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My dependent variable is an index from annual reports of companies (ranging from 0 to 1). The independent variables will be measured with Likert scales (individuals in each company will respond to the questions – a group of items rated with a Likert scale). What is the most appropriate statistic to use in this scenario? I need help please.

Dependent variable (index from one company) $=f$(Three separate Likert Scales measuring three different issues)

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  • $\begingroup$ Why is the index bounded between 0 and 1, in terms of the data-generating process? $\endgroup$
    – abaumann
    Commented Feb 27, 2014 at 20:11
  • $\begingroup$ Yes, how do you get numbers between 0 and 1 from a Likert which is most often 5 points? $\endgroup$
    – Doctorambient
    Commented Feb 27, 2014 at 20:18
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    $\begingroup$ @DoctorAmbient The (0,1) variable is the DV (the $y$), while the Likert scales are the IVs (the $x$'s). $\endgroup$
    – Glen_b
    Commented Feb 27, 2014 at 20:24
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    $\begingroup$ @Glen_b Sorry! Totally misread that! Does the index have an interpretation as a probability or as something else? The suggestions below deal with the transformation of $y$, but should the $x$'s be transformed, too? Are they all the same Likert scale, or do the scales vary? (I've seen that happen more than you think!) $\endgroup$
    – Doctorambient
    Commented Feb 27, 2014 at 20:30

3 Answers 3

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Transform the dependent variable by taking ln(y/(1-y)) in a way as with the logistic regression and regress that on the predictors. After that check the residuals for normality.

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Papke and Wooldridge (J. Appl. Econometrics, 1996) suggest a so-called fractional logit model, a GLM with a binomial distribution and a logit link function, since the traditional tobit regression is non-applicable when outcomes outside of [0,1] are unfeasible.

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I propose a much more simple model. try first to fit a simple linear model. Your likert variables can be coded as dummy variables.

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