Modelling with data deficiencies

The availability of numerically measured data without measurement errors is a requirement for any statistical analysis. However, this requirement is not met in many cases, especially in statistical applications in social sciences. In the context of social science applications, two broader types of measurement errors can be identified. Error due to data collection inefficiencies is the first type. The second type is the presence of numerically immeasurable variables. Conceptual Variables, Multi-dimensional Variables and Hidden (latent) Variables are examples of numerically immeasurable variables.

 

Measurement errors of first type would be minimized if the survey design is done with extra care. Use of proxies is one of the popular methods to overcome problems associated with second type. However, use of proxies is also criticized because it can create another form of measurement error.

 

Statisticians and econometricians have proposed various statistical methods to overcome the problem of measurement errors. This paper classified them into two as theoretical and technical. Theoretical solutions derive equations with measurable variables to represent conceptual variables. Several technical solutions are reviewed in this paper. Instrumental variable method and orthogonal distance regressions are generally accepted solutions for most forms of measurement error. Discrete choice models with measurable indicator variables and canonical regression methods are used by applied statisticians and econometricians to overcome the problems of latent dependent variable and multidimensional variables.