Model Diagnostics in the presence of measurement error

The problem of using information available from one variable X to make inferenceabout another Y is classical in many physical and social sciences. In statistics this isoften done via regression analysis where mean response is used to model the data. Onestipulates the model Y = µ(X) +ɛ. Here µ(X) is the mean response at the predictor variable value X = x, and ɛ = Y - µ(X) is the error. In classical regression analysis, both (X; Y ) are observable and one then proceeds to make inference about the mean response function µ(X). In practice there are numerous examples where X is not available, but a variable Z is observed which provides an estimate of X. As an example, consider the herbicidestudy of Rudemo, et al. [3] in which a nominal measured amount Z of herbicide was applied to a plant but the actual amount absorbed by the plant X is unobservable. As another example, from Wang [5], an epidemiologist studies the severity of a lung disease, Y , among the residents in a city in relation to the amount of certain air pollutants. The amount of the air pollutants Z can be measured at certain observation stations in the city, but the actual exposure of the residents to the pollutants, X, is unobservable and may vary randomly from the Z-values. In both cases X = Z+error: This is the so called Berkson measurement error model.In more classical measurement error model one observes an unbiased estimator W of X and stipulates the relation W = X + error: An example of this model occurs when assessing effect of nutrition X on a disease. Measuring nutrition intake precisely within 24 hours is almost impossible. There are many similar examples in agricultural or medical studies, see e.g., Carroll, Ruppert and Stefanski [1] and Fuller [2], , among others. In this talk we shall address the question of fitting a parametric model to the re-gression function µ(X) in the Berkson measurement error model: Y = µ(X) + ɛ; X = Z + η; where η and ɛ are random errors with E(ɛ) = 0, X and η are d-dimensional, and Z is the observable d-dimensional r.v.

Influence of personality factors on the consumption of personal care products

This research was undertaken with the primary objective of explaining differences in consumption of personal care products using personality variables. Several streams of research reported were reviewed and a conceptual model was developed. Theories on the relationship between self concept and behaviour was reviewed and the need to use individual difference variables to conceptualize and measure the salient dimensions of the self were emphasized. Theories relating to social comparison, eating disorders, role of idealized media images in shaping the self-concept, evidence on cosmetic surgery and persuasibility were reviewed in the study. These came from diverse fields like social psychology, use of cosmetics, women studies, media studies, self-concept literature in psychology and consumer research, and marketing. From the review three basic dimensions, namely self-evaluation, self-awareness and persuasibility were identified and they were posited to be related to consumption. Several personality variables from these conceptual domains were identified and factor analysis confirmed the expected structure fitting the basic theoretical dimensions. Demographic variables like gender and income were also considered.It was found that self-awareness measured by the variable public self-consciousness explain differences in consumption of personal care products. The relationship between public self-consciousness and consumption was found to be most conspicuous in cases of poor self-, evaluation measured by self-esteem. Susceptibility to advertising also was found to explain differences in consumption.From the research, it may be concluded that personality variables are useful for explaining consumption and they must be used together to explain and understand the process. There may not be obvious and conspicuous links between individual measures and behaviour in marketing. However, when used in proper combination and with the help oftheoretical models personality offers considerable explanatory power as illustrated in the seventy five percent accuracy rate of prediction obtained in binary logistic regression.