SULAIMAN ABDUL RAHMAN 15407111 - Factor Analysis & Hierarchical Analysis

Factor analysis:

Factor analysis is a statistical method used to describe variability among observed variables in terms of fewer unobserved variables called factors. The observed variables are modeled as linear combinations of the factors, plus "error" terms. The information gained about the interdependencies can be used later to reduce the set of variables in a dataset. Factor analysis originated in psychometrics, and is used in behavioral sciences, social sciences, marketing, product management, operations research, and other applied sciences that deal with large quantities of data.

Factor analysis is often confused with principal components analysis. The two methods are related, but distinct, though factor analysis becomes essentially equivalent to principal components analysis if the "errors" in the factor analysis model (see below) are assumed to all have the same variance.

Factor analysis in marketing

The basic steps are:

* Identify the salient attributes consumers use to evaluate products in this category.
* Use quantitative marketing research techniques (such as surveys) to collect data from a sample of potential customers concerning their ratings of all the product attributes.
* Input the data into a statistical program and run the factor analysis procedure. The computer will yield a set of underlying attributes (or factors).
* Use these factors to construct perceptual maps and other product positioning devices

The analysis will isolate the underlying factors that explain the data. Factor analysis is an interdependence technique. The complete set of interdependent relationships are examined. There is no specification of either dependent variables, independent variables, or causality. Factor analysis assumes that all the rating data on different attributes can be reduced down to a few important dimensions. This reduction is possible because the attributes are related. The rating given to any one attribute is partially the result of the influence of other attributes. The statistical algorithm deconstructs the rating (called a raw score) into its various components, and reconstructs the partial scores into underlying factor scores. The degree of correlation between the initial raw score and the final factor score is called a factor loading. There are two approaches to factor analysis: "principal component analysis" (the total variance in the data is considered); and "common factor analysis" (the common variance is considered).

Note that principal component analysis and common factor analysis differ in terms of their conceptual underpinnings. The factors produced by principal component analysis are conceptualized as being linear combinations of the variables whereas the factors produced by common factor analysis are conceptualized as being latent variables. Computationally, the only difference is that the diagonal of the relationships matrix is replaced with communalities (the variance accounted for by more than one variable) in common factor analysis. This has the result of making the factor scores indeterminate and thus differ depending on the method used to compute them whereas those produced by principal components analysis are not dependent on the method of computation. Although there have been heated debates over the merits of the two methods, a number of leading statisticians have concluded that in practice there is little difference (Velicer and Jackson, 1990) which makes sense since the computations are quite similar despite the differing conceptual bases, especially for datasets where communalities are high and/or there are many variables, reducing the influence of the diagonal of the relationship matrix on the final result (Gorsuch, 1983).

The use of principal components in a semantic space can vary somewhat because the components may only "predict" but not "map" to the vector space. This produces a statistical principal component use where the most salient words or themes represent the preferred basis.

Hierarchical analysis:

"A hierarchy is an organization of elements that, according to prerequisite relationships, describes the path of experiences a learner must take to achieve any single behavior that appears higher in the hierarchy (Seels & Glasgow, 1990, p. 94)". Thus, in a hierarchical analysis, the instructional designer breaks down a task from top to bottom, thereby, showing a hierarchical relationship amongst the tasks, and then instruction is sequenced bottom up. For example, in the diagram below, task 4 has been decomposed into its enabling tasks implying that the learner cannot perform the third task until he/she has performed the first and second tasks respectively.