Overview

Positioning analysis software incorporates several mapping techniques that enable firms to develop differentiation and positioning strategies for their offerings/products. By using this tool, managers can visualize the competitive structure of their markets, as perceived by their customers. Typically, data for mapping include customer perceptions of existing offerings (and new concepts) along various attributes, customer preferences for offerings, and measures of the behavioral responses of customers toward the offerings (e.g., current market shares).

Positioning analysis uses perceptual mapping and preference mapping techniques. Perceptual mapping helps firms understand how customers view their offering(s) relative to competitive offerings. The preference map plots preference vectors for each respondent on a perceptual map. The ideal point represents the location of the (hypothetical) offering that most appeals to a specific respondent. The preference vector indicates the direction in which a respondent’s preference increases. In other words, a respondent’s ideal offering is as far up the preference vector as possible. 

Positioning analysis also helps firms answer such questions as: 

• How should we position our new product with respect to existing products in the market?
• According to customer perceptions, which target segments are the most attractive for our brand?
• How do our customers view our brand, relative to other brands?
• Which brand is most closely associated with the attributes that our target segment perceives as desirable?
• Which brands do our target segments consider to be our closest competitors?
• What category attributes are most responsible for the perceived differences among offerings/brands?

Getting Started

The Positioning model allows you to either use preloaded data or upload your own data directly into Enginius. Because the positioning model requires a specific data format, users with their own data should either use the Enginius Template feature to create a template to enter your data or review the data set included with this tutorial to become familiar with the appropriate data structure.

Creating a template

The template feature can be found by clicking the “Templates” dropdown in the left column of the Dashboard and selecting the Positioning option. The template set up options include:

Perceptual data

• Number of objects (e.g. brands): Creates a column for each object in the Perceptual data data block. Enter as many columns as there are brands (or stimuli) to be compared. 
• Number of attributes: Provides a row for each attribute’s average rating. Enter the number of attributes (rows) along which the brands will be compared (e.g., price, quality, design, safety, power, service quality).

Preference data

• Include preference data: Creates an additional data block for entering respondent preferences.
• Number of respondents (only available if “Include preference data” is selected): Enter the number of respondents (customers) who are included in the data.
• Include segment membership (only available if “Include preference data” is selected): Creates an additional column that is appended to the Preference data table.  If used and populated, Positioning will display Segment vectors on the perceptual map.  Note: Positioning does not provide the functionality to determine the needed segments.  Segment assignments should be made using the Segmentation model, and those Segment Membership results should then be copied under the segment column.. 
• Include current market shares (only available if “Include preference data” is selected): Creates an additional data block where you can enter existing market shares for each brand.

Note: the check box at the bottom of the dialog box will cause the template to populate with sample (random) data that will allow you to run positioning immediately so you can see the type of output produced. 

After selecting the desired model options, click “Run” to generate the data collection template containing the appropriate data blocks for your analysis.

Data block options

A positioning analysis consists of at least one data block containing perceptual data. Preference data and Current market shares data blocks are optional:

• Perceptual data describe the market space occupied by various offerings or offerings, as perceived by customers in the target segment(s).  These data do not necessarily describe the attributes of an offering; rather, they refer to customer perceptions of the offerings along those selected attributes. For example, they indicate how the target market perceives Volvo on the “Safety” dimension (but not actual safety ratings of Volvo cars).
• Preference data summarize customer preferences for the various offerings, and therefore, clarify whether a customer prefers Offering A or Offering B.  Preferences may translate into purchases of the preferred offerings if no constraints (e.g., budget) prevent customers from expressing their preferences through purchase.  If preference data are not available, in some cases, you may substitute past purchase or market share data to represent customer or segment preferences.
• Market share -

To apply positioning analysis, you can use your own data directly or one of the existing Enginius data sets.  Under both options, the first row contains column headings for the offerings, and the first column contains attribute labels and/or identifiers denoting each respondent/customer.

Perceptual data

Data consists of attributes (rows) along which the offerings will be compared (e.g., price, quality, design, safety, power, service quality). This option is enabled only with perceptual data.

Preference data

Data consists of preferences of respondents (customers) for the same offerings used in the perceptual data.  Inclusion of preference data for analysis is optional, but the software is most useful when we do include such data.

In some cases, you may have partitioned respondents into different segments.  If so, you may include the segment assignment data for each respondent as shown below.  The remainder of this tutorial will use output with Segments included.

