0
$\begingroup$

I am conducting a multiple linear regression (OLS) and would like to test the assumptions related to these regressions. My OLS regression involves one dependent variable and 3 independent variables. All my VIF scores are below 2 so I believe that means that there is no multicollinearity. For the other assumptions I have these pictures below. However I have trouble interpretating them.

  1. I believe that the pp-plot shows violation of linearity? If so, does it mean that I cannot interpret the results of the regression?

  2. Also, what does the scatterplot tell me in regards to the assumptions for OLS?

Thank you very much for your insights. enter image description here enter image description here

Improve this question
$\endgroup$
4
  • 4
    $\begingroup$ Neither plot tells you anything about linearity. The basic problem is that your response look like it is related to a small count--it is discrete, bounded on one side, and skewed--and would therefore benefit from applying a different model, such as a logistic regression. $\endgroup$
    – whuber ♦
    Commented Aug 20, 2023 at 14:31
  • 1
    $\begingroup$ The PP plot tells you that your residuals are pretty close to normal. For the first plot, see @whuber 's comment. I also noticed that the DV is "Intention" . How is that measured? From the plot, it looks like it is measured ordinally, probably on a Likert scale. And, as whuber says it is skewed. This plot ought to look blobby. $\endgroup$
    – Peter Flom
    Commented Aug 20, 2023 at 14:52
  • $\begingroup$ @whuber Thank you. $\endgroup$
    – Sabine
    Commented Aug 20, 2023 at 14:57
  • $\begingroup$ @PeterFlom yes my dependent variable was measured on a Likert scale. Could you tell me whether any of these pictures show violation of assumptions for OLS? Thank you $\endgroup$
    – Sabine
    Commented Aug 20, 2023 at 14:59

1 Answer 1

Reset to default
0
$\begingroup$

Welcome to CV.

In your comment you say that your DV is ordinal and ask if any of the pictures show violation of OLS.

When your DV is ordinal, you don't need pictures. OLS assumes that the DV is continuous.

As Whuber noted, your first plot does show this, but interpreting that plot requires experience and expertise. I also noted that that plot should be blobby. That is, it shouldn't have patterns.

But never mind that. Your DV is ordinal. Maybe a 7 point scale. OLS will make nonsensical predictions. None of the predicted values will be integers (although they might be close) and some might be below 1 or above 7.

You should use ordinal logistic regression, at least as a starting point.

Improve this answer
$\endgroup$
11
  • 1
    $\begingroup$ @Sabine For a weird flex, you could treat the three question responses as a single DV but with mixed effects ordinal logistic regression where there are random effects for the question. $\endgroup$
    – Galen
    Commented Aug 20, 2023 at 15:25
  • 1
    $\begingroup$ I am unaware of any authority that asserts the response variable must be continuous. Maybe you meant to use a different term than "continuous"? $\endgroup$
    – whuber ♦
    Commented Aug 20, 2023 at 15:26
  • 2
    $\begingroup$ @PeterFlom The whole level of measurement thing has to do with enforcing symmetries of the actions of certain algebraic structures (usually, and classically, groups). If you don't care about those symmetries for a given analysis, then it is optional whether you limit your operators to respect that structure. The success of word embedding techniques (some of them using least squares in the parameter estimation) in natural language processing show strong counterexamples to the notion that one must respect what seems like the prima facie 'natural' structure of the data. $\endgroup$
    – Galen
    Commented Aug 20, 2023 at 15:42
  • 1
    $\begingroup$ @Sabine All that disagreement notwithstanding, if you are doing a frequentist analysis I suggest lavaan for R and semopy for Python. Similarly, if you do a Bayesian analysis, you can use RStan for R and PyStan for Python. $\endgroup$
    – Galen
    Commented Aug 20, 2023 at 15:56
  • 1
    $\begingroup$ @PeterFlom TBH I miss your blog. But yes, I think we agree that something using ordinal regression alongside other techniques (e.g. SEM) would be useful to Sabine. $\endgroup$
    – Galen
    Commented Aug 20, 2023 at 16:06

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.