Abstract
Composite indicators of latent variables can be constructed by NonLinear Principal Components Analysis when data are collected by multiple-item scales. The aim of this paper is to establish the stability of the contribution made by each item to the composite indicator, by means of a resampling-based procedure able to take account of the hierarchical structure that often exists in the data, that is when individuals are nested in groups. The procedure modifies the standard nonparametric bootstrap technique and was applied to real data on job satisfaction from the most extensive survey on Italian social cooperatives.
Keywords
- Resampling-based Procedure
- Italian Social Cooperatives
- Nonlinear Principal Component Analysis
- Multiple-item Scales
- Composite Indicator
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Notes
- 1.
In the literature (Michailidis and de Leeuw 2000), NL-PCA was also extended to hierarchical data structures to examine how variables are related across groups and how groups vary.
- 2.
All the computations were performed by R 2.13.1.
- 3.
Missing values were imputed according to Carpita and Manisera (2011). From the entire sample of the ICSI 2007 survey, the cooperatives with less than 5 workers were removed. The data used in this study result from a preliminary Rasch analysis (Carpita and Golia 2011), which identified the 11 selected job satisfaction items as related to a “global” job satisfaction latent trait, and suggested merging response categories to obtain a 5-point response scale for each item, ranging from 1 = “very dissatisfied” to 5 = “very satisfied”, with mid-point 3 = “neither dissatisfied nor satisfied”.
- 4.
Other papers investigated the drivers of job satisfaction by means of regression models with job satisfaction items as independent variables and the overall job satisfaction as a dependent variable (see, for example, Carpita and Zuccolotto 2007, Vezzoli and Zuccolotto 2010). Unlike the current paper, their aim was to identify which facets of job satisfaction drive, from a psychological point of view, the individual perception of the overall job satisfaction, since the latter is measured by a single item in the questionnaire.
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Manisera, M. (2013). Assessing Stability in NonLinear PCA with Hierarchical Data. In: Giudici, P., Ingrassia, S., Vichi, M. (eds) Statistical Models for Data Analysis. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Heidelberg. https://doi.org/10.1007/978-3-319-00032-9_25
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DOI: https://doi.org/10.1007/978-3-319-00032-9_25
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