How to 'normalize' data to account for level at baseline?

Question

In the beginning of an experiment, subjects are required to report on their initial emotions / mood using Questionnaire#1. After the experiment is conducted, the subjects fill another mood questionnaire#2.

How do we interpret these two sets of data (from the initial questionnaire and the final questionnaire)?

Since it is not possible for every participant to have the same initial emotions or level on the Likert scale (which goes from strongly disagree to strongly agree) at the start of the experiment, how do we analyze the data to "normalize their emotions" from questionnaires.

Answer 1

The analysis method you are looking for is called Mixed Models for Repeated Measures. See this similar question Which statistical analyses should I use?

Briefly, the data are model as:

$$\mathbf{Y} = \mathbf{X}\beta + \mathbf{Z}\mathbf{u} + \varepsilon$$

Where $\beta$ is a vector of fixed effects, and $\mathbf{u}$ is a vector of random effects. The random errors $\varepsilon$ have have covariance matrix $\mathbf{R}$ and the random effects $\mathbf{u}$ have covariance matrix $\mathbf{G}$. The variance of $\mathbf{Y}$ is then $\mathbf{ZGZ' + R}$. A brief overview can be found in its Wikipedia entry. An introduction to Mixed Models is typically a one semester course at a university.

This model addresses your problem because each subject has their own $\mathbf{R}$ matrix (which can have many different covariance structures - such as unstructured, compound symmetry, autoregressive, and more - a structure that is common for all subjects).

Answer 2

I don't think the Mixed Models for Repeated Measures and include the the baseline emotional responses as a covariate is a right way to solve your question, since it seems that you do not have a control group. only you have two groups, you can treat the baseline emotional response as a covariate to adujst the this potenial confounding factors between groups.