Supplementary Statistical Materials

This page contains worked examples of various statistical teaching materials using NZAVS data along with supplementary materials and data from some of our published papers for use in teaching. Please note that this page is focused on providing examples for teaching purposes. The complete archive of Mplus syntax for the statistical models reported in our published research articles is provided on the NZAVS Statistical Models page. 

Bayesian Linear Regression Model Predicting Religious Change

This file contains Mplus syntax and data for the predictive model developed by Chris Sibley and William Hoverd forecasting the total proportion of the New Zealand population expected to affiliate with a Christian group or denomination in the 2013 census. The model demonstrates how to estimate a predicted score and associated crediblity interval using Bayesian regression. The model is based on New Zealand Census data from 1966 - 2006, and predicts that the proportion of the population that will identify as Christian in the 2013 New Zealand Census should be on or around 47.8% (95% Credibility Interval: 44.4% - 51.1%).

Regression Approach to ANOVA

This file contains Mplus syntax and data demonstrating a Bayesian 2 x 4 Between-Groups ANOVA using a series of regression interactions. The model uses diffuse priors. The model is demonstrated using data on naming preferences from Sibley et al. (2011), originally analysed using a standard (Frequentist) 2 x 4 ANOVA in SPSS.

Sibley, C. G., Houkamau, C. A., & Hoverd, W. J. (2011). Ethnic group labels and intergroup attitudes in New Zealand: Naming preferences predict distinct ingroup and outgroup biases. Analyses of Social Issues and Public Policy, 11, 201-220.

Moderated Regression (Plotting Interactions Between Continuous Variables)

This file contains Mplus syntax and data demonstrating how to conduct a moderated linear regression model in Mplus. The syntax calculates simple slopes, and also estimates points to plot at conditional values of the moderator with associated standard errors for the point estimates. The moderator and predictor variables may be continuous or categorical. This model is demonstrated using data from Sibley and Kurz (in press).

Sibley, C. G. & Kurz, T. (in press). A model of climate change belief profiles: How much does it matter if people question human causation? Analyses of Social Issues and Public Policy.

Item Response Theory

This file contains Mplus syntax and data demonstrating how to conduct Item Response Theory analysis. The syntax tests a two-parameter logistic item response model of items from the Group Membership Evaluation subscale of the Multi-Dimensional Model of Māori Identity and Cultural Engagement. The model is demonstrated using data from Sibley and Houkamau (in press).

Sibley, C. G., & Houkamau, C. A. (in press). The multi-dimensional model of Māori identity: Item Response Theory analysis of scale properties. Cultural Diversity and Ethnic Minority Psychology.

Bayesian Mediation

This file contains Mplus syntax and data demonstrating how to conduct a test of mediation (or indirect effect) using Bayesian estimation with diffuse priors. This method recognizes that the confidence interval of the indirect effect may be asymmetric. Alternative syntax using a bias corrected bootstrap approach is also provided. The model is demonstrated using a re-analysis of data from Manuela and Sibley (in press).

Manuela, S., & Sibley, C. G. (in press). Why do Pacific people with multiple ethnic affiliations have poorer subjective wellbeing? Negative ingroup affect mediates the identity tension effect. Social Indicators Research. 

Latent Growth Curve Analysis

This file contains Mplus syntax and data demonstrating how to conduct a Latent Growth Model with another variable predicting the intercept and slope (or rate of change). This syntax further demonstrates how to estimate the growth curve at conditional values of a predictor variable. The model is demonstrated using data on regional levels of economic deprivation from the last 4 consecutive New Zealand censuses (1991-2006).

Bayesian Three-way Regression Interaction

This file contains syntax and data demonstrating how to conduct a three-way moderated linear regression interaction with Bayesian estimation in Mplus. The syntax calculates simple slopes and credibility intervals at conditional values of the two moderating variables. Simple slope difference tests, that is, tests of the difference between each pair of simple slopes are also estimated. Points to plot and associated credibility intervals for the three-way regression interaction are also provided. This syntax can be easily adapted to solve a three-way regression interaction between any given combination of categorical (dummy coded) and continuous predictor and moderator variables. The model is demonstrated using a continuous predictor and two continuous moderators.

The Multidimensional Model of Māori Identity and Cultural Engagement

This file provides a copy of the questionnaire, SPSS scoring template and supporting information for the Multidimensional Model of Māori Identity and Cultural Engagement developed by Houkamau and Sibley (2010).

See further details on the official Maori identity survey website

Houkamau, C. A., & Sibley, C. G. (2010). The Multi-Dimensional Model of Māori Identity and Cultural Engagement. New Zealand Journal of Psychology, 39, 8-28.

A Social Representations Primer: Latent Profile Analysis Syntax and Sample Data

This file provides supporting information for Liu and Sibley's (in press) Social Representations Primer using Latent Profile Analysis. The file contains Mplus syntax and sample data demonstrating how to conduct a Latent Profile Analysis of Likert scale data.

Liu, J. H., & Sibley, C. G. (in press). From ordinal representations to representational profiles: A primer for describing and modelling social representations of history. Papers on Social Representations.