**MULTIDIMENSIONAL SCALING**

**TECHNIQUE**

**Introduction**

Multidimensional scaling is a powerful statistical technique used for representing the preferences of respondents into the groups of ‘**Dimensions and Map’**. MDS is useful in measuring the perception and distinctive images of the stimuli used in research. Perceived relationships among stimuli are then represented by means of a visual display using geometric relationships among points in a multidimensional space. The geometric representation is often called spatial maps. It attempts to plot these data in a map; indicating the similarities and dissimilarities as the distances between points .The distance between plotted points in spatial map based on preference data indicate the differences in preferences. The important aspect of MDS is the identification of the **dimensions** of favouring and not favouring the stimuli.

**MDS can be conducted by using similarity data or preference data.**

**Conducting MDS with similarity data**

When the purpose is to determine the grouping of stimuli or objects then the intention is to measure the similarity between the pairs of objects. Similarity judgments are ratings on all possible pairs of stimuli in terms of their similarity using a Likert type scale.

**CASE ANALYSIS-1**

**PROBLEM**

Let us take the example of 8 brands of bathing soap (Lux, Life-buoy, Cinthol, Vivel, Margo, Fiama Diwillis, Breeze and Dettol) available in the Indian market. The purpose is to find out the appropriate number of dimensions the consumers seem to be using, when they think of using bathing soap.

**Method of Data Collection**

Each of sample respondents is asked to judge how similar or dissimilar the product categories are, using 1-7 point likert scale, 1-denoting very dissimilar and 7- denoting very dissimilar. Thus for 8 product categories of bathing soap, pairs are to be judged. These similarity judgments are then presented in a matrix form. A single distance matrix is to be constructed with integral values by averaging consumers’ judgment matrix to an approximated figure. The single matrix of comparison with 28 respondents is as follows.

**Table-1:** MDS Collected data

**INPUT DATA**

The data so collected in pair wise are collated to represent the aggregate dissimilarities between eight bathing soap product categories in the following 8 x 8 data matrix.

The particular distance matrix is treated as input data to be analyzed by SPSS.

**Table-2:** MDS Input data

**Performing the Analysis with SPSS**

For SPSS Version 11, click on **Analyze ⇒****Scale ⇒Multidimensional Scaling. **This will bring up the SPSS screen dialogue box as shown below.

After clicking on **Multidimensional Scaling**, the SPSS screen gives the following dialogue box. Select the variables lux, lifebuoy…….dettol from the list and move them into the variable box.

Select “**Data are distances**” and click on shape, this will show the following dialogue box.

Select the **Square symmetric** and then** Continue **button. This will return us to the **Multidimensional Scaling** dialogue box. Then click **Model**, this will bring up the following dialogue box.

Select **Interval** to specify the level of measurement and type the maximum and minimum dimension. Generally, minimum can be either 1 or 2, and maximum can be 3 or 4 for moderate sample size. The dimensionality can increase with the increase in sample size. Then** Continue **button. This will bring the **Multidimensional Scaling** dialogue box. Then click **Options**, this will bring up the following dialogue box.

Select **Individual subjects plots** and then** Continue **button. This will bring the following **Multidimensional Scaling** dialogue box.

Now click on the button OK in **Multidimensional Scaling** dialogue box. The output so produced is illustrated on the following pages.

**SPSS Output**

**Output-1: Alscal**

**Output -2**

**Interpretation of 3-Dimensional solution**

The SPSS output provides the step-by-step solution history. It can be seen **(output-1)** that there is an improvement (decrease) in Young’s S-Stress as the iterations proceed. The iterations will continue until the last improvement in S-Stress is obtained. The RSQ (squared correlation coefficient between the distances and the data) and Kruskal’s stress index are used as the measures of goodness of fit for the solution. A lower stress value (**0. 09629)** and higher RSQ **(0.89924)** are considered good for solution.

The dimensions are the yardsticks to judge the similarity of the stimuli. The SPSS output-2 generates the dimensions as follows.

On **dimension-1**, Cinthol, Vivel and Breeze have the maximum weightage of (1.2445), (1.3911) and (1.0006), Dettol has the least weightage of (-2.0987). Cinthol is Godrej’s product, Breeze is HUll products and Vivel is ITC’s product, popular for international brand. Both HUL and Godrej are market leaders. Dettol has stood for “trusted production” in India since the 1930’s. The brand Dettol is endorsed by the Indian Medical Association (IMA) and has been listed as India’s Most Trusted Brands in recent years. Looking at their positions, the dimension is named as **“Brand Image”.**

Lifebuoy (1.1223) is leading in **dimension-2** at one end and Fiama (-1.9577) is leading at another end. Lifebuoy is well positioned as “health and hyegine” soap bar. Fiama Diwillis soap bar is famous for great fragrance and good quality. Thus **dimension-2** is named as “**Health and skin care”. **

Vivel and Breeze have the extreme weightage of (1.6634) and (-1.0810) in **third dimension**. Vivel soap bar offers an alternative to consumers with its wide range of products .The soap bar is popular amongst young consumers who are ready to flirt with new brands through its different variants. Breeze soap fulfills the aspirations of women of rural India by offering beauty at an affordable price, making them look and feel beautiful. Thus **dimension-3** is named as **“Beauty Care and value for money”. **

**Output -3**

**Output -4**

**Interpretation of 2-Dimensional solution**

A lower stress value (**0. 09629)** and higher RSQ **(0.89924)** are considered good for solution.

