Unidimensional Unfolding Model Research Articles

Constructing a Scale of Attitudes toward School Science Using the General Graded Unfolding Model

The present study aimed at constructing an attitude scale toward school science using the generalized graded unfolding model (GGUM). A 47-item scale (24 positive, 23 negative) with 4-point response format was used to measure attitudes toward science among 9th (n=424) and 10th (n=420) grade students in 38 sections distributed randomly over 22 schools in Irbid district. Respondents selected one of four options to represent their level of agreement with each item. The findings support the hypothesis that the data form a single unidimensional unfolding model. Furthermore, the findings showed that the GGUM didn’t fit the data of 7 items, leaving the final scale with 40 items, where accurate estimates of these item parameters were derived and the GGUM was appropriate. Cronbach's alpha for the internal consistency, and the test retest reliability coefficients of the final scale were 0.932 and 0.875, respectively.

Constructing a Scale of Attitudes toward School Science Using the General Graded Unfolding Model

The present study aimed at constructing an attitude scale toward school science using the generalized graded unfolding model (GGUM). A 47-item scale (24 positive, 23 negative) with 4-point response format was used to measure attitudes toward science among 9th (n=424) and 10th (n=420) grade students in 38 sections distributed randomly over 22 schools in Irbid district. Respondents selected one of four options to represent their level of agreement with each item. The findings support the hypothesis that the data form a single unidimensional unfolding model. Furthermore, the findings showed that the GGUM didn’t fit the data of 7 items, leaving the final scale with 40 items, where accurate estimates of these item parameters were derived and the GGUM was appropriate. Cronbach's alpha for the internal consistency, and the test retest reliability coefficients of the final scale were 0.932 and 0.875, respectively.

Constructing a Scale of Attitudes toward School Science Using the General Graded Unfolding Model

The present study aimed at constructing an attitude scale toward school science using the generalized graded unfolding model (GGUM). A 47-item scale (24 positive, 23 negative) with 4-point response format was used to measure attitudes toward science among 9 th (n=424) and 10 th (n=420) grade students in 38 sections distributed randomly over 22 schools in Irbid district. Respondents selected one of four options to represent their level of agreement with each item. The findings support the hypothesis that the data form a single unidimensional unfolding model. Furthermore, the findings showed that the GGUM didn’t fit the data of 7 items, leaving the final scale with 40 items, where accurate estimates of these item parameters were derived and the GGUM was appropriate. Cronbach's alpha for the internal consistency, and the test retest reliability coefficients of the final scale were 0.932 and 0.875, respectively.

Discrete Choice Models for Ordinal Response Variables: A Generalization of the Stereotype Model

In this paper I present a class of discrete choice models for ordinal response variables based on a generalization of the stereotype model. The stereotype model can be derived and generalized as a random utility model for ordered alternatives. Random utility models can be specified to account for heteroscedastic and correlated utilities. In the case of the generalized stereotype model this includes category-specific random effects due to individual differences in response style. But unlike standard random utility models the generalized stereotype model is better suited for ordinal response variables and can be interpreted as a kind of unidimensional unfolding model. This paper discusses the specification, interpretation, identification, and estimation of generalized stereotype models. Two applications are provided for illustration.

Arrangements and Ranking Patterns

In the unidimensional unfolding model, given m objects in general position on the real line, there arise 1 + m(m − 1)/2 rankings. The set of rankings is called the ranking pattern of the m given objects. Change of the position of these m objects results in change of the ranking pattern. In this paper we use arrangement theory to determine the number of ranking patterns theoretically for all m and numerically for m ≤ 8. We also consider the probability of the occurrence of each ranking pattern when the objects are randomly chosen.

The Extra-Factor Phenomenon Revisited: Unidimensional Unfolding as Quadratic Factor Analysis

The application of linear factor analysis to a set of unfoldable (unidimensional) items produces a two-dimensional solution, called the extra-factor phenomenon, which potentially results in incorrect conclusions about the nature of a set of items (van Schuur& Kiers, 1994). Many explanations have been offered for this phenomenon. This study attempted further clarification within the general theory of factor analysis. Specifically, it was demonstrated that the extra-factor phenomenon arises because: (1) the metric unidimensional unfolding model is equivalent to the unidimensional quadratic factor model; and (2) at the level of covariance structure, the unidimensional quadratic factor model is not distinguishable from the two-dimensional linear factor model (McDonald, 1967). Also discussed are a number of theoretical linkages and bases of distinguishability that exist between unidimensional unfolding and linear factor analysis.

Why Factor Analysis Often is the Incorrect Model for Analyzing Bipolar Concepts, and What Model to Use Instead

Factor analysis of data that conform to the unfolding model often results in an extra factor. This artificial extra factor is particularly important when data that conform to a bipolar unidimensional unfolding scale are factor analyzed. One bipolar dimension is expected, but two factors are found and often are interpreted as two unrelated dimensions. Although this extra factor phenomenon was pointed out in the early 1960s, it still is not widely recognized. The extra factor phenomenon in the unidimensional case is reviewed here. A numerical illustration is provided, and a number of diagnostics that can be used to determine whether data conform to the unidimensional unfolding model better than to the factor model are discussed. These diagnostics then are applied to an empirical example.

Nonparametric Unidimensional Unfolding for Multicategory Data

This article describes a nonparametric unidimensional unfolding model for dichotomous data (van Schuur 1984) and shows how it can be extended to multicategory data such as Likert-type rating data. This extension is analogous to Molenaar's (1982) application of Mokken's (1970) nonparametric unidimensional cumulative scaling model. The model is illustrated with an analysis of five-point preference ratings given in 1980 to five political presidential candidates by Democratic and Republican party activists in Missouri.

Constraint in European party activists’ sympathy scores for interest groups

Abstract. This paper presents an analysis, country by country, of sympathy scores given by European party activists from 58 political parties in 11 countries of the European Community to more than 100 different national interest groups. In all countries but one, the left‐right dimension is the predominant criterion for interpreting the sympathy scores given. In Belgium, the exception, a regional (Flemish‐Walloon) cleavage line is most important. The analyses were performed with a new adapted version of the unidimensional Coombsian unfolding model. Bad fit to the unidimensional model is not remedied by postulating additional common dimensions, but by identifying and removing stimuli (interest groups) that do not conform to the unidimensional unfolding model. The nonrepresentability of these stimuli can be attributed to lack of agreement among activists about the location of these stimuli on the left‐right dimension. More specifically, certain relatively popular stimuli are perceived by most respondents as close to their own location on the left‐right scale, and, conversely, certain relatively unpopular stimuli are perceived by most respondents as distant from their own location.

On a metric, unidimensional unfolding model for attitudinal and developmental data

If stimulus responses are linearly related to squared distances between stimulus scale values and person scores along a latent continuum, (a) the stimulus × stimulus correlation matrix will display a simplex-like pattern, (b) the signs of first-order partial correlations can be specified in an empirically testable manner, and (c) the variables will have a semicircular, two-factor structure. Along the semicircle, variables will be ordered by their positions on the latent dimension. The above results suggest procedures for examining the appropriateness of the model and procedures for ordering the stimuli. Applications to developmental and attitudinal data are discussed.

Laterality effects in the method of triads

The method of triads for psychophysical judgments was analyzed in terms of the unidimensional unfolding model of Coombs (1964). This model predicts laterality effects on the stochastic transitivity of triples for which existing models have been unable to account. An experiment was conducted in which triadic judgments were made on circles differing in area. The results confirmed the stochastic transitivity predictions, but a quantitative formulation of the model proved unsatisfactory.