I am not sure about this plot if it looks good as the dots appear around the line. So I just want to ask if it looks okay. My data is quite large (almost 3000 observations) and maybe that is why it looks like this.
Solved – Does this residual plot look bad
residuals
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By "biased" you presumably mean that there is some non-linear structure left in the residuals. It's by no means obvious to me that this is the case here.
Before leaping to any conclusions - and certainly before losing any information by transforming variables into a less-informative state - I would look at more residual plots. An obvious one would be to give a different colour or shape to the residuals where the suspect variable has a value of zero and see how this impacts on the residuals.
A dependent mixture model (hidden Markov model) may be of use, depending on the type of deviations expected.
Assume that your observations come from two distributions (or states), both of which are normally distributed, but have different mean and variance.
A number of parameters can be estimated: The initial state probabilities (2 parameters), the state transition probabilities between neighbouring data points (4 parameters) and finally the mean and variance of the two distributions (4 parameters).
In R, this model can be estimated using the depmixS4 package:
library(depmixS4)
set.seed(3)
y = rnorm(100)
y[30:35] <- rnorm(6,mean=4,sd=2)
plot(1:100,y,"l")
m <- depmix(y~1,nstates=2,ntimes=100)
fm <- fit(m)
means <- getpars(fm)[c(7,9)]
lines(1:100,means[fm@posterior$state],lwd=2,col=2)
See http://cran.r-project.org/web/packages/depmixS4/vignettes/depmixS4.pdf for references
Best Answer
Have you tried plotting this using ggplot2 in R? It has a nice semi transparency feature with the Cairo package which makes guesstimating the mean for such residual plots easy. For example you could have each point semi transparent and you could visually check if they are centered around 0. But overall by looking at the image you posted, no reason to think otherwise.