# Interpret regression output using a likert scale IV (using STATA)

I want to run a regression with an binary DV and a likert scale ( 1=strongly disagree, 2=disagree, 3=agree, 4=strongly agree) IV. I think the right model to use is a probit regression, or what would you guys recommend? Or would it be better to code the likert scale as an dummy variable and then use a logistic regression?

If I use the likert scale IV and a run probit regression I am actually not sure how to interpret the results/coefficients of the regression.

It would be great if you help me or give me some hints. I´m really new to this stuff. Thanks in advance!

Since you have a binary dependent variable, you can use a binary logistic regression. If you ignore the fact that your independent variable is ordinal in nature, you can capture its effect on the DV using dummy variable coding. In other words, define the following dummy variables:

D2vs1 = 1 if study subject disagrees, 0 else D3vs1 = 1 if study subject agrees, 0 else D4vs1 = 1 if study subject strongly agrees, 0 else

and include them in your binary logistic regression model. The model will be stated as:

$$\log(p/(1-p)) = \beta_0 + \beta_1 * D2vs1 + \beta_2 * D3vs1 + \beta_3 * D4vs1$$

where $$p$$ denotes the conditional probability that DV = 1 given the IV and $$\log(p/(1-p))$$ represents the conditional log odds that DV = 1 (rather than DV = 0) given the IV.

After fitting this model to the data, you can test whether the IV has an effect on the log odds that that DV = 1 by testing the composite hypotheses:

$$H_0: \beta_1 = \beta_2 = \beta_3 = 0$$

$$H_a:$$ at least one of $$\beta_1, \beta_2$$ and $$\beta_3$$ is $$\neq 0$$

If you reject the null hypothesis, you can follow-up with post-hoc multiple comparisons to determine where the differences in log-odds occur between pairs of levels (or categories) of your DV.

How would you interpret the coefficients in your model? First, notice that the following relationships hold.

• The log odds that DV = 1 among subjects in your study population who strongly disagree are given by: $$\log(p/(1-p)) = \beta_0$$;

• The log odds that DV = 1 among subjects in your study population who disagree are given by: $$\log(p/(1-p)) = \beta_0 + \beta_1$$;

• The log odds that DV = 1 among subjects in your study population who agree are given by: $$\log(p/(1-p)) = \beta_0 + \beta_2$$;

• The log odds that DV = 1 among subjects in your study population who strongly agree are given by: $$\log(p/(1-p)) = \beta_0 + \beta_3$$.

So you can work out that:

• $$\beta_1$$ denotes the difference in the log odds that DV = 1 between subjects in your study population who disagree and those who strongly disagree;

• $$\beta_2$$ denotes the difference in the log odds that DV = 1 between subjects in your study population who agree and those who strongly disagree;

• $$\beta_3$$ denotes the difference in the log odds that DV = 1 between subjects in your study population who strongly agree and those who strongly disagree.

You can exponentiate the coefficients $$\beta_1$$, $$\beta_2$$ and $$\beta_3$$ to move your interpretation from the log odds scale to the odds scale.

• Thanks a lot! This is very helpful. But what would happen if I just run the logistic regression in stata without creating the dummy variables? The output is the same, so why should I create the dummy variables? Thanks in advance!
– R.K.
Jun 22, 2020 at 11:18