • $\begingroup$ Thank you so much for these pointers. Since the DV is not zero, I tried log (base e and 10) transformations. The residual qq plots are slightly better. I guess I need to read and explore GLMMadaptive. $\endgroup$
    – SanMelkote
    Sep 19, 2018 at 19:41
  • $\begingroup$ although the Time.to.obtain.loan is not a count variable, can one use poisson model from GLMMAdaptive? $\endgroup$
    – SanMelkote
    Sep 20, 2018 at 2:55

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