01/09/2016
How to do Factor analysis in SPSS
Factor Analysis is frequently used to develop questionnaire. After all if researcher want to measure ability or trait, Researcher need to ensure that the questions asked relate to construct that researcher intend to measure. More over factor analysis is used to reduce the large number of items into small number of factors.
Check List before Executing Factor analysis
Sample Size: Correlation coefficient fluctuates from sample to sample much more so in large sample to small sample. Therefore the reliability of factor analysis is also dependent on sample size. Field (2005) review many suggestions about the sample size necessary for factor analysis and concluded that it depends on many things. In General above 300 cases is probably adequate but commonalities after extraction should probably be above 0.5.
Data Screening: SPSS will nearly always find a factor solution to set of variables. However the solutions is unlikely to have any real meaning if the variable analyzed are not sensible.
What are expecting at your end?
Before conducting factor analysis
Look at the Inter- correlation of variable. If our test questions underlying the same underlying dimensions then we would expect them to correlate with each other.
If you find any variable that do not correlation with other variables then you should consider that variable for exclusion from analysis.
The correlation between variable can be checked through correlation procedure in SPSS. However the correlation matrix is also part of Factor analysis Output.
Extreme Multi- co linearity should be avoid as Multiple regression
Singularity should be avoided. Singularity cause problem in factor analysis, because it become impossible to determine the unique contribution to factors that are highly correlated.Look at the interrelation of variables you should ensure that variable have roughly normal distribution and are measure at internal. The assumptions of normality are important only if you wish to generalize the results of your analysis beyond the sample collected.
Running the analysis.
Note: Exclude any variable that were identified as problematic during data screening.
Access the Main dialogue Box by using Analyze => Data reduction => Factor menu path.
Select all variable you want to include in analysis.
There are several options available which can be access in the following order.
Descriptive
Check the Following items and uncheck the remaining items.
Univariate descriptive
Coefficient : This Option produce the R-Matrix
Significance levels: This will produce significant values of each correlation in R matrix.
Determinant: this Option is vital to checking multicollinearity or singularity. The Determinant of R – Matrix should be greater than 0.00001. if it is less than the said value , you should go through the R-Matrix to check for high correlated values and consider eliminate one or more variable depends on extent of the problem. The choice of eliminating variable is fairly arbitrary and finding multicollinearity in date should raise the questions of choice of items with in your questionnaire.
KMO and Bartlett’s Test of Sphericity: it will measure Kaiser –Meyer –Olkin measure of sample adequacy and Bartlett’s test. The value of KMO should be greater than 0.5 if the sample is adequate.
Extractions :
Click on extraction
Principal component Analysis (By Default) – Mostly used.
Check:
Un-Rotated Factor Solution. The un-rotated solution is assessing improvement of interpretation due to rotation. If the rotated solution is little better than un-rotated then is possible that inappropriate rotation method has been used.
Scree Plot: it is vital in finding the Useful way of establishing how many factors should be retained in analysis.
Eigen Value (In extract Box): The extract box provides options pertaining to retention of factors. You have the choice of either selecting factors with Eigen value greater than user -specified value or retaining fixed numbers of factors. For Eigen value over option Kaiser Recommendations of Eigen value over 1. It is probably best to run primary analysis with Eigen value over 1. Select a scree plot and Eigen value over 1 and compare the Results.
If Looking at Scree plot and Eigen Value over 1 leads you to retain the same numbers of factors then continue with the analysis.
If two Criteria give different results and examine the communalities and decide yourself which criteria to believe.
If you decide to choose Scree plot, then you may redo the analysis and specify the number of factors to retain/extract which is specified in extract box plot with space provided.
Rotations
The interpretability can be improved through rotation, Rotation maximize the loading of each variable on one of the extracted factors whilst minimizing the loading on all other factors. Rotation Work through changing the absolute value of the variable whilst keeping their differential values constant.
Click on Rotation tab to access the rotation dialogue box.
Score: This option allow you to save factor Score for each subject in data editor. These Score can be used for further analysis or identify the group of the subject who score highly on particular factor.
Options: In tab, SPSS Will list all variable in order in which they are entered into data editor by default. However this format is often convenient when interpreting factor it can be useful to list variables by size. By select by size SPSS will order the variable by factor loading. There is also option to surpass absolute value less than a specified value of +/- 1 by default. You can change it to 0.3 or .4 (recommended).
Interpreting Output From SPSS
Preliminary Analysis
SPSS output 1 will Show reduce version of R- matrix, the Top half of the table contains the Pearson coefficient correlation between all pairs of questions where as bottom half contain one tail significant of these coefficients.
We can use correlation matrix to check the pattern of relationship. First Scan the significance value and look for any variable for which majority values are greater than 0.05. Then scan the correlation coefficient themselves and look for value greater than 0.90. if there is value like that that you should aware, that there is a problem and it can raise a problem of singularity , check the determinant of correlation matrix If necessary eliminate one of the two variable which are causing Problem . The Determinant of correlation matrix will be listed at the Bottom of Output -1
Output -2: SPSS output -2 shows several very important parts of output. The Kaiser –Meyer-Olkin measure of sampling adequacy and Bartlett’s test of Sphericity. The KMO Statistics varies between 0 and 1. A Value of 0 Indicates that Sum of partial correlation is large relative to the Sum of Correlations indicating diffusion in pattern of correlation. A value close to 1 indicates that pattern of correlation are relative compact and factor analysis should yield distinct and reliable factor. Kaiser (1974) recommended that accept value above 0.5 and value below should lead you to either collect more data or re-think which variable to include.
As for as Bartlett test are concerned, its measures to test the null hypothesis, that original correlation matrix is identity matrix. In factor analysis we need some relationship between variables and if R-matrix is an identity matrix then all correlation co-efficient would be zero. Therefore we want this test to be significant and have a significance value less than 0.05.
Output -3
Factor Extraction (Total variance explained).
In this output SPSS list Eigen value associated with each linear component (factor) before extraction. We know that there should be as many Eigen Vector as there are variable so there should be as many factor as variable. The Eigen Value associated with each factor represents the variance Explained by those particular linear components.
In this output First few factors will explain relative large amount of variance while subsequent factors explain small amount of variance.
SPSS then extract factor with Eigen value greater than 1, which leave us the amount to factor which should be composed to extent of research. These Eigen Values associated with this factor will be displayed again in extraction sum of Square loading. The values in table are the same as value before extractions except the discarded factors.
In the Final Part of the table labeled as Rotation Sum of Square loading. The Eigen value after the rotations will be displayed. One of effect of rotation is it optimize the factor structure and one consequences of this step is relative importance of the factors is equalized.
(You can check the variance of rotation of squared loading and Extraction Sun of squared loadings)
SPSS Output 4
This Output is about component matrix before rotation. This output contain the loadings of each variable onto each factor, by default SPSS display all loadings, but you have to tell SPSS ,that Suppress the loadings value less than .40 or according to researcher choice, but most research set the Suppress loading values to .40. This output matrix is not particular important for interpretation.
Scree Plot
The Scree plot is Use to compare the extracted factor through component matrix and by scree plot. If the sample size is very large and both criteria given different results and research can redo the analysis by Specify the exact numbers of factor to be extracted in SPSS and then compare the results of Eigen value and exact factor extracted.
Output -5
Factor rotations (rotated Component Matrix)
In this output look into the contents of the question that load onto same factor and try to identify themes and develop a constructs. If mathematical factor produce by analysis represent some real world constructs then common theme among highly loading questions can help researcher identify what construct might be.
