# XLSTAT-Conjoint Analysis

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XLSTAT-Conjoint Analysis module is a statistical software for marketers. It empowers you to find out the expectations of consumers towards new products and to model their choices thanks to conjoint analyses – crucial steps of a marketing analysis. Two methods of conjoint analysis are available: full profile conjoint analysis and choice based conjoint analysis (CBC).

XLSTAT-Conjoint Analysis software is a complete statistical program which allows you to run through all the analytical steps of conjoint analysis from the design of experiments to the simulation of new markets, through data analysis with specific regression methods – MONANOVA, logit multinomial, etc.

## Features

Some tutorials are available for in depth descriptions on how to use the product.

## Demo version

A trial version of XLSTAT-Conjoint Analysis is included in the main XLSTAT-Base download.

## Prices and ordering

These analyses are included in the XLStat-Marketing and XLStat-Premium packages.

# DoE for conjoint analysis

### Why do we use design of experiments for conjoint analysis

The principle of conjoint analysis is to present a set of products (also known as profiles) to the individuals who will rank, rate, or choose some of them.

In an "ideal" analysis, individuals should test all possible products. But it is soon impossible; the capacity of each being limited and the number of combinations increases very rapidly with the number of attributes (if one wants to study five attributes with three categories each, that means already 243 possible products). We therefore use the methods of experimental design to obtain a acceptable number of profiles to be judged while maintaining good statistical properties.

XLSTAT-Conjoint includes two different methods of conjoint analysis:

1. the full profile analysis
2. and the choice based conjoint (CBC) analysis.

### Design of experiments for full profiles conjoint analysis

The first step in a conjoint analysis requires the selection of a number of factors describing a product. These factors should be qualitative. For example, if one seeks to introduce a new product in a market, we can choose as differentiating factors: the price, the quality, the durability ... and for each factor, we must define a number of categories (different prices, different lifetimes ...). This first step is crucial and should be done together with experts of the studied market.

Once this first step done, the goal of a conjoint analysis is to understand the mechanism of choice: Why people choose one product over another?

To try to answer this question, we will propose a number of products (combining different modalities of the studied factors). We can not offer all possible products, so we will select products by using design of experiments before presenting them to people who will rate them or rank them.

The full profile method is the oldest methods of conjoint analysis; we seek to build an experimental design that includes a limited number of full profiles that each individual interviewed will then rank or rate.

XLSTAT-Conjoint uses fractional factorial designs in order to generate profiles that will then be presented to respondents. When no design is available, XLSTAT-Conjoint uses algorithms to search for D-optimal designs.

# DoE for choice based conjoint (CBC) analysis

### Principle of design of experiments for choice based conjoint (CBC) analysis

The principle of conjoint analysis is to present a set of products (also known as profiles) to the individuals who will note, class, or choose some of them.

In an "ideal" analysis, individuals should test all possible products. But it is soon impossible; the capacity of each being limited and the number of combinations increases very rapidly with the number of attributes (if one wants to study five attributes with three categories each, that means already 243 possible products). We therefore use the methods of experimental design to obtain a acceptable number of profiles to be judged while maintaining good statistical properties.

XLSTAT-Conjoint includes two different methods of conjoint analysis: the full profiles analysis and the choice based conjoint (CBC) analysis.

### Design of Experiment for Choice Based Conjoint analysis (CBC)

The principle of choice based conjoint (CBC) analysis is based on choices in a group of profiles. The individual respondent chooses between different products offered instead of rating or ranking products.

The process of CBC is based on comparisons of profiles. These profiles are generated using the same methods as for full profile conjoint analysis. Then, these profiles are put together in many comparison groups (with a fixed size). The individual respondent then chooses the profile that he would select compared to the other profiles included in the comparison.

The statistical process is separated into 2 steps:

1. Fractional factorial designs or D-optimal designs are used to generate the profiles.
2. Once the profiles have been generated they are allocated in the comparison groups using incomplete block designs.

### Selecting the factor for choice based conjoint analysis

The first step in a conjoint analysis requires the selection of a number of factors describing a product. These factors should be qualitative. For example, if one seeks to introduce a new product in a market, we can choose as differentiating factors: the price, the quality, the durability ... and for each factor, we must define a number of categories (different prices, different lifetimes ...). This first step is crucial and should be done together with experts of the studied market.

### Generating the design of experiments for the choice based conjoint analysis

Once past this first step, the goal of a conjoint analysis is to understand the mechanism for choosing one product over another. Instead of proposing all profiles to the individual respondents and asking to rate or rank them, CBC is based on a choice after a comparison of some of the profiles. Groups of profiles are presented to the individual respondents and they have to indicate which profile they would choose (a no choice option is also available in XLSTAT-Conjoint).

This method combines two designs of experiments, the fractional factorial design to select the profiles to be compared and the incomplete block design to generate the comparisons to be presented.

XLSTAT-Conjoint enables you to add the no choice option if the individual respondent would not choose any of the proposed profiles.

