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I have searched and read the answers to similar questions, however I am still not sure I have the appropriate solution. I am running multiple regression with 4 predictors, one categorical and 3 "interval" predictors. The three predictors and the dependent variable are all scales, calculated from several items, each of which has 4 possible Likert-type answers. I suspect that this may be a problem for the dependent variable, as it may not be "continuous enough", based on the residuals plot, which I have included here. What do you think?

Scatterplot

Scortchi - Reinstate Monica
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kikiriki
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  • Why do you see linearity as the problem here as your title suggests? How many distinct values do your predictors and outcome have? – mdewey Jul 25 '18 at 08:50
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    A better diagnostic to examine to test linearity is the scatterplot of your outcome variable against your fitted values. It's easier to see the relation between your linear regression equation and the outcome. – Heteroskedastic Jim Jul 25 '18 at 11:42
  • @mdewey, I am concerned about that diagonal pattern showing. The outcome has 30 distinct values, ranging from 1 to 4, as the scale is calculated as mean of 10 items. The predictor variables are similar. Thanks! – kikiriki Jul 25 '18 at 19:27

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Apart from the discreteness shown, there is nothing particularly suspect in that residual plot, neither nonconstant variance nor curvature shows up. 30 distinct values should be enough so that the discreteness is not a big problem. If you are still concerned with modelinh a likert response with multiple regression, you can try ordinal response regression models, see for instance Analysis for ordinal categorical outcome

kjetil b halvorsen
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