Using survey data from intentions to purchase personal computers (PC) and demographic variables Hsiao, Sun and Morwitz (2002) find that:

- A remarkably stable relationship between intentions and purchase over time.
- True intentions are not represented by stated intentions. A better representation of the true intentions should be a weighted average of stated intentions.
- Family, education, and demographic variables are complementary to intentions in predicting purchasing behavior. Demographic variables should be used to improve predictive power.
- Modelling intentions based on demographics and then using that output to then model purchases is difficult to do accurately. There is value from asking potential customers about their intentions.
- There is significant evidence that exogenous shocks (fired, death in family, etc.) lead to a change in intentions and these are not captured in the social-demographic factors in their study. Further research is needed on how to model these.

The purpose of this posts is to introduce the logic and models used arrive to these conclusions. Please note that these findings may not be externally valid for other products, because this study focused on the intent to purchase personal computers. These findings may be different for other types of products, having said that the models below can be leveraged to test these kinds of hypothesis about intentions and demographic influences on new product purchases.

**MODEL 1**

The first model assumes that information shapes people’s true intentions and these intentions translate into a true response (i.e. purchase). It is assumed that peoples true intentions are influenced by social demographic variables. The mathematical formula below describes these relationship. True population variables are indicated with an asterisk while observed variables are missing asterisks. These postulations can be described mathematically as:

In order to build a probability model one must assume that crossing the threshold of purchasing be coded as a binary response. It this construct it is irrelevant whether or not a person purchased 1 or more products or services, but any positive value is coded as a 1 and no purchase or a return of an item purchased outside the time period of observation is coded as a zero. Furthermore this first model assumes that stated intentions and demographic information can help one determine true intentions; further more if stated intentions equals true intentions then the demographic information is irrelevant. This can be stated more formally with a probability function (F) as follows

**MODEL 2
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The second relaxes the assumption that people’s stated intentions equal their actual intentions. Research has shown that asking people questions like “How likely are you to buy product X in the next 6 months” on a 5-point scale (definitely will=5; definitely will not buy =1) can be a better measure of true intentions. Further research has shown that people will tend to understate low intentions and overstate high intentions. This second model assumes that true intentions are a weighted average of a stated intention scale, formally this model would look similar to model one, but with the following modelling on stated intentions

**MODEL 3
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The third model uses family, education, and demographic variables along with a binary response variable for intentions. It has been postulated that people may be giving their best-point prediction of a future event when answering questions such as “Do you wish to buy a certain product in the next so many months”. In other words they answer the question as would a statistician in terms of estimating probabilities of certain event s happening, then translating that into a “yes” answer if their probability of actually buying the product is greater than 50% based on their assessment of their life at the time of the survey. Under these assumptions the probability of purchasing given true intentions and demographic information is equivalent to the probability of purchasing given true intentions, demographics would add nothing, but given that we have only stated intentions and only a probabilistic assessment of true intentions we need to state things differently. Theoretically models that omit demographic information are suboptimal likewise models that ignore stated intentions would also be lacking in explanatory power, hence both variables are used in this model

**MODEL 4**

In addition to differences between stated intentions and purchases there can be factors that influence purchasing that may or may not be independent of demographics. There could be a change in intentions due to several factors outside of the scope of the person responding to the survey (raise, promotion, fired, price changes, etc.). This model accounts for shocks to individuals intentions based on these select factors