XLSTAT-Conjoint enables to obtain a global table for CBC analysis but also individual tables for each respondent and each comparison in separated Excel sheets. References are also included so that when a respondent select a profile in an individual sheet, it is directly reported in the main table.

# Conjoint analysis

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### Principle of conjoint analysis

Conjoint analysis is a comprehensive method for the analysis of new products in a competitive environment.

This tool allows you to carry out the step of analyzing the results obtained after the collection of responses from a sample of people. It is the fourth step of the analysis, once the attributes have been defined, the design has been generated and the individual responses have been collected.

Full profile conjoint analysis is based on ratings or rankings of profiles representing products with different characteristics. These products have been generated using a design of experiments and can be real or virtual.
The analysis is done using two statistical methods:

• Analysis of variance based on ordinary least squares (OLS).
• Monotone analysis of variance (Kruskal, 1964) that uses monotonic transformations of the responses to better adjust the analysis of variance (MONANOVA).

### Results of conjoint analysis

Conjoint analysis therefore provides for each individual what is called partial utilities associated with each category of the variables. These utilities provide a rough idea of the impact of each modality on the process of choosing a product.

In addition to utilities, conjoint analysis provides an importance associated with each variable.

It shows how each variable in the selection process associated with each individual is important.

The full profile conjoint analysis details the results for each individual separately, which preserves the heterogeneity of the results.

XLSTAT-Conjoint also proposes to make classifications on the individuals. Using the utilities, XLSTAT-Conjoint will obtain classes of individuals that can be analyzed and be useful for further research. Classification methods used in XLSTAT-Conjoint are the agglomerative hierarchical classification and the kmeans method.

### Type of data for conjoint analysis

XLSTAT-Conjoint offers two types of input data for the conjoint analysis: rankings and ratings.
With rankings, the best profile will have the lowest value, whereas with a rating, it will have the highest value.

# Choice based conjoint analysis

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### Principle of choice based conjoint analysis (CBC)

Conjoint analysis is a comprehensive method for the analysis of new products in a competitive environment.
This tool allows you to carry out the step of analyzing the results obtained after the collection of responses from a sample of people. It is the fourth step of the analysis, once the attributes have been defined, the design has been generated and the individual responses have been collected.

In the case of CBC models, individuals have to choose between selections of profiles. Thus, a number of choices are given to all individuals (we will select a product from a number of products generated).

Analysis of these choices is made using a multinomial logit model based on a specific conditional logit model. For more details see the help on the conditional logit model.

### Results of a choice based conjoint analysis

As part of the choice based conjoint analysis and differently from full profile conjoint analysis, we obtain aggregate utilities, that is to say, one utility for each category of each variable associated with all the individuals. It is impossible to make classifications based on the individuals.

XLSTAT-Conjoint proposes to include a segmentation variable that will build separate models for each group defined by the variable.
In addition to utilities, conjoint analysis provides the importance associated with each variable.

# Simulation for conjoint analysis

### Principle of simulation for conjoint analysis

Conjoint analysis is a comprehensive method for the analysis of new products in a competitive environment.

Once the analysis has been performed, the major advantage of conjoint analysis is its ability to perform market simulations using the obtained utilities. The products included in the market do not have to be part of the tested products.

Outputs from conjoint analysis include utilities which can be partial (associated to each individual in full profile conjoint analysis) or aggregate (associated to all the individuals in CBC). These utilities allow computing a global utility associated to any product that you want to include in your simulated market.

Four estimation methods are proposed in XLSTAT-Conjoint: first choice, logit, Bradley-Terry-Luce and randomized first choice.

### Simulation for conjoint analysis

The obtained market shares can then be analyzed to assess the possible introduction of a new product on the market. The results of these simulations are nevertheless dependent on the knowledge of the real market and the fact that all important factors associated with each product in the conjoint analysis have been taken into account.

XLSTAT-Conjoint can also add weights to the categories of the factors or to the individuals.

XLSTAT-Conjoint can also take into account groups of individuals when a group variable (segmentation) is available. It can be obtained, for example, with the segmentation tool associated with the conjoint analysis.

### Data type for simulation

XLSTAT-Conjoint proposes two models for conjoint analysis. In a full profile analysis, a constant is associated to the utilities and there are as many utilities as individuals in the study.
You have to select all the utilities and their constant. In the case of CBC, there is no constant and you have to use the utilities without the labels associated to the name of the categories.

