Problems with the factor analysis of items: Solutions based on item response theory and item parcelling

Abstract

The factor analysis of items often produces spurious results in the sense that unidimensional scales appear multidimensional. This may be ascribed to failure in meeting the assumptions of linearity and normality on which factor analysis is based. Item response theory is explicitly designed for the modelling of the non-linear relations between ordinal variables and provides a strong alternative to the factor analysis of items. Items may also be combined in parcels that are more likely to satisfy the assumptions of factor analysis than do the items. The use of the Rasch rating scale model and the factor analysis of parcels is illustrated with data obtained with the Locus of Control Inventory. The results of these analyses are compared with the results obtained through the factor analysis of items. It is shown that the Rasch rating scale model and the factoring of parcels produce superior results to the factor analysis of items. Recommendations for the analysis of scales are made. Opsomming Die faktorontleding van items lewer dikwels misleidende resultate op, veral in die opsig dat eendimensionele skale as meerdimensioneel voorkom. Hierdie resultate kan dikwels daaraan toegeskryf word dat daar nie aan die aannames van lineariteit en normaliteit waarop faktorontleding berus, voldoen word nie. Itemresponsteorie, wat eksplisiet vir die modellering van die nie-liniêre verbande tussen ordinale items ontwerp is, bied ’n aantreklike alternatief vir die faktorontleding van items. Items kan ook in pakkies gegroepeer word wat meer waarskynlik aan die aannames van faktorontleding voldoen as individuele items. Die gebruik van die Rasch beoordelingskaalmodel en die faktorontleding van pakkies word aan die hand van data wat met die Lokus van Beheervraelys verkry is, gedemonstreer. Die resultate van hierdie ontledings word vergelyk met die resultate wat deur ‘n faktorontleding van die individuele items verkry is. Die resultate dui daarop dat die Rasch ontleding en die faktorontleding van pakkies meer bevredigende resultate lewer as die faktorontleding van items. Aanbevelings vir die ontleding van skale word gemaak.