Factor Analysis

FACTOR ANALYSIS Presented By Hassan

MULTIVARIATE ANALYSIS Multivariate analysis in statistics describes a collection of procedures which involve observation and analysis of more than one statistical variable at a time All statistical methods that simultaneously analyze to measurements on each individual or object under investigation Multivariate analysis used to measure, explain, and predict the degree of relationship among variates (combination of variables) These analysis are being used widely around the world.

Factor analysis was invented nearly 100 years ago by psychologist Charles Spearman, who hypothesized that the enormous variety of tests of mental ability--measures of mathematical skill, vocabulary, other verbal skills, artistic skills, logical reasoning ability, etc.--could all be explained by one underlying "factor" of general intelligence

FACTOR ANALYSIS

A statistical approach that can be used to analyze interrelationships among a large number of variables and to explain these variables in terms of their common underlying dimensions (factors). Factor analysis is a statistical method used to explain variability among observed random variables in terms of fewer unobserved random variables called factors The statistical approach involving finding a way of condensing the information contained in a number of original variables into a smaller set of dimensions (factors) with a minimum loss of information

FACTOR ANALYSIS  Deals

with the grouping of like variables in sets.

 Sets

are formed in decreasing order of importance.

 Sets

are relatively independent from each other.

 Commonly

used factor analytic technique:

◦ The Exploratory technique ◦ The Confirmatory technique  One

of the most commonly used technique in social and psychological sciences

EXPLORATORY FACTOR TECHNIQUE  This technique deals with exploring the structure of the data.  The

variables involved under the study are equally important.

 Variables

are grouped together on the basis of their closeness.

 This

technique exactly explains the covariances of the variables.

CONFIRMATORY FACTOR TECHNIQUE

• Assessing the degree to which the data meet the expected structure •Confirmatory factor technique is a theorytesting model • It is used to fine the correlation between the variables in the form of matrix called variance/covariance matrix • By searching for the highest correlation among the correlations of a variable with the principal components, we know which variable causes high overall variability in the data

TYPES OF FACTOR ANALYSIS Two main types: Principal component analysis -- this method provides a unique solution, so that the original data can be reconstructed from the results. It looks at the total variance among the variables, so the solution generated will include as many factors as there are variables, although it is unlikely that they will all meet the criteria for retention. There is only one method for completing a principal components analysis; this is not true of any of the other multidimensional methods described here. Common factor analysis -- this is what people generally mean when they say "factor analysis." This family of techniques uses an estimate of common variance among the original variables to generate the factor solution. Because of this, the number of factors will always be less than the number of original variables. So, choosing the number of

EXAMPLE OF FACTOR ANALYSIS

"leadership" has been observed to be composed of "task skills" and "people skills" you are developing a new questionnaire about leadership and you create 20 items,10 will reflect "task" elements and 10 "people" elements, When you analyze your data, you do a factor analysis to see if there are really two factors, and if those factors represent the dimensions of task and people skills. If they do, you will be able to create two separate scales, by summing the items on each dimension. If they don't, well it's back to the drawing board.

EIGENVALUES Eigenvalues are a special set of scalars associated with a linear system of equations(i.e., a matrix equation) that are sometimes also known as characteristic roots, characteristic values (proper values, or latent roots) Eigenvalues are multipliers. They are numbers that represent how much stretching has taken place or, in other words, how much something has been scaled up by. In the sentence 'I am 3.2 times taller than when I was born' the number 3.2 is acting as an Eigenvalue It represents the amount of variance accounted for by a factor

STEPS IN CONDUCTING A FACTOR ANALYSIS There are four basic factor analysis steps: • Data collection correlation matrix

and

generation

of

the

• Extraction of initial factor solution • Rotation and interpretation • Construction of scales or factor scores to use in further analyses

ADVANTAGES OF FACTOR ANALYSIS • Factor Analysis can be used to identify the hidden dimensions or constructs which may or may not be apparent from direct analysis. • It is fairly easy to do, inexpensive, and accurate • It is based on direct inputs from customers • There is flexibility in naming and using dimensions • Data reduction. • Construct a test instrument

ADVANTAGES OF FACTOR ANALYSIS • Discover and summarize pattern of intercorrelations among variables.

• Reduction of number of variables, by combining two or more variables into a single factor eg: performance at running, ball throwing, batting, jumping and weight lifting could be combined into a single factor such as general athletic ability

DISADVANTAGES • Usefulness depends on the researchers' ability to develop a complete and accurate set of product attributes - If important attributes are missed the value of the procedure is reduced accordingly • Naming of the factors can be difficult - multiple attributes can be highly correlated with no apparent reason. • If the observed variables are completely unrelated, factor analysis is unable to produce a meaningful pattern • If sets of observed variables are highly similar to each other but distinct from other items, Factor analysis will assign a factor to them. It is not possible to know what the 'factors' actually represent; only theory can help inform the researcher on this

Example of Factor Analysis Suppose many species of animal (rats, mice, birds, frogs, etc.) are trained that food will appear at a certain spot whenever a noise--any kind of noise--comes from that spot. You could then tell whether they could detect a particular sound by seeing whether they turn in that direction when the sound appears. Then if you studied many sounds and many species, you might want to know on how many different dimensions of hearing acuity the species vary. One hypothesis would be that they vary on just three dimensions--the ability to detect high-frequency sounds, ability to detect low-frequency sounds, and ability to detect intermediate sounds. On the other hand, species might differ in their auditory capabilities on more than just these three dimensions. For instance, some species might be better at detecting sharp click-like sounds while others are better at detecting continuous hiss-like sounds

THANK YOU