Project 3 – CFA of Locomotion and Assessment scales

The purpose of this project is examine the dimensionality of the locomotion and assessment scales from Kruglanski et al., 2000 using confirmatory factor analysis. Again, the dataset we will be using for many of the projects is in a SPSS file. This data was collected on 240 undergraduates and consists of numerous personality variables thought to influence performance on a complex radar tracking task. The items locomotion and assessment measures (scales?) are found in the included dataset (labeled loco1-loco12; assess1-assess12). The responses were collected using a 5 point “strongly disagree” to “strongly agree” scale (5=strongly agree). The midpoint of this scale (3) was labeled as “neither agree nor disagree.”

  1. Examine the article and determine the expected dimensionality of the locomotion and assessment scales. Next examine the items and think about the dimensionality that YOU might expect from these items. Do you see anything in the items that might lead to fewer or more dimensions than you would expect based on the article?
  1. Using AMOS (or any other CFA software) construct the measurement model for the locomotion and assessment items allowing the latent variables to be correlated. When constructing this model use a loading constraint (1.0) on an indicator to scale the latent variables. Compute the number of available degrees of freedom (t-rule) and then determine the number of parameters estimated in the measurement model. Is this value less than the available degrees of freedom? Using the identification rules, evaluate whether the model is identified or not.
  1. Now run the model and evaluate the fit of the resulting model using the Chi-Square goodness of fit test and the fit indices. Be sure to evaluate whether the model converged to a solution? How do your results from this model compare to those reported in the manuscript?
  1. Next, run the same model but constrain the latent variances to 1.0 (standardized latent variables) instead of constraining a loading (lambda). Run the model and evaluate the fit of the model. How do the results of this model compare to those from the model run above?
  1. Compare the fit of the models (using the Chi-Square difference test) where one model estimates the latent correlation between assessment and locomotion and the other model constrains them to be independent. Are these models nested? What should be the difference in degrees of freedom between these models? Does the constraint significantly reduce the fit of the model?
  1. Using the orthogonal model from 5, compute the reliability of each scale. Then compare this reliability to Cronbach alphas estimated for each scale. What might be responsible for the obtained differences in the estimate of reliability?
  1. If the correlated latent variable model does not fit well, can you improve its fit to the data while maintaining simple structure? Examine the factor loadings and see whether dropping some items might improve model fit. Another way to do the same thing is to average similar items to form parcels of items. If there are conceptually similar items, they can be averaged and then the model can be refit to the smaller set of items. You can use modification indices to suggest possible model modifications in this process if you like.
  1. Based on these analyses, what is your impression of the scales? Are the scales reliable and valid? Could they be improved? If so, how would you go about improving the scales?