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I absolutely need your help with my research. When I checked for heteroskedasticity I obtained a weird result from the white test (p value = 0). When I plot the residuals, these are the results:

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Honestly I've never seen something like that before.

Here some details about my research: I have individual data (6/7000 obs.) about the amount of movies watched by each respondent during the last year, on different channels (Theatres, Netflix, exc). I created a new variable as the sum of the movie watched on each channel, and then I divided the other variables in order to create a kind of market share. What I want to investigate is the relationship between the different market shares, so I thought that a linear (multiplicative) model would have been the best solution. These plots are related to the model where the market share of movie theatre is my DV, as IVs I have Netflix share, digital rent share, and physical share, and some control variables related to channel preferences, socio-demographic variables and the sum of all the movies watched (the variable I created before).

Multiple R-squared = Adj. R-squared = 0.9885 (this also seems weired to me)

  • no multicollinearity
  • no autocorrelation

I really need your help. Thanks in advance to everyone.

AS231
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1 Answers1

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This is the type of residual plot you will typically observe when you fit a linear regression to data where the response is a count value. Those lines of points you are seeing in the plot are for each particular count values for the response variable. Most professional statisticians have seen these types of plots many times before, so they are not at all surprising to us --- indeed, I could tell you were using a count valued response as soon as I saw the residual plot, without needing to read your data description.

For the type of data you are dealing with, you are better off using a model for count regression. I'd suggest you start with the negative binomial regression model, which is designed for cases where your response variable is a count value. (Don't use Poisson regression; it is a terrible model.) This model should give you a generally better fit and a more sensible (deviance) residual plot.

Ben
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  • Thank you, it is really helpful. I started with the negative binomial regression model and the residual plot looks better. The problem that I have now is related to the overdispersion, how can I fix it? What are the usual causes of that? – AS231 May 09 '22 at 12:34
  • The negative-binomial model already estimates "overdispersion" correctly so there is nothing you need to do about it (see related question here). The meaning of "over-dispersion" in this context is merely that the data exhibits higher variance than would be the case in a Poisson model --- it is not really a terribly useful concept to begin with. The usual cause is that the underlying data is a mixture of Poisson models with different rates (see e.g., here). – Ben May 09 '22 at 22:15