What is the meaning of getting say 2 or 3 factors in Factor Analysis?
A factor is nothing more than a grouping of scale items that have high degree of inter-correlation between them. It is a mathematical feature based on responses, and that is all that it means.
One must look at the content of the grouped items to determine if there is any meaning associated with the grouping. The determination that a factor "represents" something is a qualitative analysis of the content of the quantitatively associated items.
Hi Mohd,
The factors obtained as a result of factor analysis are related to the structure to be measured. For example, let's want to measure intelligence. If the scale used is developed according to Gardner's multiple intelligence theory then it is expected to be 8 factors. This point is also important in operational defining the structure to be measured. As a result, the factors that are obtained as a result of factor analysis are composed of related items. But these factors are also related to the structure to be measured at the same time.
The factors, theoretically, are meaningful concepts to which each of the individual items included have some relationship. If there were a "perfect" item to measure each concept (that is, without error) multiple items would be unnecessary and correlations among a group of items would represent the true relations among the underlying concepts themselves. In the real world of imperfect items the relations among items are used as an indicator of the existence and nature of the presumed real underlying concepts. If we think we know the nature of a given underlying concept and create the items to measure an individual's position on that concept then a pattern of high intercorrelation among items produced to represent that concept, coupled with low intercorrelations of these same items with items not meant to measure that underlying concept (factor) provides evidence for its existence. The nature of the items can be used to help us more closely define the definition of the factor. That is, those items more highly correlated with the factor are 'closer' to the concept than are those with lower levels of correlation.
In a case where we are exploring a topic or set of ideas that we have no preconceived concepts for, we may compile a set of items we think are important for our understanding and carry out a factor analysis on them. Such is often called an 'exploratory' factor analysis. We review the correlations among the items and where we find high intercorrelation we may attempt to interpret the meaning of these clusters as representing a heretofore unrecognized concept with its meaning largely our understanding of what respondents were indicating when completing the items. This is a bit questionable and has been criticized by a number of scholars. It is often the case that the resulting factors and the concepts induced from the items that produced them do not hold up well when replication is attempted.
In any case, the factors are thought to represent some 'real' concepts found in the empirical world but not so directly measurable as are length, weight, etc. Multiple items are used to best approximate such a more straightforward measure of them.
- Badges
- Science topic
- Similar topics
- Social Science
- Sociology