Concept: Factor Analysis

Introduction

This concept explains what factor analysis is, how this statistical technique of can be used in research, and how MCHP has measured the adequacy of the factor analysis. Information for this concept comes directly from the deliverable Composite Measures/Indices of Health and Health System Performance by Metge et al. (2009).

This concept also includes a section identifying where factor analysis has been used in MCHP research, and provides links to this additional information. This includes specific concepts where factor analysis is described in the methodology (e.g.: development of the composite health indices) and to MCHP deliverables that describe how factor analysis was used in the research.

What is Factor Analysis?

A composite index is a mathematical combination of several indicators in order to form a single number. This index can be used to describe an entire set of indicators and allow for global differences between places and across time to be assessed. The indices can be developed using a procedure known as factor analysis.

Factor analysis is a statistical procedure that identifies the common variance amongst a set of observed variables (i.e., indicators), and creates a factor (i.e., index) comprised of that common variance. The factor scores are calculated with a linear equation that incorporates a weighted contribution of each of the variables that are included in the analysis. The contribution (i.e., weight) of each variable is relative to the amount of variance in common with the other variables.

The basic premise of factor analysis is fairly straightforward; indicators (i.e., rates) that tend to vary together are grouped together. That is, when comparing the different rates that make up an index (e.g., Pap and mammography rates in the Prevention and Screening Index), one might find relationships (i.e., correlations) between the RHAs, which would suggest the two rates have something in common. The methods employed for creating a composite index look for this common variance among the indicators.

The theory behind factor analysis is that two (or more) indicators are correlated because of an underlying "factor" causing the performance on the two indicators to be related. The factor cannot be measured directly, but is only seen in the indicators (i.e., rates) that can be measured. If the results of the analysis indicate that there is one underlying factor, then a single factor score could be used to describe the entire set of indicators. Because this factor influences all rates, a region's rate for one indicator can tell you something about their rates on the other related indicators.

The output of a factor analysis provides a mathematical combination of the indicators that is similar to a regression formula, where a certain portion of each indicator contributes to an overall factor score. The degree to which each indicator contributes to the composite index depends on the degree of commonality with the entire set of indicators. The contribution of an indicator to a factor is known as a factor loading, and can range from -1 to +1. The larger the absolute size, the greater the variance of the indicator explained by the factor.

Factor loadings indicate whether or not an index can be reasonably or validly constructed. In MCHP research, the rule of thumb used to decide if an indicator is associated with (or part of) the factor is a factor loading with an absolute value of at least 0.40. In some instances, the indicators included in a factor analysis may form two or more distinct dimensions. In these cases, the factor loadings would indicate the factor, or composite index, to which an indicator belongs.

Testing the Adequacy of the Factor Analysis

In Metge et al. (2009), a three-step process was employed to construct and test the adequacy of the composite indices developed through factor analysis. The initial step was to calculate the age- and sex-adjusted region rates for the indicators. The second step was to conduct an initial factor analysis of the indicators for the first time period. If a single factor composed of the majority of the indicators emerged or if multiple factors encompassing the majority of the indicators emerged, then a third step - a second confirmatory factor analysis - was conducted using the data from the second time point. For this analysis, the loadings for the indicators were constrained to be equal to the loadings from the first analysis. This constraint forces the calculation of the factor scores to be identical, and allows for comparisons over time. It also enables a test of whether the factor structure itself remains stable over time; if the results of the second factor analysis are different, this means that the structure does not hold together.

Factor Analysis Applied in MCHP Research

Factor analysis methods have been used in several indices developed at MCHP. For more information, please read the following concepts:


• Composite Health Indices;
  
• Social and Material Deprivation Indices;
  
• Socioeconomic Factor Index (SEFI) - Version 2 (SEFI-2).

Factor analysis has been described in several MCHP research publications. For more detailed information on factor analysis, please read:


• Appendix 5 - Statistical Methods Used to Create the Composite Indices in the deliverable Composite Measures/Indices of Health and Health System Performance by Metge et al. (2009).
  
• Appendix 3 - Social Complexity Index in the deliverable A Comparison of Models of Primary Care Delivery in Winnipeg by Katz et al. (2016).