count data as a dependent variable consist of five levels likert scale

Question

I have few Likert type questionnaires (items) as responses recorded from 1 to 5. I am using these responses as a dependent variable against three independent variables( one contentious and two others are categorical). I am trying to fit gzlm into these data . I tried to use one item of the questionnaire at a time. I have my responses in one column. I tried to use the cut command to the dependent variable so that it gives me five boundaries (the first will be treated as reference and the rst four will be compared to it) and when I apply the model

glm(y ~ IV1*IV2*IV3, data=young, family=poisson)

I keep getting errors like

**Error: 'family' argument seems not to be a valid family object.**

I need some direction if some knows please.

Answer 1

Why do you think a 5 point Likert-scale item is a count variable? I don't know your data but a 5-point Likert scale item does not sound like a variable that is a count variable with a Poisson distribution (Poisson Distribution) and thus you don't want to specify family=poisson.

If your DV is a 5-point Likert scale (ordered categorical variable), you can either use linear models (e.g., multiple linear regression) or logistic models (ordered logistic regression, for example by using the polr function of the R package MASS).

In my opinion, you should use ordered logistic regression instead of linear regression if there are floor or ceiling effects in your DV, that is, if most people selected the highest or lowest category of the DV. You can check floor and ceiling effects by looking at a histogram of the DV and by looking at the mean score of the DV (A mean lower than 2 or higher than 4 could indicate a floor effect and ceiling effect, respectively).

A consequence of floor and ceiling effects is that linear models underestimate the regression coefficients unless the independent variable(s) shows the same floor and ceiling effect, respectively. That's why equally difficult items of a scale are often higher correlated than unequally difficult items (McDonald & Ahlawat, 1974).

Answer 2

There are two common approaches for this kind pf problems: (a) threat the Likert data as Normal and use a linear regression, (b) use logistic regression model, in particular an Item Response Theory-based one.

As @MichaelGrosz noticed, Likert data is not Poisson distributed, as your error message suggests, so using a Poisson model is wrong in here. It was also noticed that linear regression has its pitfalls with this kind of problems while being used very often in social sciences for this kind of problems. However the most up-to-date approach would be to use IRT-based model (see here and here for examples and further details). The simple case of such model would be Rasch model

$$ P(X_{ij} = 1) = \frac{\exp(\theta_i - \beta_j)}{1+\exp(\theta_i - \beta_j)} $$

that is a variation of logistic regression model that models individual response $Y_{ij}$ as a function of the latent trait $\theta_i$ and the item "difficulty" (think of it as a measure of how often people in one range of the latent trait answer the item accordingly comparing to the ones on the opposite side of the continuum) $\beta_j$. Simple Rasch model is used for binary-valued items but there are also models for polytomous items that follow similar logic e.g. Graded Response model (examples e.g. here). In R there are several packages for estimating IRT models, you can check ltm (Rizopoulos, 2006) and mirt (Chalmers, 2012) packages and their documentation for further information.