Current market shares

NEED DESCRIPTION 

The above examples are from the Example/OfficeStar data on Enginius.  You may also use data you have prepared on your computer (using Excel, for example) and copy/paste the data into new data blocks that you can create on Enginius.  If the data you create is to be used in further analyses, you may save the data under your personal account on Enginius.  For further information on data storage/manipulation on Enginius, please refer to the online video tutorial found at www.enginius.biz.

Running Analysis

To analyze the data you have selected, simply click on the RUN POSITIONING ANALYSIS link found on the Enginius Dashboard under QUICK LINKS.  The following menu will appear to allow you to make the selections for analysis.  The remainder of this tutorial was generated with the settings shown below.

Options

You may select the Perceptual Data block from the drop-down box shown above.  If Preference data is to be included in your analysis, please check the Check Box “Include preference data” and make the appropriate data selection using the drop-down box.  If you have segment-assignment data for your respondents and want to include the segment-level analysis, create a data block similar to the one named Preference data with segments.  Once done, check the box Segment Preference data, and select the appropriate data block.  Finally, use the drop down in the Column with segment id and select the appropriate column of the data that defines the segment assignments.  

You can also choose the “Automatic” option under “Segment preference data” if you would like Enginius to automatically determine the segment structure of the preference data.  Enginius will then use Ward’s Hierarchical segmentation and/or the K-means segmentation tools (see tutorial on segmentation module in Enginius) to automatically determine the segment structure and assign each respondent to the appropriate segment. Ward’s hierarchical segmentation is used for data sizes up to 2,000 respondents.  For larger data sizes, the default segmentation tool applied is K-Means. 

Use the drop-down menu for the Decision Rule you would like to use for the analysis.  If you choose the First-Choice rule, you are specifying that customers will only choose the offering they prefer the most.  This First-Choice rule typically applies if the offerings fall in the high-involvement purchase category for the customer (e.g., high-price, high social-relevance, infrequently purchased, etc.). If you choose the Share-of-Preference rule, you are specifying that the customer will choose each offering in the set of offerings in proportion to how much they prefer that offering relative to their preferences for the other offerings.  This decision rule typically applies if the offerings fall in the low-involvement purchase category (frequently purchased products, low-priced items, etc.).

You may choose to specify the number of dimensions for the positioning map (2-D or 3-D) or allow Enginius to automatically determine the number of dimensions to use for displaying the positioning map.  Note:  If you wish to do “interactive re-positioning” of a focal offering, along with market share calculations associated with such re-positioning, you should select the “3 dimensions” analysis option. 

You may also specify a Focal Offering which will highlight that offering within the generated report.

After making the desired, selections, press the “Run” icon and analysis will begin.  When analysis is complete, the following dialog box will appear:

Click “Show Report” and the Positioning Analysis report will open in a separate tab within your browser.

Interpreting the Results

­­The report generated by Positioning module contains several sections, as described below.

Dimensions

This section of the report explains how many dimensions were retained and what percent of the variance is described by the analysis.  When deciding whether to retain two or three dimensions, you should choose three dimensions only if the third factor captures significantly more variance (compared with the first two). In the OfficeStar example, the first two factors capture 97.7% of the variance in the initial data, and adding a third factor captures only an additional 2.3%. 

Cumulative variance explained (shown for the 2-D map)

Cumulative variance explained. The first 2 dimensions account for 97.7 % of the variance in the data.

3-D Visualization             

If you have requested three dimensions, the interactive portion of the map will be generated.  The screen capture below shows a static image of the map, with text below the image to explain the options available to the viewer. 

There are several different visual representation of the map, including 2-D renditions of 3-D maps.  Each component is shown and described below.  The full capabilities of this software are best understood when using the 3-D maps in the web page report format.

In the interactive Map display, you can choose to view the positioning map along any of the three available axes (X-Y, X-Z, Y-Z) options by clicking on one of them (1).  The various check boxes (2) will display or suppress attributes, preferences, etc. along the displayed axes.  By using the mouse, you can also rotate the the map about the origin along any orientation. to get other views in addition to the three default display options. 

You will also see the Market Shares realized by each offering displayed in the map next to the offering name.  An offering’s position on the map may be manipulated (i.e., changed) by using the Objects option as shown in the map below to change an offering’s value along any attribute.  When you make changes to an offering’s position, its realized market share (according to the decision rule you have chosen) will also be displayed on the 3-D map.

In the Objects interactive display (1) below, you can select the offering you would like to modify (2) and then move the attribute sliders (3) to see which attribute changes would improve an offering’s performance (in terms of market share) relative to the competitors.  Please note that near each offering, the market share percentage is also displayed:

Objects

This section of the report presents maps of the offerings (brands, in this case) analyzed.  Positioning analysis can produce either two- or three-dimensional maps. If you select the 2-D map option the maps will be displayed two dimensions at a time. When you view the final results of the mapping analysis for the 2-D analysis, the software will only display a two-dimensional view showing the first two axes, X and Y.  The three-dimensional map is represented in three charts that show pairwise representations of the three axes, namely (X,Y), (X,Z), and (Y,Z).  

