Factor analysis is another way of drawing out patterns and relationships in large sets of quantitative data (large could mean over 350 records, not necessarily the huge sets of data associated with big data).

To carry out factor analysis you need to identify which independent variables you are assuming are likely to influence a dependent variable. This creates the same kind of challenge as in all quantitative data analysis: how can these variables (or dimensions in factor analysis) be measured and to what degree do they influence the observed phenomenon?

The relationship of variable to phenomenon might of course be guessed at by practical experience of the context, or indeed by common sense and ‘intuition’. However in most cases it is backed up by considerable literature review looking closely at reported relationships and approaches to measurement. This leads on to a series of hypotheses which explicitly set out the relationship of X to Y in the form of a statement such as H1: X positively affects Y.

This is confirmatory factor analysis and it is used as long as you have a specific idea about the dimensions and their relationship to the thing you are trying to investigate. (A second approach is exploratory factor analysis in which you test each association and. to an extent, see what you come up with. This is a more bottom up approach but it is important to remember that you can only test what you have collected, so if there is something missing it will stay missing.

Once data have been collected (or accessed in the case of secondary data analysis) the validity of a measurement of a concept can be tested by Cronbach’s alpha. Put simply this tests whether what you you are measuring what you intended to measure by looking at the consistency of response. If satisfied about the validity of your measure you are then ready to carry out a series of tests of association to find out a. if there is evidence to back up the hypothesis you set out and b. to what the extent to which each dimension can be said to account for the independent variable.

These kind of associations are given as factor loading scores. Factor loadings are similar to correlation coefficients in that they can vary from -1 to 1. The closer factors are to -1 or 1, the more they affect the variable. A factor loading of zero would indicate no effect.

The paper below looks at food festivals and the authors want to use factor analysis to understand what factors or dimensons seem to influence perception of Festival quality in the specific example of the Macau food festival. Quality is an aspiration for those putting on festivals but a troubling concept for what does quality mean? From a review of the literature the authors identify a number of key factors associated with quality which they reduce to five: access, program, environment, interaction and outcome. Quality in turn is seen as influencing loyalty and satisfaction.

This provisional modelling of factors enable them to construct 13 specific hypotheses about the relationship of dimensions with quality. The authors then explain that a questionnaire was designed to measure these key variables as well as collect additional demographic data. A survey was then carried out of those attending the Macau food festival - taking a representative systematic random sample of attendees as they the festival ground.

The tests show that the hypotheses at the start of the paper were shown as supported (some partially, some fully) and the model was seen as fitting. In other words quality was strongly related to these five dimensions, mediated by other variables.

Similar arguments can be made for factor analysis as for quantititve methodology in general (e.g. the extent of data suggests greater reliability, measurement has great precision). Similarly the arugments against are well rehearsed (Is the extent of data collection at the expense of depth? can concepts be measured accurately and, if they can, should they be treated as stable?). Only with factor analysis the for's and against's are accentuated as the methodology offers a very detailed modelling as to the effect of each factor. For detractors the precision is misleading, relationships are often tautological or no more than common sensical.

Wong, J., Wu, H-C., and Cheng, C-C (2015) An empirical analysis of synthesizing the effects of festival quality, emotion, festival image and festival satisfaction on festival loyalty: a case study of Macau food festival, International Journal of Tourism Research, 17: 521–536.