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The Model
A major limitation of objective and perceived customer value measures is that they are estimates based on information or judgments before a purchase.
They don't have the credibility associated with measures derived from actual observations of purchase behavior. Measures of behavioral customer
value use observations of the actual past behaviors of customers as the basis for estimating value. Choice models use past behavior often linked
with rating-scale information, to estimate value or utilities for product characteristics that most closely explain or predict actual behavior.
A good way to understand choice models is to contrast them with perceived measures of value obtained through surveys. In standard survey methods, we try to infer
value (measured as importance weights) through some sort of direct questioning. However with choice models, we observe choice
and infer value (again, measured as importance weights). The output of a choice model is the estimate of those importance weights along with purchase
probabilities for each market alternative for each customer.
A simple and powerful choice model is the multinomial logit model, which uses a specific form of customer utility function and assumes that a customer's purchase
probability for brand A is equal to the utility of A divided by the sum of that customer's utilities for alternative brands he is considering (Relevant Alternatives):
Purchase Probability (A) = Utility of A / Sum of Utilities of Relevant Alternatives.
The utility of product option A (and the utilities of alternatives) is based on a customer's evaluation of product A on its various attributes and the revealed
importance weights of these attributes from the logit model. We interpret these weights similar to the way we interpret regression coefficients.
The Multinomial Logit Analysis (MNL) model is an individual-level response model that helps to analyze and explain the choices individual customers make in the market.
The MNL model helps firms to understand the extent to which such factors as price of a brand or its ease of installation influence a customer's choice of a brand.
A brand's purchase probability at the individual level is equivalent to the brand's market share at the market level.
This Logit Analysis software implements a nonnested multinomial logit model.
Getting started
Before you start running our software, please take a look at the Compatibility List.
Due to our intensive use of various Web technologies you may experience difficulties running a software under your browser.
We apologize for any inconvenience this may cause and are working on full browser compatibility.
You may have to enable Javascript, Cookies and/or accept Active X Controls. Please refer to the Compatibility List
Read this help section and the Tutorial carefully before running the software. You can also see how the software actually works by running
the Demo.
You can download here an example file (ABB Electric Case) you can load into the software.
Running the software
Step by Step instructions on how to run the software can be found at the Demo Section.
You will find a complete, commented Demo of the Logit Analysis.
Understanding the results
The program produces an extensive set of diagnostics, organized into ten components.
The two final diagnostic components help you determine the overall statistical significance of the chosen model.
- Input Data Summary
The number of rows of data that Multinomial Logit Program used for the analysis, and means of each variable.
- History of parameter estimation
The parameters of the logit model are estimated by a statistical procedure called "maximum likelihood". It attempts to find the parameters of the probability
distribution for the specified model that will make the observed sample of data to be the most likely sample from the underlying probability distribution.
The likelihood of a sample is measured by a likelihood function (or, more conventionally, a log-likelihood function). The iterative maximum likelihood
procedure stops if one of the following three criteria is met (within a desired tolerance) for successive iterations: (1) the likelihood function does
not improve, (2) the parameter estimates do not change, or (3) the search gradients do not change. The history of the estimation summarizes what happened
at each iteration.
- Asymptotic Variance-Covariance Matrix
The matrix displays the variance and covariance of the estimated parameters.
- Estimated Parameters
The first table displays the parameter estimates of the variables that influence the customer's choice behavior,
the standard error of these estimated, coefficients and the t-statistic for each coefficient.
- Estimated Probabilities Matrix
This matrix displays the probability of each customer choosing each product alternative (regardless of the segment to which a customer belongs).
- Hit Rate
The higher the hit rate, the higher the predictive ability of the model. If the estimation and prediction samples are not distinct,
then the hit rate is a measure of the goodness-of-fit, rather than the predictive ability of the model.
- Market Share (Choice Share) Forecasts
The estimated choice probabilities (see Estimated Probabilities Matrix) can be used to derive a market-share estimate (share of choices) for each alternative.
The choice shares provide aggregate forecasts of market performance for each alternative. If a holdout sample is used for prediction, then the choice shares
are computed on the holdout sample; otherwise, the choice shares are computed on the data used for model estimation.
- Elasticities Using Estimation Sample
This set of diagnostics consists of a series of elasticity matrices, one for each independent factor, for each segment. For example, in the elasticity
of Quality matrix below, the number 4.3174 indicates that if the quality of Product 1 increases by 1% the choice share of this product increases by 4.3174%.
Similarly, the number -1.2843 indicates that if the quality of Product 1 increases by 1% then the choice share of Product 2 will decrease by 1.2843%.
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Product 1 |
Product 2 |
Product 3 |
| Product 1 |
4.3174 |
-1.2843 |
-1.3057 |
| Product 2 |
-1.7857 |
2.3335 |
-0.3940 |
| Product 3 |
-1.8210 |
-0.4423 |
2.2674 |
- Hypotheses Tests
This set of diagnostics compares the performance of the model against two naive models:
a) The "null model" is one in which all parameters, including alternative-specific constants are set to zero. This naive model
essentially assigns equal probabilities to each choice alternative (=1/n where n is the number of alternatives). If the
resulting Chi-Square statistic is significant, it indicates that the selected model (which includes all the variables,
including alternative-specific constants if any) performs better than the naive model.
b) The second naive model sets all parameters, other than alternative-specific constants, to be zero. This model is useful for assessing the statistical
significance of just the independent variables, taken as whole. Again, a Chi-Square statistic value that is significant indicates that the chosen model is
better than this naive model.
- Other Measures of Goodness-of-fit
Rho-square is similar to the R-Square measure in regression. It is also an index of the extent to which the chosen model performs better than the first naive model
above, with all parameters set to 0. Rho-Bar-Square adjusts for the number of parameters, penalizing models with a large number of variables, where the variables
may not contribute to explaining the observed choices.
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