Desarrollo del método de Costeo Basado en Actividades

Factor analysis is a modeling approach that was first developed by psychol- ogists as a method to study unobservable, hypothetically existing variables, such as intelligence, motivation, ability, attitude, and opinion. Latent vari- ables typically represent not directly measurable dimensions that are of substantive interest to social and behavioral scientists, and a widely ac- cepted interpretation of a latent variable is that an individual’s standing on this unobserved dimension can be indicated by various proxies of the di- mension, which are generally referred to as indicators. These are directly measurable manifestations of the underlying latent dimension, such as scores on particular tests of intelligence that indicate one’s intellectual abil- ity (see Chap. 1).

Like path analysis, factor analysis has a relatively long history. The origi- nal idea dates back to the early 1900s, and it is generally acknowledged that the English psychologist Charles Spearman first applied early forms of this approach to study the structure of human abilities. Spearman (1904) pro- posed that an individual’s ability scores were manifestations of a general ability (called general intelligence, or justg) and other specific abilities, such as verbal or numerical abilities. The general and specific factors com- bined to produce the ability performance. This idea was labeled the

two-factor theory of human abilities. However, as more researchers be- came interested in this approach (e.g., Thurstone, 1935), the theory was ex- tended to accommodate more factors and the corresponding analytic method was referred to as factor analysis.

In general terms,factor analysisis a modeling approach for studying hy- pothetical constructs by using a variety of observable proxies or indicators of them that can be directly measured. The analysis is considered exploratory, also referred to as exploratory factor analysis (EFA), when the concern is with determining how many factors, or latent constructs, are needed to explain well the relationships among a given set of observed measures. Alternatively, the analysis is confirmatory, formally referred to as confirmatory factor analy- sis (CFA), when a preexisting structure of the relationships among the mea- sures is being quantified and tested. Thus, unlike EFA, CFA is not concerned with discovering a factor structure, but with confirming and examining the details of an assumed factor structure. In order to confirm a specific factor structure, one must have some initial idea about its composition. In this re- spect, CFA is considered to be a general modeling approach that is designed to test hypotheses about a factor structure, when the factor number and in- terpretation in terms of indicators are given in advance. Hence, in CFA (a) the theory comes first, (b) the model is then derived from it, and finally (c) the model is tested for consistency with the observed data. For the latter pur- pose, structural equation modeling can be used. Thereby, as discussed at length in Chap. 1, the unknown model parameters are estimated so that, in general, the model reproduced matrixS(g)comes as close as possible to the sample matrixS(i.e., the model is ‘given’ the best chance to emulateS). If the proposed model emulatesSto a sufficient extent, as measured by the good- ness-of-fit indices, it can be treated as a plausible description of the phenome- non under investigation and the theory from which the model has been derived is supported. Otherwise, the model is rejected and the theory—as embodied in the model—is disconfirmed. We stress that this testing rationale is valid for all applications of the SEM methodology, not only those within the framework of confirmatory factor analysis, with its origins being traditionally rooted partly in the factor analytic approach.

This discussion of confirmatory factor analysis (CFA) suggests an impor- tant limitation concerning its use. The starting point of CFA is a very demand- ing one, requiring that the complete details of a proposed model be specified before it is fitted to the data. Unfortunately, in many substantive areas this may be too strong a requirement since theories are often poorly developed or even nonexistent. Due to these potential limitations, Jöreskog & Sörbom (1993a) distinguished aptly between three situations concerning model fit- ting and testing: (a) a strictly confirmatory situation in which a single formu- lated model is either accepted or rejected; (b) an alternative-models or competing-models situation in which several models are formulated and preferably one of them is selected; and (c) a model-generating situation in which an initial model is specified and, in case of unsatisfactory fit to the data, is modified and repeatedly tested until acceptable fit is obtained.

The strictly confirmatory situation is rare in practice because most re- searchers are unwilling to reject a proposed model without at least suggest- ing some alternative model. The alternative- or competing-model situation is not very common because researchers usually prefer not to specify, or cannot specify, particular alternative models beforehand. Model genera- tion seems to be the most common situation encountered in empirical re- search (Jöreskog & Sörbom, 1993a; Marcoulides, 1989). As a consequence, many applications of CFA actually bear some characteristic features of both explanatory and confirmatory approaches. In fact, it is not very frequent that researchers are dealing with purely exploratory or purely confirmatory analyses. For this reason, results of any repeated modeling conducted on the same data set should be treated with a great deal of caution and be con- sidered tentative until a replication study can provide further information on the performance of these models.

AN EXAMPLE CONFIRMATORY FACTOR ANALYSIS MODEL