Conjoint Analysis in 10 minutes - Business Performance Management

conjoint analysis or stated preference analysis is a statistical technique that originated in mathematical psychology today it is used in many of the social science and applied science including marketing product management and operations research let's assume you go to a shop to buy a smartphone or mp3 player now the sales person tells you you can either get the model with 32 gigabyte of the shelf or you get a model with 64 gigabyte but then you have to wait one week for the delivery now the question is what is your preference your preference for one of the alternatives will reveal the part worth utilities of individual attributes in our example attribute one is the memory size and attribute tool the delivery time when you choose model a it will show that you put higher emphasis on your short delivery time choosing model B will reveal your higher emphasis on a large memory size so in a conjoint analysis the part worth utilities of individual attributes in our case memory size and delivery time are calculated based on the selection or ranking of a defined set of combinations of attribute values let's make our example a little more complex we take into consideration three attributes we look at color green or red we look at memory size 16 or 64 megabyte and we look at delivery time one day or one week combining all attributes with their individual values will result in eight different company patience in order to solve this problem with a mathematical method we code the values or levels with minus one and plus one each so for example green is coded as minus one and red is coded as plus one here is the list of combinations with their coding we call it the design matrix for K attributes there are two to the power of K possible combinations using all possible combinations is called a full factorial design we treat the three attributes as variables each of them with the value of minus one or plus one in a graphical illustration each combination is represented as a point in a corner of a cube one dimension of the cube shows the color the second shows the memory size and the third the delivery time the next step in a conjoint analysis is to ask a person for ranking of the possible combinations for example to give one for the most preferred combination going down to eight for the least preferred combination then we use a simple linear model function to describe the ranking and to find the part worth utilities the ranking is expressed as part worth of attribute one color multiplied by the level four attribute one minus one or plus one plus the part worth of attribute two multiplied by the level for attribute 2 plus part worth of RT Bute 3 multiplied by level four attributes 3 plus a constant as a mathematical equation it's shown here where better are the part worth utilities now we can set up a system of linear equations using the coded combinations and the ranking for each combination given by the person this system of linear equations can be solved with a multi variant linear regression axel is a possibility to handle the case for our simple example here we calculate the part worth utilities in the following way to find the main effect for attribute one color we take the average ranking for all model combinations with x1 equals +1 that means red color and subtract the average ranking for all combinations with x1 equals minus 1 that means green color in our cube it corresponds to the sum of ranking values for all points on the right side of the vertical plane minus the sum of ranking values for all points on the left side of the vertical plane we divide by 4 as we take the average of four points each and set it in relation to the total variation of the x value from minus one to plus one so we divide by two as a result we get a part worth utility for color of minus 0.5 in the same way we proceed for the other two dimensions as a result we get the wanted part worth utilities for color memory and delivery the ranking calculated with the model function fits exactly the actual ranking to calculate the relative preference for each individual attribute we have to look at the total range of variations for our level X equal minus 1 and plus 1 which is 7 our example so for the attribute color we get a relative preference of 1 over 7 or 14% for memory 4 over 7 or 57% and for delivery to over 7 or 29% now let us compare the conjunct analysis with the analytic hierarchy process AHP the attributes in conjoint analysis correspond to the criteria or sub criteria which are compared in AHP instead of calculating part worth utilities in AHP we calculate the principal eigenvector to find the relative weights in conjoint analysis we code attribute values as levels in AHP we use a ratio scale the ranking corresponds to the evaluation of alternatives now in a conjoint analysis with a full factorial design 2 to the power of K combinations have to be ranked in AHP we need only K square minus K over 2 pairwise comparisons for example with four attributes or criteria there are 16 combinations to be ranked in conjoint analysis but only 6 pairwise comparisons in AHP so the question is can we reduce the number of combinations to be ranked in a conjunct analysis yes we can use a so called fractional factorial design instead of all eight combinations in our example we select half fractional designs have a notation as shown here so finding the part worth utilities we use only two of the four combinations to build the average in each dimension and we come to the same result as for the full factorial design using a fractional design we can reduce the number of combinations as you have seen in this presentation a simple conjoint analysis can be done with linear regression but more complex statistical models and solutions are available

Channel: BPMSG

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Keywords: Conjoint, conjoint analysis, stated preference analysis, linear regression, product management, marketing, part-worth, utilities, relative preference, statistics, analytic hierarchy process, AHP

Id: yiRNcHU2ZGU

Length: 9min 32sec (572 seconds)

Published: Sat Jul 10 2010