Dettol (1.9077) is leading in **dimension-1** at one end and vivel (-1.5991) at another end. Dettol soap bar is famous for the trusted brand in India and Vivel is popular amongst youngsters for its varieties of products. Thus **dimension-1** is named as “**Brand and Beauty care”. **

On **dimension-1**, Fiama has the maximum weightage (1.7088) in one direction, Breeze (-1.1064) and Lifebuoy (-1.0102) have the maximum weightage at another direction. Thus **dimension-2** is named as “**Health and skin care”. **

**Output -5: Spatial map (3 dimensional solutions)**

It is difficult to interpret the spatial map of 3-dimensional solution. So, it is always advisable to go for the interpretation of 2-dimensional solution of spatial map.

**Output -6: (3 dimensional solutions)**

Finally, the MDS Output-6 provides the scatter plot of fit between the scaled input data (horizontal axis) against the distances (vertical axis). It is important to examine the “scatter” of the objects along a perfect diagonal line running from the lower left to the upper right to assess the fit of the data to the distances. Ideally, when there is a perfect fit, the disparities and the distances will show a straight line of points. As the points go away from the straight line, the fit or accuracy of the map decreases. When stress levels are very low, the points are close to the straight line. The worse the fit (and the higher the stress), the more the points diverge from the straight line. In SPSS Output 6, the “scatter” of the objects shows that the objects have a good fit.

**Output -7: Spatial map (2 dimensional solutions)**

The coordinates used in the map of each object are the coordinates displayed in output-6 for two dimensions. The horizontal axis represents the degree of “**Brand and Beauty care**” that the people are deriving from the usage soap bar. Thus the vertical axis depicts the nature of soap bar in terms of “**Health and skin care**”.

In spatial map, the stimuli closer to each other create the similar image. It can be observed from the map that **‘Breeze’** and **‘Cinthol’** have the similar image and facing stiff competition among them. The soap bar **Dettol **and** Fiama** are placed in high positions along horizontal and vertical axes. **Dettol** soap bar is positioned highly with respect to **Brand and Beauty care **and **Fiama** is perceived as the popular soap bar for** Health and skin care.** It is clear from the map that **“Lifebuoy”** has the unique brand image and has no real competition with others. The same judgment holds for **Margo**, **Vivel** and **Lux **to some extent.

**Output -8: (2 dimensional solutions)**

In SPSS Output- 8, the “scatter” of the objects shows that the objects have a lower degree of good fit in comparison to 3-dimensional solution.

**Interpretation of the Results**

- It is clear from the above discussion that 3-dimensional solution is better than 2-dimensional solution.
- The derived dimensions for soap bar are
**‘Brand Image’, ‘Health and skin care’**and**‘Beauty Care and value for money’.**

**MDS with preference data**

MDS with preference data is meant to measure the selection or rejection of objects or brands. The process makes use of two types scaling techniques — simple ranking system or ordinal scaling technique.

**CASE ANALYSIS-2**

**PROBLEM**

The case undertakes the use of multi dimensional scaling technique in positioning the shampoo brand in Indian scenario. For that purpose eight different product categories of shampoos such as **Sun silk, Dove, Clinic plus, Head & Shoulder, Pantene, Chick, Nyle, Vatika** have been included in the survey. The basic objective is to place the brands of selected shampoos on the ground of consumers’ perception using Multi dimensional scaling approach.

** ****Method of Data Collection**

Each of sample respondents is asked to rank the different brands of shampoo as per their preference using 1-8 rating scale. The data so collected from 25 respondents is given in table-1.

**Table-1:** MDS Collected data

**(1=most preferred and 8=least preferred)**

**Performing the Analysis with SPSS**

For SPSS Version 11, click on **Analyze ⇒****Scale ⇒Multidimensional Scaling. **This will bring up the SPSS screen dialogue box as shown below.

After clicking on **Multidimensional Scaling**, the SPSS screen gives the following dialogue box. Select the variables sunsilk, dove etc. from the list and move them into the variable box.

Select “**Create distances from the data**” and this will show the following dialogue box.

Then select **Eucledian distance** and click **Continue** button, this will bring the Multidimensional dialogue box then click on model; this will show the following dialogue box.

Select **Interval** to specify the level of measurement and type the maximum and minimum dimension. Here, the minimum value is 2 and the maximum is 3. Then click** Continue **button. This will bring the **Multidimensional Scaling** dialogue box. Then click **Options**, this will bring up the following dialogue box.

