Common factors

This phrase has two meanings in our field: a psychological/therapy one, and a statistical/psychometric one.
The first refers to the features of psychological therapies that are likely to be common to different theoretical approaches and methodologies and are thought to predict good outcomes. For example, empathic listening; therapeutic alliance; collaboration; common goals.
The second is part of the methodology of Factor analysis: this is typically used to look at the correlation matrix of the scores from individuals on items in a measure. Factor analysis uses the fact that you can always consider the scores on k items to be made up of contributions from common factors and variance (unreliability, noise) that is specific to the item. (This latter variance goes by “specific factors” and “error factors”.

Details #

We don’t think the first meaning needs more explanation here but the second probably does. Take the HADS (Hospital Anxiety and Depression Scales). This is a 14 item self-report questionnaire designed to measure anxiety and depression as distinct phenomena and specifically designed to be used with people who may have physical health problems (hence the “Hospital” in the name and the fact that it doesn’t cover all the phenomena generally considered to reflect anxiety and depression, omitting those likely to be cause by physical health problems).

As there are 14 items there are 21 correlations between the items. If the factor model fits perfectly to responses from a variety of individuals on the 14 items then these 21 correlations would fit a model in which the seven depression items share covariance (extent to which the scores vary together, related to correlation but reflecting that there may be more variance across scores on one item than another, correlation removes that) from a common factor of the varying extent to which the participants are “depressed” and the seven anxiety items similarly share covariance down to a common factor of “anxeity” and those two common factors, which would probably be correlated, would mop up all shared variance between items leaving only error variances (specific factors), one per item.

In most such studies of the HADS the fit to that model isn’t perfect but it’s pretty good.

Reference #

Zigmond, A. S., & Snaith, R. P. (1983). The Hospital Anxiety and Depression Scale. Acta Psychiatrica Scandinavica, 67(6), 361–370.

Try also … #

Factor analysis
Exploratory factor analysis
Principal component analysis
Confirmatory factor analysis

Chapters #

Chapters 3 and 4.

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