Day 8 Team G

Factor analysis aims to describe a large number of variables or questions by only using a reduced set of underlying variables, called factors. It explains a pattern of similarity between observed variables. Questions which belong to one factor are highly correlated with each other.

Factor analysis is a method of data reduction. This analysis is based on dependent variables and independent variables. For example, Sales of any product is generally dependent on factors like customer satisfaction, marketing speed, product, etc. So in this case, factors like customers satisfaction, marketing speed, product are independent variables, and sales, on the other hand, is dependent variable.

Reasons to perform Factor Analysis

• ·  To reduce the variables and remove the correlation between them, so that we get a better picture of the scenario.
• ·   To see and find the common underlying theme and label them.

There are two types of factor analysis: Exploratory and Confirmatory.

• ·         Exploratory factor analysis is driven by the data, i.e. the data determines the factors.
• ·         Confirmatory factor analysis, used in structural equation modelling, tests and confirms hypotheses.

Factor analysis is often used in customer satisfaction studies to identify underlying service dimensions, and in profiling studies to determine core attitudes. For example, as part of a national survey on political opinions, respondents may answer three separate questions regarding environmental policy, reflecting issues at the local, regional and national level. Factor analysis can be used to establish whether the three measures do, in fact, measure the same thing.

It can also prove to be useful when a lengthy questionnaire needs to be shortened, but still retain key questions. Factor analysis will indicate which questions can be omitted without losing too much information.

Factor analysis is based on the correlation matrix of the variables involved, and correlations usually need a large sample size before they stabilize.  In this analysis, only scale numbers are considered.

Reasons to perform Factor Analysis

• ·    To reduce the variables and remove the correlation between them, so that we get a better picture of the scenario.
• ·        To see and find the common underlying theme and label them.

Conducting Factor Analysis

Analyze Menu> Data reduction > Factor

After we click on factor, the following dialog box appears

String variables are not selected, only scale variables need to be selected. From the Descriptive, we check the Initial solution option. From the Extraction, check Scree plot, and check eigenvalue to be greater than 1.From the Rotation, check Varimax option.

Now after the output file we get, we see the Communalities output.

Communalities Output

In this table, the Initial column shows that the variance for the different variables, and the Extraction column shows that the amount of extraction that is possible from that particular variable. The thumb rule is that if the extraction value for any variable is below 0.5, then we drop it.

After this, we copy the data of one variable, suppose price to excel sheet. And find the average of the entire data and find out the variance from the average. We also find out the standard deviation of the data, which helps us to find the Z score (Variation/Std Dev). The properties of the Z score is that it retains the distribution of the data, and, their mean = 0, and Std. Dev = 1.

Components are made of some amount of variance of all types. In the table ‘Total Variance’, Total resembles Variance.

Component Matrix

Then we come to the Component matrix, it shows the relation of the component with the variable.

Screen Plot

Scree plot helps in choosing the number of components out of the total number of variables. 

Author
Akhil Aggarwal
Team G