Select **Individual subjects plots** and then** Continue **button. This will bring the following **Multidimensional Scaling** dialogue box

Now click on the button OK in **Multidimensional Scaling** dialogue box. The output so produced is illustrated below.

** ****SPSS Output**

**Output-1**

**Output-2**

**Output-3**

**Output-4**

**Output-5**

**Output-6**

**Output-7**

**Output-8**

**Interpretation of the output**

The choice of number of dimensions fitting the data is based on the stress value of 2 and 3 dimensional solutions.

Stress value for 3-dimensioanl solution = 0.06297** (Output-1)**

Stress value for 2-dimensioanl solution = 0.14581 (**Output-3)**

Both the stress values are closer to zero, so both are better. But, 3-dimensioanl solution is the best as its stress value is closer to zero. R-square values **(RSQ) **in both the dimensions are more than 0.5, the solutions are acceptable.

The disparities and the distances (**output-6**) show a straight line of points indicating a good fit .In SPSS Output-8 (2-dimensinal solution), the “scatter” of the objects shows that the objects do not have a good fit. So for the present problem 3-dimensional solution is better than 2-dimensional solution.

**Interpretation of results**

**3-DIMENTIONAL SOLUTION**

On **dimension-1**, Sunsilk and Head & Shoulder have the maximum weightage of 2.0330 and 1.1578, Vatika has the least weightage of (-2.1433), Chik and Nyle have the next minimum weightage of (-1.4955) and (-1.2727). HUL launched **Sunsilk** as ‘normal cleaning shampoo’ and Procter and Gamble contributed to shampoo market with its ‘anti-dandruff product’ **Head and shoulder**. **Vatika** shampoo was launched by Dabur with herbal intact and claimed for ‘naturalness in hair’,** Nyle** was launched by Cavin Care and offers benefits through herbal contents and Cavin Care launched** Chik **as popular brand of shampoo among rural Indians. Thus dimension-1 is named as **“Hair care”.**

Dove (1.3612) and Pantene (-1.3138) shampoo are leading in **dimension-2** at two opposite ends. Dove is HUL product and Pantene is P&G product. Both HUL and P&G are leading the market and enjoying their brand image. Looking at their positions, the dimension is named as **“Brand Image”.**

Clinic plus (1.1617) and Dove shampoo (-1.0103) lead in **dimension-3**. Clinic plus is the popular brand and commonly used for all the cleaning purpose. Dove came into existence by HUL as ‘mild soap contents for daily hair care’ with substantially high price. The dimension is so named as **“Value for Money”.**

**2-DIMENTIONAL SOLUTION**

The interpretation of 2-dimensional solution is same as that of 3-dimensional solution.

Sunsilk, Head & Shoulder, Chik, Nyle and Vatika occupy two extreme ends; the dimension is named as **“Hair care”.** Looking at the shampoo categories; Dove and Pantene are getting high scores at two extreme points in dimension-2. Thus the dimension can be named as **“Brand Image”.**

**Spatial map of 2-dimensional solution**

The spatial map of 2-dimensional solution is given in output-6. The shampoo products closer to each other create the similar image in customers’ mind. The product which stands alone is perceived uniquely by the customer. X-axis represents the Brand Image **(dimension-1)** and Y-axis represents Hair care **(dimension-2).**

It is clear from the map that **“Dove”** has the unique brand image and has no real competition with others. The same argument holds for **Pantene** and **Sunsilk** to some extent. **Dove **and** Sunsilk** have the similar image. **Nyle, Chik **and** vatika** are perceived to be similar in product categories.

**SPSS Command**** Conducting MDS with similarity Data**

- Click on ANALYZE at the SPSS menu bar (in older versions of SPSS, click on STATISTICS instead of ANALYZE).
- Click on SCALE followed by MULTIDIMENSIONAL SCALING.
- Select the variables and move them to variable box.
- Select DATA ARE DISTANCES
- Click on SHAPE AND Select the SQUARE SYMMETRIC and then CONTINUE
**.** - Click MODEL of Multidimensional Scaling box and select INTERVAL to specify the level of measurement and type the maximum and minimum dimension.
- Then click OPTIONS and then select INDIVIDUAL SUBJECTS PLOTS and then CONTINUE
- Finally click on the button OK in Multidimensional Scaling dialogue box

**SPSS Command**** Conducting MDS with Preference Data**

- Click on ANALYZE at the SPSS menu bar (in older versions of SPSS, click on STATISTICS instead of ANALYZE).
- Click on SCALE followed by MULTIDIMENSIONAL SCALING.
- Select the variables and move them to variable box.
- Select CREAT DISDANCES FROM THE DATA and select EUCLEDIAN DISTANCE and click CONTINUE
- Click MODEL of Multidimensional Scaling box and select INTERVAL to specify the level of measurement and type the maximum and minimum dimension.
- Then click OPTIONS and then select INDIVIDUAL SUBJECTS PLOTS and then CONTINUE
- Finally click on the button OK in Multidimensional Scaling dialogue box.