A Note on the Eigensystem of the Covariance Matrix of Dichotomous Guttman Items
نویسندگان
چکیده
We consider the covariance matrix for dichotomous Guttman items under a set of uniformity conditions, and obtain closed-form expressions for the eigenvalues and eigenvectors of the matrix. In particular, we describe the eigenvalues and eigenvectors of the matrix in terms of trigonometric functions of the number of items. Our results parallel those of Zwick (1987) for the correlation matrix under the same uniformity conditions. We provide an explanation for certain properties of principal components under Guttman scalability which have been first reported by Guttman (1950).
منابع مشابه
Implicational Scaling of Reading Comprehension Construct: Is it Deterministic or Probabilistic?
In English as a Second Language Teaching and Testing situations, it is common to infer about learners’ reading ability based on his or her total score on a reading test. This assumes the unidimensional and reproducible nature of reading items. However, few researches have been conducted to probe the issue through psychometric analyses. In the present study, the IELTS exemplar module C (1994) wa...
متن کاملSimultaneous Monitoring of Multivariate Process Mean and Variability in the Presence of Measurement Error with Linearly Increasing Variance under Additive Covariate Model (RESEARCH NOTE)
In recent years, some researches have been done on simultaneous monitoring of multivariate process mean vector and covariance matrix. However, the effect of measurement error, which exists in many practical applications, on the performance of these control charts is not well studied. In this paper, the effect of measurement error with linearly increasing variance on the performance of ELR contr...
متن کاملMOOCs Meet Measurement Theory: A Topic-Modelling Approach
This paper adapts topic models to the psychometric testing of MOOC students based on their online forum postings. Measurement theory from education and psychology provides statistical models for quantifying a person’s attainment of intangible attributes such as attitudes, abilities or intelligence. Such models infer latent skill levels by relating them to individuals’ observed responses on a se...
متن کاملThe effects of the violation of local independence assumption on the person measures under the Rasch model
Local independence of test items is an assumption in all Item Response Theory (IRT) models. That is, the items in a test should not be related to each other. Sharing a common passage, which is prevalent in reading comprehension tests, cloze tests and C-Tests, can be a potential source of local item dependence (LID). It is argued in the literature that LID results in biased parameter estimation ...
متن کاملA Comparative Study of Exact Algorithms for the Two Dimensional Strip Packing Problem
In this paper we consider a two dimensional strip packing problem. The problem consists of packing a set of rectangular items in one strip of width W and infinite height. They must be packed without overlapping, parallel to the edge of the strip and we assume that the items are oriented, i.e. they cannot be rotated. To solve this problem, we use three exact methods: a branch and bound method, a...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Frontiers in psychology
دوره 6 شماره
صفحات -
تاریخ انتشار 2015