### Simulation algorithms

XLSTAT-Conjoint offers four methods for simulation of market share.
The first step consists of calculating the global utility associated with each new product. Thus, for a CBC analysis for analyzing men's shoes with three factors: the price (50 dollars, 100 dollars, 150 dollars), their finishing (canvas, leather, suede) and the color (brown, black). We have a table with 8 partial utilities rows and one column.
We want to simulate a market with a black leather shoe with price equal USD 100. The utility of this product is: UP1 = Uprice-100 + UF-Leather + UC-Black.
We calculate the utility for each product in the market and we seek the probability of choosing this product using different estimation methods:

• First choice: it is the most basic; you select the product with maximum utility with a probability of 1.
• Logit: this method is based on the exponential function to find the probability, it is more accurate than the method first choice and it is generally preferred. It has the disadvantage of the IIA assumption (assumption of independence of irrelevant alternatives). It is calculated for the product P1:
PP1 = eUP1β / Σi eUPiβ
with beta = 1 or 2.
• Bradley-Terry-Luce is a method close to the logit method without using the exponential function. It always involves the assumption of IIA and demands positive utilities (if beta = 1). It is calculated for the product P1:
PP1 = UP1β / Σi UPiββ
with beta = 1 or 2.
• Randomized first choice: it is a method midway between logit and First Choice. It has the advantage of not assuming the IIA assumption and is based on a simple principle: it generates a large number of numbers from a Gumbel distribution and creates a new set of utilities using the initial utilities adding the numbers generated. For each set of utilities created, the first choice method is used to select one of the products. So we will accept slight variations around the calculated values of the utilities. This method is the most advanced but also more suited to the case of conjoint analysis.

When more than one column of utilities (with a conjoint analysis with full profiles) are selected, XLSTAT-Conjoint uses the mean of the probabilities.

# MONANOVA - Monotone regression

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### Principle of MONANOVA model

Monotone regression and the MONANOVA model differ only in the fact that the explanatory variables are either quantitative or qualitative. These methods are based on iterative algorithms based on the ALS (alternating least squares) algorithm. Their principle is simple, it consists of alternating between a conventional estimation using linear regression or ANOVA and a monotonic transformation of the dependent variables (after searching for optimal scaling transformations).

The MONANOVA algorithm was introduced by Kruskal (1965) and the monotone regression and the works on the ALS algorithm are due to Young et al. (1976).

These methods are commonly used as part of the full profile conjoint analysis. XLSTAT-Conjoint allows applying them within a conjoint analysis (see chapter on conjoint analysis based on full profiles) as well as independently.

The monotone regression tool (MONANOVA) combines a monotonic transformation of the responses to a linear regression as a way to improve the linear regression results. It is well suited to ordinal dependent variables.

XLSTAT-Conjoint allows you to add interactions and to vary the constraints on the variables.

### MONANOVA method

Monotone regression combines two stages: an ordinary linear regression between the explanatory variables and the response variable and a transformation step of the response variables to maximize the quality of prediction.

The algorithm is:

• Run an OLS regression between the response variable Y and the explanatory variables X. We obtain the beta coefficients.
• Calculation of the predicted values of Y: Pred (Y) = beta * X
• Transformation of Y using a monotonic transformation (Kruskal, 1965) so that Pred(Y) and Y are close (using optimal scaling methods).
• Run an OLS Regression between Ytrans and the explanatory variables X. Thisgives new values for the beta.
• Steps 2 through 4 are repeated until the change in R² from one stage to another is smaller than the convergence criterion.
•

# Conditional Logit model

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### Principle of conditional Logit model

The conditional logit model is based on a model similar to that of the logistic regression. The difference is that all individuals are subjected to different situations before expressing their choice (modeled using a binary variable which is the dependent variable). The fact that the same individuals are used in taken in account by the conditional logit model .

(NB: the observations are not independent within a block corresponding to same individual).

The conditional logit model is a method mostly used in conjoint analysis, it is nevertheless useful when analyzing a certain type of data. It is McFadden (1973) who introduced this model.

Instead of having one line per individual like in the classical logit model, there will be one row for each category of the variable of interest. If one seeks to study transportations, for example, there will be four types of transports (car / train / plane / bike), each type of transport have characteristics (their price, their environmental costs...) but an individual can choose only one of four transportations. As part of a conditional logit model, all four options are presented to each individual and the individual choose his preferred option. We have for N individuals, N * 4 rows with 4 rows for each individual associated with each transportation. The binary response variable will indicate the choice of the individual (1) and 0 if the individual did not choose this option.

In XLSTAT-Conjoint, you will also have to select a column associated with the name of the individuals (with 4 lines per individual in our example). The explanatory variables will also have N * 4 lines.

### Conditional Logit model method

The conditional logit model is based on a model similar to that of the logistic regression except that instead of having individual characteristics, there will be characteristics of the different alternatives proposed to the individuals.

The probability that individual i chooses product j is given by:

Pij = eβTzij / ΣkeβTzik

From this probability, we calculate a likelihood function:
l(β) = Σi=1..nΣj=1..J yij log(Pij)

With y being a binary variable indicating the choice of individual i for product j and J being the number of choices available to each individual.

To estimate the model parameters β (the coefficients of the linear function), it seeks to maximize the likelihood function. Unlike linear regression, an exact analytical solution does not exist. It is therefore necessary to use an iterative algorithm. XLSTAT-Conjoint uses a Newton-Raphson algorithm.

Kovach Computing Services (KCS) was founded in 1993 by Dr. Warren Kovach. The company specializes in the development and marketing of inexpensive and easy-to-use statistical software for scientists, as well as in data analysis consulting.

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