Chapter 8 - Multilevel Models

Music Performance Joy

Lab Setup

  1. Copy the project lab folder located at Home -> STA363_inst_files-> labs. If you check the box next to the folder name, then click the small gear icon you can “copy to” and put a copy of the folder in your newly created folder.
  2. Now, click File-> Open Project and navigate to the project file in the folder you just copied.
  3. You can place your responses in the file qmd file included.

Introduction

In this chapter, we studied models for predicting music performance anxiety, as measured by the negative affect scale from the PANAS instrument. Now we will examine models for predicting the happiness of musicians prior to performances, as measured by the positive affect scale from the PANAS instrument.

The data musicdata.csv come from the Sadler and Miller (2010) study of the emotional state of musicians before performances. The dataset contains information collected from 37 undergraduate music majors who completed the Positive Affect Negative Affect Schedule (PANAS), an instrument produces a measure of anxiety (negative affect) and a measure of happiness (positive affect). This analysis will focus on negative affect as a measure of performance anxiety.

The primary variables we’ll use are

  • id = unique musician identification number
  • diary = cumulative total of diaries filled out by musician
  • perf_type = type of performance (Solo, Large Ensemble, or Small Ensemble)
  • audience = who attended (Instructor, Public, Students, or Juried)
  • memory = performed from Memory, using Score, or Unspecified
  • na = negative affect score from PANAS
  • pa = positive affect score from PANAS
  • gender = musician gender
  • instrument = Voice, Orchestral, or Piano
  • mpqab = absorption subscale from MPQ
  • mpqpem = positive emotionality (PEM) composite scale from MPQ
  • mpqnem = negative emotionality (NEM) composite scale from MPQ

Models

To begin, run the following models:

  • Model A = unconditional means model
  • Model B = indicator for instructor audience type and indicator for student audience type at Level One; no Level Two predictors
  • Model C = indicator for instructor audience type and indicator for student audience type at Level One; centered MPQ absorption subscale as Level Two predictor for intercept and all slope terms
  • Model D = indicator for instructor audience type and indicator for student audience type at Level One; centered MPQ absorption subscale and a male indicator as Level Two predictors for intercept and all slope terms

Questions

  1. Perform an exploratory data analysis by comparing positive affect (happiness) to Level One and Level Two covariates using appropriate graphs. Comment on interesting trends, supporting your comments with appropriate summary statistics.

  2. Report estimated fixed effects and variance components from Model A, using proper notation from this chapter (no interpretations required). Also report and interpret an intraclass correlation coefficient.

  3. Report estimated fixed effects and variance components from Model B, using proper notation from this chapter. Interpret your MLE estimates for \(\hat{\alpha}_{0}\) (the intercept), and \(\hat{\sigma}_{u}\) (the Level Two standard deviation for the intercept). Also report and interpret an appropriate pseudo R-squared value for model A vs model B.

  4. Write out Model C, using both separate Level One and Level Two models as well as a composite model. Be sure to express distributions for error terms. How many parameters must be estimated in Model C?

  5. Report and interpret the following parameter estimates from Model C: \(\hat{\alpha}_{0}\), \(\hat{\alpha}_{1}\), \(\hat{\gamma}_{0}\), \(\hat{\beta}_{1}\), \(\hat{\sigma}_{u}\), \(\hat{\sigma}_{v}\), and \(\hat{\rho}_{uv}\). Interpretations for variance components should be done in terms of standard deviations and correlation coefficients.

  6. Report and interpret the same parameter estimates listed above from Model D. In each case, the new interpretation should involve a small modification of your interpretation from Model C. Use underlines or highlights to denote the part of the Model D interpretation that differs from the Model C interpretation.

  7. Also report and interpret the following parameter estimates from Model D: \(\hat{\alpha}_{2}\) and \(\hat{\beta}_{2}\).

  8. Use a drop in deviance statistic (likelihood ratio test) to compare Model C vs. Model D. Give a test statistic and p-value, then state a conclusion. Also compare Models C and D with appropriate pseudo R-squared value(s) and with AIC and BIC statistics.