1,721,019 research outputs found
CATANOVA for two-way cross classified categorical data
No full textIn this article we develop an extension of categorical analysis of variance for one response and two factors, based on a partitioning of a measure of predictability for three-way contingency tables, known as Gray and Williams’s index. At the first instance moment the decomposition of this multiple measure of association in partial association measures is shown. Finally, for ordinal-scale variables, we propose an extension of this decomposition using a particular set of orthogonal polynomials
Correspondence Analysis for doubly cumulative contingency table.
No full textA suitable measure of association for two ordered variables is the doubly cumulative chi-squared statistic (Hirotsu, 1994). This statistic is obtained by considering the cumulative sum of cell frequencies across the variables. In this paper we explore the development of correspondence analysis which takes into account the presence of two ordered variables by partitioning the doubly cumulative chi-squared statistic
Evaluation of Passenger Satisfaction using three-way contingence table with ordinal variables
No full textThe aim of this paper is to evaluate the Passenger Satisfaction (PS) starting from quality factors (punctuality, safeness, staff aspect and conduct, modal integration, etc.). Carrying out two or more ways contingence tables, crossing the overall satisfaction (PS) and the quality factors we can study the dependency between the overall satisfaction and quality factors. In particular, the partition of Marcotorchino index for a three-way contingency table with one, two and three ordered categorical variables (Beh E.J., Simonetti B., D'Ambra L., 2007) will allow us to analyze the asymmetric and ordinal structure of the data and to pick up the nonlinear relationship within the data. To complement the survey Ordered Non-Symmetric Correspondence Analysis (ONSCA) will be carried out
Estimating multinomial logit model with multicollinear data
No full textThe multinomial logit model is used to study the dependence relationship between a categorical response variable with more than two categories and a set of explicative variables. In presence of multicollinearity, the estimation of the multinomial logit model parameters becomes inaccurate. To solve this problem we develop an extension of principal component logistic regression. Finally a simulation study illustrates the advantages of the method
Uno studio sui livelli di competenza in matematica: analisi delle differenze tra gli studenti italiani e campani
No full textProgramme for International Assessment (PISA) collected information on 15-yearold
students in participating countries in 2000, 2003 and 2006. Performances differed widely
between countries, and also between local areas and between schools in Italy. This study compares
results for Campania and Italy using the Partial Credit Model. The PISA test shows good
test-retest property, items show good fit to PCM and there are some significant differences
between results for Campania and Italy
THE RASCH MODEL FOR EVALUATING ITALIAN STUDENT PERFORMANCE
Full text linkIn 1997 the Organisation for Economic Co-operation and Development (OECD) launched the OECD Programme for International Student Assessment (PISA) for collecting information about 15-year-old students in participating countries.Our study analyse the PISA 2006 cognitive test for evaluating the Italian student performance in mathematics, reading and science comparing the results of different local governments. For this purpose the most proper statistic methodology is Item Response Theory - IRT that collects several models, the simplest is Rasch Model – MR (1960). As the items used in the analysis are both dichotomous that polytomous, we apply Partial Credit Model (PCM)
Singly and doubly ordered cumulative correspondence analysis.
No full textThe classical approach to correspondence analysis (CA) is designed to allow its user to a graphically summarize
the association between two or more categorical variables that form a contingency table. Despite its
popularity and utility, the classical approach does not take in consideration the structure of ordered variables.
One way to performing CA when the variables have an ordered structure is to consider the Taguchi’s statistic
(Taguchi, 1974). Beh, D’Ambra, Simonetti (2010) demonstrated the applicability of considering this statistic
which takes into account the ordered structure by considering the cumulative sum of cell frequencies across
the variable. Thus, the statistic is defined by summing the chi-squared statistic for each I × 2 contingency
table obtained by aggregating the column categories 1 to j and aggregating the column categories (j+1)
to J. For this reason, the Taguchi’s statistic is also referred to as cumulative chi-squared statistic (Nair; 1987).
Cuadras (2002) proposes an approach to correspondence analysis based on double cumulative frequencies.
However, it does not decompose any known index. In this paper we explore a generalization of Taguchi’s
statistic which takes into account the presence of two ordinal categorical variables by considering their cumulative
sum of cell frequencies. This generalization is analogous to the doubly cumulative chi-squared statistic
which is constructed by summing the chi-squared statistic for each 2×2 sub-table formed by pooling adjacent
rows and columns of the original contingency table; see Hirotsu (1986).
We illustrate this approach to CA using a partition of the statistic proposed by Hirotsu. Its application
presents some interesting properties and allows the analyst to represent the variations of row and column
categories rather than the categories on the space generated by cumulative frequencies
Three-Mode Factor Analysis for Contingency Tables with Ordinal Variables
No full textThe Tucker3 model is truly a three-way model since it explicitly establishes a relationship between factors in the three modes spanned by the data array. In this paper, the authors propose a variant of Tucker3 model using orthogonal polynomials for contingency tables with ordinal variables that guarantees that the ordinal structure of these variables is maintained
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