For example, individuals may not treat an apparently equal-interval scale as such (Stevens, 1946). Hence, for example, if for some reason college students fit a model differently from the general population, studies of '40 college sophomores' are potentially misleading.Ī variety of measurement problems occur which will affect the size of goodness of fit measures. Goodness of fit measures' ability to estimate a model's usefulness are obviously limited to the population represented by the sample. On the other hand, a high goodness of fit measure suggests that a useful model which is equally or even more valuable than the original model may be developed because of its empirical goodness of fit. Criticisms of research on this basis are widespread (Cohen, et al., 1972 Taylor & Gutman, 1973). In other words, the operationalization of the theoretical model may be due to the type of data available for examining the model. One obvious situation where goodness of fit measures are not appropriate for estimating a model's usefulness is when the operationalization of the model does not match the model. Unfortunately, there are a variety of reasons why perfect goodness of fit measures should not be expected from useful models. It is very easy to rely on goodness of fit measures as a means of evaluating model usefulness. Yet in spite of their advantages, goodness of fit measures have some important limitations as indicators of the truthfulness and usefulness of models. Fourth, they appear as output in canned computer programs, which is no small reason for their prominence in reported research results. Third, they can be used as a means of deducing new or modified models from a set of data. Secondly, there exist established statistical procedures for testing these measures for significance. First, they are quantitative indices which can be compared across models so that the best of a set of models can be selected. Goodness of fit measures have some obvious advantages in model development. Hence because of difficulties with the predictive testing approach, as well as different training, most research on consumer behavior has tended to focus on goodness of fit measures as an indicator of useful relationships. Secondly, in many cases several competing models exist, and with notable exceptions (Bass & Clarke, 1972), more than one of them can fail to be rejected. This is especially true for models which do not assume causality. In the first place, it requires considerable ingenuity to deduce meaningful conclusions from models which can be falsified by data. Hence lack of certainty over what the model is makes predictive testing very difficult.Įven when a model is specified, the predictive testing approach is often difficult to utilize. Moreover, it is possible to specify the relationship between A and B to be causal or merely correlational and to assume a large random component exists. A could be hypothesized to:Ģ) be related to B in some specific mathematical way (eg., A = c + dB)ģ) be related to B in some specific mathematical way with constraints on the parameters (eg., A = c + dB where c > 1 and 0 < d < 1) Even when a model is present, it is often poorly specified. One reason for this is that in much research, a model is not extant prior to data analysis. The predictive testing approach, in spite of its obvious appeal, is not used widely in most research on consumer behavior. This approach consists of deducing conclusions from the model and seeing if the data supports the conclusions. In the social sciences, this type of model investigation has been labeled predictive testing (Basmann, 1965).

Data is then collected and the model rejected if the data and the model conflict. The first step in formal research is often the specification of a model, either explicitly or implicitly.

In addition, a procedure for assessing the appropriateness of a linear regression model is presented. Several obvious discrepancies between model 'validity' and goodness of fit results due to such causes as measurement problems, model mis-specification, and stochastic behavior are described. This paper describes the relationship between the truthfulness and usefulness of a model or hypothesized relationship between two or more variables and the goodness of fit which results from an empirical investigation of the model or hypothesis. VALIDITY AND GOODNESS OF FIT IN DATA ANALYSIS Mary Jane Schlinger, Ann Abor, MI : Association for Consumer Research, Pages: 741-750.Īdvances in Consumer Research VolPages 741-750 Lehmann (1975) ,'Validity and Goodness of Fit in Data Analysis', in NA - Advances in Consumer Research Volume 02, eds.

Goodness of fit social work journal