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Causal Modeling

  • Causal modeling is a data modeling technique that is known by several names, including structural modeling, path modeling, and analysis of covariance structures. This sophisticated extension of linear regression analysis offers two primary advantages. First, it can solve multi-equation models that simulate complex systems or process. Second, it gets around some of the assumptions and limitations of standard regression modeling.
  • As an example, suppose you wanted to make a better soft drink. You might start by measuring the impact of product performance attributes (i.e., sweetness, amount of carbonation, number of calories, etc) on the overall rating of leading soft drinks. One typical way to do this is to regress the overall rating on the attribute ratings. This is very easy to do in a variety of statistical programs or even spreadsheets, but the results they produce are based on several assumptions. These are usually referenced as BLUE (Best Linear Unbiased Estimator) or "all things being equal" if they are mentioned at all. Regression actually makes quite a few assumptions about the data and the model being solved, including that the model is ‘correctly specified’ and that the independent variables are not correlated.
  • Virtually every set of attributes ever put on a questionnaire has had some degree of correlation between the individual attributes. Usually there are several that are at least moderately correlated. There are statistical procedures (i.e., factor analysis) for dealing with correlated independent variables, though often times the correlated attributes are used as inputs to the regression model. Suppose the soft drink model creating using standard showed that both sweetness and the number of calories were related to the overall rating of a soft drink. Then the regression coefficients would indicate the impact, ‘all things being equal’, that changing the perceived sweetness level would have on the overall acceptance. But since the sweetness level and the number of calories are correlated, all things are definitely not equal, and there is a bias in the model.
  • The potential ‘model specification error’ is harder to deal with. Regression assumes that the model (i.e., the equation it was asked to solve) is an accurate representation of the problem or system being studied – with nothing added and nothing left out. Getting back to the soft drinks, if the brands are identified to the respondents, then the image of the brands will have a significant impact on their ratings. (Anyone who doubts this has never seen ratings of the same products rated blind, identified, and misidentified.)
  • Using typical regression modeling you could add some image attributes to the model, but the model would probably still be misspecified because it is nearly impossible to capture every nuance of a product’s image and performance. Some parts of these are almost always ‘left out’ or otherwise impossible to quantify. A more accurate way to specify the model would be to conclude that there are a series of performance attributes that drive overall ‘Product Performance’ and a series if image attributes that drive overall ‘Product Image,’ and these in turn drive the overall product rating.
  • Measuring the overall performance and image of a product is similar to measuring a person’s IQ. They can’t be measured directly, but can be derived from a series of indicators. Causal modeling will derive the measures (called ‘unobserved exogenous variables’), and parcel out the impact of each on the overall rating. And since image has an impact on taste, the direct effect of image, and the indirect effect of image (through it’s impact on product performance) on the overall rating can be computed. Further, if taste in turn has an impact on image, that effect can be quantified as well. Graphically, this would appear as follows:
  • The arrows or paths in the diagram represent the flow of 'causality' (i.e., effect) in the model. These indicate that there is a statistically significant relationship between the variables. Sometimes the path coefficients (i.e., regression coefficients) are included on the arrows to indicate the impact one variable has on the next. They have been omitted in this example.

 

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