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I have a question about statistical models. In particular, whether it is correct/meaningful to build a statistical prediction for a response variable based on the other dependent variables from the same experiment.

Simplified example:

I conducted a study to see how different types of interaction influence subjects' performance (measured objective variable) and perception (subjective variables collected with a questionnaire).

In my experiment design, I have two factors (Independent Variables, IV): i) partner with 3 levels, ii) connection with 8 levels. I used full factorial design (repeated measurements on both factors) – each participant experiences every combination of factor levels i) and ii) - 24 trials.

I measured a number of dependent variables (DV): (1) error in task, (2) preference, (3) predictability of interaction and (4) how helpful and (5) natural the interaction feels. DV (1) was measured (continuous) and (2)-(5) were reported by participants with a questionnaire (5-point Liker scale).

In the first step of the analysis, I conducted rmANOVA for parametric data and rm ART ANOVA for Likert scales. I checked all assumptions and, if necessary, adjusted p-values. I also analyzed the data in detail with Post-Hoc analysis.

Now I am interested in whether DV “preference” could be predicted with other DVs. E.g. whether the preference is increasing when the error is small, the interaction is perceived as predictable, helpful and natural. I have already looked at the correlations between all DVs, but I cannot draw cause-and-effect conclusions in this case, just whether the values have an association with each other or not. My first idea was to use GLM (Generalized Linear Model), but I am not sure how appropriate it is.

To summarise, I want to have a model where I can predict preference as a function of the other DVs (error, predictability as well as scales “helpful” and “natural”).

Questions:

1) Is it correct to make a prediction about one DV based on other DVs?

2) What would be the appropriate method for this? (I am using R software and would also appreciate any advice packages and functions)

3) In this case, should I create a model including all factors at the same time or do I need several models - one for each factor?

I hope that the question formulation is clear. Since I could not find any answers online, I would appreciate suggestions for this one. Thank you!

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What you are doing is fine. Regression models don't indicate causation, they are generally a way to describe association and in particular to predict one variable from another.

It's easiest to model these things when all dependent variables are continuous and can be assumed to have a joint normal distribution. (This doesn't apply to your data, but will provide a motivation.) In this case, as long as cases are independent of each other, it is perfectly fine to use a standard linear regression model to predict one dependent variable from the others: you are just studying the conditional distribution of that variable given the others, and that is a normal distribution.

Your case is more complicated, because the variable you want to predict is Likert-scale (ordered discrete) while some predictors are Likert and others are not. Models for this kind of data are complicated, but it should be fine to use a model that is appropriate for predicting Likert-scale data. Just remember to interpret the results as a way to describe associations, not causation.

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