# Interpret this observed-vs-fitted plot

I have this OvF plot with the outcome being a ln-transformed continuous variable (length of stay in days).

This plot is the result of a survey-adjusted weighted mixed-level (1 level random intercept), linear regression done in stata 14.

I don't know how to interpret this plot. There seems to be a weird horizontal pattern accross the o=f line that i cannot understand. Please advise.

Also if you know another method of assessing the model fit for generalized linear regression (continuous outcomes), please let me know (stata commands --> extra kudos!)

• Your observed values are presumably integer days, which lead to those unequally spaced values when you take their natural logarithms, but cannot fill the gaps – Henry Oct 11 '16 at 20:43
• how can we fix that? – Paris Char Oct 11 '16 at 20:56
• As Henry says, this is what you would expect when the dependent variable is discrete - you don't need to fix it. There are several answers concerning diagnostic for log-linear/Poisson models. For example, have a look at this, this, or this. – matteo Oct 11 '16 at 20:56
• @MatteoLisi i appreciate your answer but none of the 3 sources can help me out. number of days should treated as continuous discete variable, not as ordinal categorical. Do you suggest i ran Poisson regression instead? Im not sure how these sources help me out here - do i need a different kind of plot? The above sources point to residuals vs fitted instead. – Paris Char Oct 11 '16 at 21:29
• "Continuous discrete variable" is a contradiction in terms: by definition, "discrete" is as far from "continuous" as one can get. – whuber Oct 12 '16 at 19:40

Your variable is measured in days, so the lowest value is $1$ day or $\ ln 1=0$, the second lowest value is $2$ days or $\ln 2\approx0.69$, the third is $3$ days or $\ln 3\approx1.10$, etc. That is what you see in the graph; the bottom three horizontal lines of points happen at about the values $0$, $0.69$, and $1.10$. So the graph accurately represents what is happening in your data.