An ordinal approach to the measurement of inequality in asset ownership: methodology and an application to Mexican data.

Asset indices based on durable goods ownership and housing characteristics are widely used to proxy wealth when income or expenditure data are not available. In this paper, we propose an ordinal approach to using data on assets when estimating the wealth of a household (or individual). Using Correspondence Analysis, we derive a ranking of the correlations between the various assets and the first factor, a latent variable assumed to represent the standard of living. We then use this correlation ranking of the assets to derive indices of ordinal inequality that have been recently proposed in the literature. We also use the information on the proportion of individuals holding each type of assets to derive again ordinal measures of inequality in asset ownership. Our empirical analysis, based on data covering the various states of Mexico in 2000 and 2010, shows that the correlation between measures of ordinal inequality in asset ownership derived from correspondence analysis and traditional Gini indices of household income is high, and even higher than that between these Gini indices and ordinal inequality indices based on the percentage ownership of the different assets.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

How Good are Our Measures? Investigating the Appropriate Use of Factor Analysis for Survey Instruments

Background: Evaluation work frequently utilizes factor analysis to establish the dimensionality, reliability, and stability of surveys. However, survey data is typically ordinal, violating the assumptions of most statistical methods, and thus is often factor-analyzed inappropriately. Purpose: This study illustrates the salient analytical decisions for factor-analyzing ordinal survey data appropriately and demonstrates the repercussions of inappropriate analyses. Setting: The data used for this study are drawn from an evaluation of the efficacy of a drama-based approach to teaching Shakespeare in elementary and middle school.  Intervention: Not applicable. Research Design: Survey research. Data Collection and Analysis: Four factor analytic methods were compared: a traditional exploratory factor analysis (EFA), a full-information EFA, and two EFAs within the confirmatory factor analysis framework (E/CFA) conducted according to the Jöreskog method and the Gugiu method. Findings: Methods appropriate for ordinal data produce better models, the E/CFAs outperform the EFAs, and the Gugiu method demonstrates greater model interpretability and stability than the Jöreskog method. These results suggest that the Gugiu E/CFA may be the preferable factor analytic method for use with ordinal data. Practical applications of these findings are discussed. Keywords: factor analysis; ordinal data; E/CFA; survey research

Ordinal Versions of Coefficients Alpha and Theta for Likert Rating Scales

Two new reliability indices, ordinal coefficient alpha and ordinal coefficient theta, are introduced. A simulation study was conducted in order to compare the new ordinal reliability estimates to each other and to coefficient alpha with Likert data. Results indicate that ordinal coefficients alpha and theta are consistently suitable estimates of the theoretical reliability, regardless of the magnitude of the theoretical reliability, the number of scale points, and the skewness of the scale point distributions. In contrast, coefficient alpha is in general a negatively biased estimate of reliability. The use of ordinal coefficients alpha and theta as alternatives to coefficient alpha when estimating the reliability based on Likert response items are recommended. The choice between the two ordinal coefficients depends on whether one is assuming a factor analysis model (ordinal coefficient alpha) or a principal components analysis model (ordinal coefficient theta)

An Ordinal factor analysis of requirements and challenges of information and communication technology system to train private agricultural insurance brokers in Iran

This study was conducted to identify challenges and requirements of an information and communication technology (ICT) system to train brokers. Using the ordinal factor analysis, the challenges and requirements have been classified into six factors (Human, Organisational, Technical,Social, Financial, and Legal) and four factors (instructional,technical, organisational, and cultural) respectively. Finally a conceptual framework is presented for the challenges and requirements of the ICT training system

Factor Analysis Of Ordinal Data Based On Weighted Ranking And Its Application To Reduce Perception Variables To Math Lessons Of Senior High School Student

The objectives of research are to reduce dimension of ordinal data using factor analysis based on weighted ranking correlation. In general, the correlation is used Spearman ranking correlation. This papers will discuss about application of both methods on the case of simplify of student’s perception variables on math lessons. The samples of this research are 791 students which consist of questionnaire. Factor analysis based on the weighted ranking correlation have given the results the number of factors and variables domination on factors more good than Spearman ranking correlation. The factors that influence perception of senior high school students towards Math lesson are an internal motivation of students, negative assessment of the Math lesson, teaching methods of Math teacher, habit of learning of students in Math and the support of parents, and knowledge of impact and benefits of Math. Key Words: factor analysis, weighted ranking, perception, mat

The Behavior of Rotation Criteria in Exploratory Factor Analysis with Ordinal Data: The Role of Number of Indicators and Number of Factors

The Behavior of Rotation Criteria in Exploratory Factor Analysis with Ordinal Data: The Role of Number of Indicators and Number of Factor

Clustering South African households based on their asset status using latent variable models

The Agincourt Health and Demographic Surveillance System has since 2001 conducted a biannual household asset survey in order to quantify household socio-economic status (SES) in a rural population living in northeast South Africa. The survey contains binary, ordinal and nominal items. In the absence of income or expenditure data, the SES landscape in the study population is explored and described by clustering the households into homogeneous groups based on their asset status. A model-based approach to clustering the Agincourt households, based on latent variable models, is proposed. In the case of modeling binary or ordinal items, item response theory models are employed. For nominal survey items, a factor analysis model, similar in nature to a multinomial probit model, is used. Both model types have an underlying latent variable structure - this similarity is exploited and the models are combined to produce a hybrid model capable of handling mixed data types. Further, a mixture of the hybrid models is considered to provide clustering capabilities within the context of mixed binary, ordinal and nominal response data. The proposed model is termed a mixture of factor analyzers for mixed data (MFA-MD). The MFA-MD model is applied to the survey data to cluster the Agincourt households into homogeneous groups. The model is estimated within the Bayesian paradigm, using a Markov chain Monte Carlo algorithm. Intuitive groupings result, providing insight to the different socio-economic strata within the Agincourt region.Comment: Published in at http://dx.doi.org/10.1214/14-AOAS726 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org