The effect of higher order latent spaces on the robustness of unidimensional nonlinear item response models

• Author / Creator

  Beaulne, Albert Leo.

• Abstract
  (description taken from the article)
  Latent Trait or Item Response Theory (IRT) relies heavily on a number of strong assumptions (Lord, 1980; Lord & Novick, 1968). Unidimensionality is considered to be the most essential of these assumptions (Hambleton, Swaminathan, Cook, Eignor and Gifford 1978). Several procedures now exist which estimate the parameters contained in the unidimensional IRT (UIRT) model. One which has received extensive use is the joint maximum likelihood procedure employed in the parameter estimation program Logist (Wingersky, Barton, & Lord, 1982).
  The current study assessed the effects on the estimation of UIRT parameters when data sets violate the assumption of unidimensionality by exhibiting varying degrees of multidimensionality and correlations among the dimensions. The effects were assessed by generating data sets having two or three dimensions and correlations among the dimensions of 0.0,0.3,0.6, 0.95, and 0.99. Thus, ten data sets were generated, each representing a different combination of dimensionality and correlation among the dimensions.
  Procedures for generating the data are described. The data were generated using Fortran 77 and IMSL subroutines. The suitability of the compensatory (CMIRT) and noncompensatory (NMIRT) multidimensional item response models used for generating the data are also noted. The problems encountered in generating the data and the techniques used to overcome those problems are described. Methods to ensure that the data sets did indeed contain the intended characteristics were of special interest.
  The computer program Logist was employed to estimate the person and item parameters for the pseudo three parameter unidimensional IRT model (guessing parameter held constant at 0.2). The estimated parameters for each data set were compared to the parameters which were used in generating the data sets. The degree of congruity between the estimated parameters produced by Logist and the parameters inherent in the data sets was tested by examining the correlation between the IRT parameters, their means, and their sums. Mean square differences were also examined to determine the size o f the congruence when dimensionality and correlation were varied.
  Increasing dimensionality had a negative impact on the congruence between the estimated parameters and the generated parameters. Conversely, increases in the correlation between the dimensions to some extent countered the negative effects of increased dimensionality.
  Replication of Ansley and Forsythe's 1985 study, with respect to a two dimensional data structure, was completed and is presented as a part of the current study.

• Subjects / Keywords

  • Item response theory
  • Examinations--Evaluation--Data processing

• Graduation date

  1990

• Type of Item

  Thesis

• Degree

  Master of Education

• DOI

  https://doi.org/10.7939/R3639KB15

• License

  This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.