One of the most important decisions that can be made in the use of factor analysis is the number of factors to retain. Numerous studies have consistently shown that Horn's parallel analysis is the most nearly accurate methodology for determining the number of factors to retain in an exploratory factor analysis. Although Horn's procedure is relatively accurate, it still tends to error in the direction of indicating the retention of one or two more factors than is actually warranted or of retaining poorly defined factors. A modification of Horn's parallel analysis based on Monte Carlo simulation of the null distributions of the eigenvalues generated from a population correlation identity matrix is introduced. This modification allows identification of any desired upper 1 - a percentile, such as the 95th percentile of this set of distributions. The 1 - ax percentile then can be used to determine whether an eigenvalue is larger than what could be expected by chance. Horn based his original procedure on the average eigenvalues derived from this set of distributions. The modified procedure reduces the tendency of the parallel analysis methodology to overextract. An example is provided that demonstrates this capability. A demonstration is also given that indicates that the parallel analysis procedure and its modification are insensitive to the distributional characteristics of the data used to generate the eigenvalue distributions.
The concepts of expert systems and decision support systems have received considerable attention recently. While systems have been proposed for various problem areas in business, difficulties still exist in the knowledge acquisition phase of development. This paper presents a recursive partitioning analysis (MA) approach to knowledge acquisition. The RPA production system approach was applied to data sets representing the mortgage, commercial, and consumer lending problems. Comparison of the classification rates across these problems to the results of a generalized inductive inference production system (Quinlan's ID3 algorithm) and across the mortgage and commercial lending problems to traditional statistical modeling approaches indicated that the RPA approach provided superior results while using fewer variables.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.