I have 5 independent variables at 3 levels : 0, -1, +1 and dependent variable y at Likert scale (1 to 5)
The residual vs Fitted value plot doesn't look okay. Please throw some light.
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$\begingroup$ More information needed I think. What model did you fit? I suspect you fitted some kind of linear model, which is inappropriate when your response is discrete. What that ends up leading to is stratification of your errors, which the model assumes are normally distributed (I.e. continuous). If you have, then you probably want something like a proportional odds model. $\endgroup$– André.BDec 7, 2018 at 1:31
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$\begingroup$ Linear regression model. I learnt that Likert Scale can be assumed to be continuous. Will try and do the Odinal Logistic Regression $\endgroup$– GuptaDec 7, 2018 at 4:50
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$\begingroup$ How is the response entered? Is it discrete or numeric? $\endgroup$– André.BDec 10, 2018 at 7:03
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$\begingroup$ Numeric (1,2,3,4,5) $\endgroup$– GuptaDec 11, 2018 at 11:25
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$\begingroup$ Whoops! I meant discrete or continuous - really shouldn't be doing this late at night! However, that gives me enough information; I will write a proper answer below. $\endgroup$– André.BDec 12, 2018 at 17:51
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Given the information in the comments above the issue with fitting a linear model with normally distributed errors to your data is that the normal distribution runs from infinity to negative infinity (it's unbounded) and the errors can take any value between that (I.e. 0.32, 4.6). Your data is bounded, it can only take values between 1 and 5, and even then it can only take integer (whole number) values, meaning modelling the errors with a normal distributions is inappropriate - the residual plots look stratified because of this. It's hard to suggest another model without understanding what exactly you want to know but something like a proportional odds model would likely be most appropriate.
EDIT: Also the plot is not showing heteroscedasticity - just stratification. Heteroscedasticity is when the variance of the points changes systematically with the fitted value. It usually looks like a trumpet.
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$\begingroup$ Another question: On your response scale - is a value of 2 equal to twice the response of 1? If not, then the normal distribution runs askew because it implicitly assumes this. $\endgroup$– André.BDec 13, 2018 at 6:03