When interpreting the maps, keep in mind:

• The distances between offerings on the map indicate their perceived similarities.  Offerings that are close together are perceived to be similar to each other, whereas those that are far apart are perceived as being different. 
• The axes of a perceptual map are the aggregated dimensions (also referred to as latent or composite attributes) along which customers tend to discriminate the offerings. Attributes aligned close to each axis provide clues to the meaning of that axis.  The variance explained by each axis indicates the relative importance of that axis for explaining customer perceptions.  If the variance explained by the horizontal dimension is 67% and the variance explained by the vertical dimension is 31%, the horizontal dimension is twice as important in explaining customer perceptions.

Attributes

This section of the report presents another map similar to the one above but adds the orientation of each attribute on the map in relation to the offerings.  Again, if more than 2 dimensions are required or specified, 3 maps will be generated.

For interpreting the above maps, note: 

• The lines on a perceptual map indicate the direction in which an attribute increases while moving away from the origin along that line.  For example, if the “Service quality” attribute uses a 1–9 scale, in which 9 represents the highest quality, then service quality increases along that line and away from the origin.
• The length of a line on the map indicates the variance in that attribute explained by the perceptual map. The longer a line, the greater is the importance of that attribute in differentiating among the offerings in the market.
• To position an offering on any attribute on the map, you can draw an imaginary perpendicular line from the offering to the attribute. The farther an offering is from the origin along the direction of that attribute, the higher is the rating of the offering on that attribute.
• Note that if an attribute (e.g., convenience) uses a reverse scale measure (e.g., higher numbers represent lower convenience), the offerings have progressively poorer screen displays as they move along the related attribute vector, away from the origin.
• To interpret an axis/dimension, Enginius also offers the following summary that shows which attributes are most aligned with an axis (either in the positive (green) or negative (red) direction):

Dimension interpretation. Displays the names of the attributes most aligned with each dimension

Preferences

This section of the report shows an additional chart, adding respondent preferences to the offerings and the attributes shows in the previous charts.

To interpret the preference vectors, note:

• The blue lines on a joint-space map with a vector preference model indicate the preference vectors of the respondents (customers). Preference increases in the direction of the vector away from the origin. The length of the vector indicates the variance in that customer's preferences that is explained by the map. The longer the vector, the better the map captures the preferences of that respondent.

Enginius also displays the average preference values in each segment (if the preference segmentation option was chosen for analysis).

Market shares

This section of the output (below) shows simulations of the market share a new offering would achieve.  In each 2-D map, the new offering is assumed to be in the center of the map on the 3^rd dimension (if a 3-D map option was selected).  It is also assumed the existing offerings will remain in the market and will compete with the new offering.

Perceptual Data

This section of the report summarizes the perceptual data to help interpretation of the maps.  For example, it summarizes the average perceptions of each offering in the marketplace along each attribute (the perceptions of the offerings are assumed to be common for all segments).

Technical Appendix

Generation of perceptual map

The input data for the perceptual map is an m by n matrix S, where m is the number of attributes and n is the number of offerings.  Note that S is the row-standardized version of the raw data matrix (row-standardization ensures that mere changes in the scale by which an attribute is measured does not change the perceptual map).  We first obtain the singular value decomposition of S = UBV¢  where V is an n x n matrix which contains the orthonormal basis vectors for S(these are the eigenvectors of S'S), U is an m x m matrix containing the orthonormal basis vectors of SS'.  The diagonal matrix B is of size m x n, and its diagonal entries consist of the singular values of S, or equivalently, the square roots of the eigenvalues of SS' and S'S and its off-diagonal entries are equal to 0(note that the term eigenvalues only applies to square matrices).  That is, B contains the ordered non-zero square roots of the eigenvalues of SS' and S'S. 

The perceptual map is obtained as follows:  Compute U and B but retain only the first r columns of these matrices for further analysis.   The reduction in the dimensionality of the matrices from m or n to r (which is typically set to 2 or 3) results in a map displayed in 2 or 3 dimensions).  The reduction in the dimensionality of the data leads to some loss of information, but most of that loss should be random variations, and not systematic differences between the offerings.  Thus, in V¢  we only need the first r rows for further analysis.  With these restrictions, we get the Least Squares approximation to S which is equal to S* = (UB)_r(V¢)_r.  Note the size of S* is still equal to m x n (i.e., the dimensionality of the matrix S* is given by m x r x r x r x r x n = m x n).  In the map the first r columns of V represent the location of the offerings, and the first r columns of UB represent the attribute vectors where r is the dimensionality of the map. 

