Estimating of latent trait from Likert -type data: A comparison of four procedures
Likert-type rating scales are an important means of attitude assessment in the social sciences. A complex array of features is involved when constructing these scales, including scale length, response categorization, scoring method, and sample size. Using simulated data that are either linear or non-linear in nature, this study examines the effect that four variables has on the estimation of the latent trait: (1) the number of items comprising the scale (6 or 12); (2) the number of categories that define the Likert-type scale (2 through 9); (3) the size of the sample (200, 500, or 1,000); (4) the scoring method (Summated Rating Scales, Maximum-likelihood Factor Analysis, Graded Response Model, Generalized Partial Credit Model). The distribution of the true latent trait was also varied to be either normal or positively skewed. Each condition was replicated 500 times. Parameter recovery was investigated by examining the reliability of the estimated latent trait compared to the true latent trait as well as the mean square error between the estimated latent trait and the true latent trait. The results of this study are of practical consequence to researchers who are either designing surveys with Likert-type items or analyzing Likert-scaled measures. The findings suggest that the number of categories used to define a Likert-type scale has a definite impact on how precisely the latent trait is estimated. In general, the latent trait is most accurately and reliably estimated when a 12-item, 9-category scale was used; however, there appears to be a point of diminishing returns when between 5 to 7 categories are used to define the response scale. The results further suggest that if the data are adequate, there is little difference in accuracy or reliability between the various scoring procedures used. Also, the scoring methods appear to be robust to violations of normality. Finally, sample size has little effect on the estimation of the latent trait.