Browsing by Subject "Latent variables"
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Item Estimating the latent trait from Likert-type data : a comparison of factor analysis, item response theory, and multidimensional scaling(1991) Chan, Chihyu, 1959-; Koch, William R.Seven statistical procedures were compared with one another in terms of the ability to recover a unidimensional latent trait from Likert-type data. They are factor analysis based on either Pearson correlations (FA-PR) or polychoric correlations (FAPL), the graded response model in item response theory (IRT-GRM), internal unfolding (IMDU), external unfolding (EMDU), weighted unfolding (WMDU), and the common procedure of summing up successive integers assigned to response categories (SSI). Sample size, test length, and skewness of item response distributions were manipulated in this simulation study. Generally speaking, IRT-GRM performed the best and was most robust against skewness. FA-PR and FA-PL performed equally well across almost all conditions but were competitive with IRT-GRM only when item responses were normally distributed. SSI practice might be slightly worse than the two FA procedures when item responses were normally distributed, but it was better than them when item responses were highly skewed. WMDU performed as well as did SSI only when item responses were normally distributed or moderately skewed and sample size was large for MDS models (e.g., N=100). IMDU and EMDU were even worse than WMDU and appeared not appropriate for Likert-type dataItem Latent slice sampling(2022-05-06) Li, Yanxin; Walker, Stephen G., 1945-; Linero, Antonio; Viswanathan, Bindu; Guyot, Layla; Zhou, Mingyuan; Williamson, SineadThe thesis develops a new and generic Markov chain Monte Carlo sampling methodology, naming latent slice sampling, that originates from slice sampling and is capable of efficient sampling. More specifically, three angles are studied to cover different types of random variables: (i). We develop a latent slice sampler for discrete variables by designing a transition probability function that can perform direct sampling without knowing the exact form of target distributions. (ii). We manage to derive a latent slice sampler for continuous variables which has the potential to be a more efficient alternative to the Metropolis-Hasting algorithm, obviates the need for a proposal distribution, and has no accept/reject component. (iii). We further propose a novel algorithm based on latent slice sampling methodology which copes well with multi-modal problem, which can approach well-studied problems from a different angle and provide new perspectives. All the methods bring clear gains, which demonstrate the benefits of applying latent slice sampling to improve Markov chain simulation.