Generation of joint-space map (that includes perceptions and preferences)

We incorporate preferences within a perceptual map via a process akin to the “External Analysis” option in PREFMAP3 (Green and Wind 1973; Muelman, Heiser, and Carroll 1986).  The cited references provide detailed technical description of this method, which we do not repeat here.  External Analysis mapping assumes that though a group of individuals have common perceptions of a set of offerings (i.e., their “average perceptions”), they may have widely differing preferences for these offerings.  For example, some consumers prefer sporty cars, whereas others prefer sedans, although both have the perception that a Porsche 911 is a sporty car.  The PREFMAP3 model superimposes the preferences of an individual onto a common perceptual map that is typically derived from the same set of individuals for whom we have perceptions data.  Thus, the key concept here is that preferences in the target segment are a function of a common underlying set of dimensions as determined by the perceptual map. 

Given a perceptual map (i.e., the location of the offerings and the attribute vectors), in the second step, we introduce “preference vectors” on the map, one for each individual, such that an individual’s preference vector has maximal correspondence between their stated preference ratings (or rankings) for the offerings, and the preference relationships between the offerings as recovered from the map.  This is achieved through a “preference regression” model estimated for each individual to identify the direction and length of the preference vectors.   Thus, everyone in the sample is represented by a unique preference vector, starting at the origin, with their preferences increasing in the direction of the preference vector.  The length of the preference vector denotes the proportion of the variance in the preference ratings of the individual that is captured within the map (R² from the preference regression model). 

Converting preferences into market shares

We can convert preferences into market shares using various types of “choice rules” that specify how people translate their preferences into choices/purchases in the marketplace.  Two choice rules are widely used, (1) first-choice (or maximum utility rule), and (2) share-of-preference rule.  Under the first-choice rule, individuals are assumed to act by choosing the offering that they prefer the most.  Under the share-of-preference rule, individuals are assumed to act probabilistically, choosing every offering in proportion to how much it is preferred compared to the other offerings (i.e., relative to the sum of preferences for all offerings available to them).  The first-choice rule is likely to apply most to high-ticket items, and other types of “high-involvement” purchase decisions.  The share of preference rule is likely to apply most in the case of low-ticket items or low-involvement purchases.   The market shares for each offering can be computed for each individual and aggregated across individuals to obtain an overall market share for each offering (these are the market shares shown on the 3-D interactive map).

Reverse mapping

Once we obtain a perceptual map, we can do certain types of manipulations that add considerable value to positioning analysis. (1) Alter the position of an offering on the map and see the corresponding changes in S*.  (2) Alter the attribute values of an offering in the data and see the corresponding changes on the map.  (3) Introduce a new offering by directly positioning it on the map and determine the corresponding attribute values.  (4) Introduce a new product via specification of its attributes, and then see the position of the new product on the map.  In all these cases, we can continue to estimate market share corresponding to any position.  We describe below the second of these manipulations, which is implemented within the 3-D interactive map in Enginius.

Altering the attribute values of an offering (S*)

We can determine the change in the map for a change in one or more attribute values for an offering j.  From the SVD equation S = UBV¢ , we get the following formula with some re-arrangement:.  (In deriving this result, we use the fact that the inverse of an orthonormal matrix is its transpose).   Note that is straightforward to obtain -- on its diagonal, it contains the reciprocals of the diagonal values of B, and the other entries are equal to 0.  To compute v_j, we only need the first r columns of and the first r rows of U¢ (equivalently, r columns of U). Note that the dimensionality of v_j is r x 1 (=r x r x r x m x m x 1).  

The formulae for s_j and v_j allow us to go back and forth between the original data S and the map V.  These formulae are not perfect because of the loss of information due to the fact we use only r dimensions, but the matrices preserve the relationships between the original data and the map we have derived.  Perturbations to data in singular value decompositions typically result in smooth changes (unlike in nonlinear mapping).   The corresponding changes in market shares are computed by assuming all other offerings stay in their original locations, and only the focal offering j has changed its location on the map. 

References

Green, Paul E., and Yoram J. Wind (1973), Multiattribute Decisions in Marketing, The Dryden Press, Hinsdale, IL.

Muelman, J., Wilhelm Heiser, and Carroll J. Douglas (1986), “PREFMAP-3 User’s Guide, Bell Laboratories, Murray Hill, NJ.