tailieunhanh - Quantitative Models in Marketing Research Chapter 7

7 A limited dependent variable. In chapter 3 we considered the standard Linear Regression model, where the dependent variable is a continuous random variable. The model assumes that we observe all values of this dependent variable, in the sense that there are no missing observations. | 7 A limited dependent variable In chapter 3 we considered the standard Linear Regression model where the dependent variable is a continuous random variable. The model assumes that we observe all values of this dependent variable in the sense that there are no missing observations. Sometimes however this is not the case. For example one may have observations on expenditures of households in relation to regular shopping trips. This implies that one observes only expenditures that exceed say 10 because shopping trips with expenditures of less than 10 are not registered. In this case we call expenditure a truncated variable where truncation occurs at 10. Another example concerns the profits of stores where losses that is negative profits are perhaps not observed. The profit variable is then also a truncated variable where the point of truncation is now equal to 0. The standard Regression model in chapter 3 cannot be used to correlate a truncated dependent variable with explanatory variables because it does not directly take into account the truncation. In fact one should consider the so-called Truncated Regression model. In marketing research it can also occur that a dependent variable is censored. For example if one is interested in the demand for theater tickets one usually observes only the number of tickets actually sold. If however the theater is sold out the actual demand may be larger than the maximum capacity of the theater but we observe only the maximum capacity. Hence the dependent variable is either smaller than the maximum capacity or equal to the maximum capacity of the theater. Such a variable is called censored. Another example concerns the donation behavior of individuals to charity. Individuals may donate a positive amount to charity or they may donate nothing. The dependent variable takes a value of 0 or a positive value. Note that in contrast to a truncated variable one does observe the donations of individuals who give nothing which is of course 0.