In: Statistics and Probability

1. What are the different types of factor analysis and what are they used for in statistics?

Solution :-

**Factor analysis** is a technique that is used to
reduce a large number of variables into fewer numbers of factors.
This technique extracts maximum common variance from all variables
and puts them into a common score. As an index of all variables, we
can use this score for further analysis. Factor analysis is part of
general linear model (GLM) and this method also assumes several
assumptions: there is linear relationship, there is no
multicollinearity, it includes relevant variables into analysis,
and there is true correlation between variables and factors.
Several methods are available, but principle component analysis is
used most commonly.

**Different Types of factor analysis :-**

1. **Principal component analysis**

2. **Common factor analysis**

3. **Image factoring**

4. **Maximum likelihood method**

There are different types of methods used to extract the factor from the data set:

1. **Principal component analysis:** This is the
most common method used by researchers. PCA starts extracting the
maximum variance and puts them into the first factor. After that,
it removes that variance explained by the first factors and then
starts extracting maximum variance for the second factor. This
process goes to the last factor.

2. **Common factor analysis:** The second most
preferred method by researchers, it extracts the common variance
and puts them into factors. This method does not include the unique
variance of all variables. This method is used in SEM.

3. **Image factoring:** This method is based on
correlation matrix. OLS Regression method is used to predict the
factor in image factoring.

4. **Maximum likelihood method:** This method also
works on correlation metric but it uses maximum likelihood method
to factor.

5. **Other methods of factor analysis:** Alfa
factoring outweighs least squares. Weight square is another
regression based method which is used for factoring.

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a.Given the results of the test, which error
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determined)
b. If the study was replicated multiple times,
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