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I have a case study where the target variable (a single factor) gauged through multiple items. the items are measured using 5-Likert scale (Never, Seldom, Sometimes, Often, Very often, Always)

since multiple items are invovled for the dependent variable, I have calculated the mean for every object. then applied Linear Regression. Is it a correct way? or is there a better way to handle?

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  • $\begingroup$ it's not sure not that the mean will be accurate. linear regression might be a too rigid, you could try various other things like decision tree regression for instance. $\endgroup$
    – Erwan
    Oct 4, 2022 at 22:56

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That is a non-trivial question, with a long answer that will end with you making some decisions and doing more research before you decide what is right or wrong.

First things first you have a 6 level Likert Scale, you stated 5 it does matter a bit for interpretation (you will need to do some research on this).

Second:

since multiple items are invovled for the dependent variable, I have calculated the mean for every object.

Not sure if you mean you calculated the mean for each person taking the survey (having converted the answers to numerical values) or if you took the mean for each item across all respondents.

So I am just going to give my two cents:

Are your levels are ordinal or interval, they have an order and rank, but can you really quantify the distance between 'seldom' and 'sometimes'? This you have to decide, it appears you are going for interval.

Either way I would be cautious about using the values you have calculated because all the items on the scale contribute to one variable, so each person, has a single score (if using numerical values) and it is the sum of all points for all items. That is the value for the variable represented by the scale for that person.

To get a mean variable value for the whole survey sample, you would take the

Interval Analysis: If you feel that you can treat this as interval data, you can use numerical values 1-6 and for each person answering each item on your survey. You add up the total value of all items, this is their Likert score for this scaled question for this person.

You can then do descriptive analysis, look at the distribution of scores (plot a histogram and calculate mean, standard deviation and quantiles) to use to compare peoples level of whatever your are testing relative to others.

If you know specific things about individuals (other than the topic the Likert survey addresses) you can do comparisons between groups such as men & women or age groups or political parties using Pearson's Correlations Test using the row-sum for each respondent

Ordinal Analysis

If you decide that you cannot safely attribute a meaningful consistent quantifiable space between levels in your scale, then you need to treat the analysis as Ordinal. As such your analysis is a bit different.

The descriptive work involves building 'histograms' for each item (really a bar chart) and identifying the most common response (the mode) and looking at how each item is distributed.

Keep in mind you are trying to answer one question with all the items, so comparing the distribution of answers across items may be meaningful. Are they not trending the same way despite attempting to elucidate a single latent variable quality?

Again, if you know something about the people surveyed (a view point, affiliation, gender etcetera) you can use a Chi-Square to assess if the item responses are associated with the known factors.

It may be that you could use a logistic regression if you had a clear target, like "is someone likely to be omnivorous or vegan" and you had a well structured likert survey and knew whether each respondent was omnivorous or vegan and surveys from people with unknown eating habits.

You really need to choose the model or test based on what you are trying to understand or predict based on your Likert Items. It is always best to design the analysis prior to creating the items and seeking out respondents. You will be more thoughtful and get more consistent results this way.

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