Factor Analysis is a management technique or more accurately is a family of techniques which aim to simplify complex sets of data by analyzing the co-relations between them.
Given a set of scores on a number of variable, the co-relation between each of the variable can be calculated and yield co-relation matrix.
Factor analysis is used to uncover the latent structure (dimensions) of a set of variables. It reduces attribute pace from a larger number of variable to a smaller number of factors and as such is a “non-dependent” procedure that is, it does not assume a dependent variable is specify.
Factor Analysis is a designed to simplify the correlation matrix and reveal the small number of factors which can explain the co-relations.
A component on a factor explains the variants in the inter co-relation matrix, and the amount of variants is explained is known as “Eigen Value” of factor.
A factor loading is the co-relation of a variable with a factor. A loading of point 3 or more is frequently taken as meaningful. When interpreting a factor. When deciding a factor signifies, one looks to see which variables have loadings of point 3 or above.
Communality is the proportions of the various in each variable which the factors explain, the higher it is, and the more the factors explain the variables variants.
Exploratory factor analysis is employed to identify the main constructs which will explain the inter co-relation matrics.
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There are a number of considerations to bear in mind before carrying out factor analysis first; the outcome depends on the variable which have been measured and the respondents who yielded the data. Secondly, the number of respondents should not be lees than 100 (here, 135), and there should be at least twice as many respondents as variables (here, variables numbering 24). Thirdly, the respondents should be heterogeneous on the abilities or measures being studied. (Here respondents belongs to works, non works production, non-production area and their grade varies from as high as E-8 to as low as S-2)
In carrying out exploratory factor analysis one should undergone two stages on it. Stage one is the factor extraction process, where in the objective is to identify how many factors are to be extracted from the data. The most popular method for this called “Principal Component analysis”. This is a form of analysis which drives as many components as there are variables, although, these amount of variants explain by each component will decrease as more components are extracted. It is a consequence of the nature of principal component analysis that it will yield a large general factor first. The components obtained in a principal component analysis are un-correlated and emerge in the decreasing order of the amount of variance explained. Although one initially obtaines as many components as there are variables (twenty-four), the aim of factor analysis is to explain the matrix with as few factors as possible. (Output from the principal components analysis).
OUTPUT FROM THE PRINCIPAL COMPONENT ANALYSIS:
Total Variance Explained Table:
It shows the eigen values (total) and percentage of variance explained by each of the initial eigen values. The total of the eigen values equals the number of variables (7.186 + 2.554 + 1.530 + 1.491 + 1.393 + 1.155 + 1.063 + 0.925 + 0.814 + 0.761 + 0.672 + 0.641 + 0.555 + 0.514 + 0.430 + 0.402 + 0.359 + 0.315 + 0.297 + 0.265 + 0.212 + 0.182 + 0.148 + 0.134 = 24 = the number of variables). The percentage of variance is calculated from the eigen values the eigen values of the factor is divided by the sum of the eigen values and multiplied by one hundred. The right hand part of the total variance explained table shows the percentage of the variance explained just for those factors with an eigen value greater than one. This table shown 7 factor with an eigen value greater than 1
Component Matrix:
The component matrix table shows the loading of each of the variables (the co-relation of variable with a factor). On each of the seven factors which were extracted.
The principal component analysis indicated that seven factors underline these scores on variables one to twenty four.
Output from the Principal axis factor method:
The principal axis factor method is identical to principal component analysis method with one exception. In principal component, a value of one is inserted on the diagonal of the inter correlation matrix, but in principal axis method an estimate of communality is used. This is why the Initial Eigen Values Section of Total Variance Explained tables of principal component analysis and principal axis are identical.
Rotation Methods:
Rotation serves to make the output more understandable and it is usually necessity to facilitate the interpretation of factors. The sum of eigen values is not affected by rotation, but rotation will altered the eigen values of particular factors and will change the factor loadings.
Varimax Rotation :
Varimax Rotation is the orthogonal rotation of the factor axes to maximize the variance of the squared loading of a factor (columns) on the entire variable (Rows) in a factors matrix. That is, it minimizes the number of variables which have high loadings on any one given factor. Each factor will tend to have either large or small loadings of particular variables on it. A varimax solution yields results which make it as easy as possible to identify each variable with a single factor.
In deciding, weather to use orthogonal (varimax) factor rotation, one has to do the under lying exercise. Here, application of orthogonal rotation can be seen. The over-riding criterion of simple structure solution is that each factor should have a few high loadings with the rest being zero or close to zero. On this criterion, the solution shown in Rotated Factor Matrix figure is appropriate. Those variables which load at 0.4 or above on factor 1 (one, two, three, four, twenty-one, twenty three) all load less than 0.3 on factors two, three, four, five, six, seven, on the other hand where as variables that have low loading of factor one (eight, nine, ten, twelve, thirteen, fourteen, fifteen, sixteen, seventeen, eighteen, nineteen, twenty). All have quite high loadings. Respectively on factor two, two, five, five, five, three, seven, three, three, five, five, five, three, seven, three, three, six, six, four, and four. In this instance therefore, one could stop at the orthogonal varimax procedure.
INTERETATION:
In rotated Factor Matrix table these factor loadings clearly shows the close relationship of the twenty four variables with the seven underlying factors. Thus, heavy loadings of 76, 69, 64, 51, , 43, 37, 45, (Decimals omitted) against the variables, 1, 2, 3, 4, , 21,22,23 respectively. So that, factor one represents general interest in effective and systematic work culture and believe in total quality management.
Heavy loadings of 72, 82, and 59 against the variables 7, 8, 9 do, that factor ‘2’ represents general interest in profitability gaining out from I.T. networking system.
Heavy loading of 72, 85, 80 against the variables 13, 15, 16. So that factor three represents general interest re-structuring and re-engineering of IT architecture and continual updatation and up gradation of it..
Heavy loading of 45, 44, 63, 54, 48 against the variable 5,6,19, 20, 24; so, that factor four provides general interest in coordination among all the wings of I.T. and looking after its users.
Heavy loading of 65, 59, 65, against the variable 10, 11, 12’ so, that factor five represents general interest in beneficiation arising out from I.T. related functionalisms for stores and works and non-works departments.
Heavy loading of 63, 79, against the variable 17, 18, so that factor six represents general interest in individual perception indexes on availability inspection and checking of hand wares and soft wares.
Heavy loading of 56 against the variable 14; so that factor seven represents general interest in knowing talent of I.T. professionals working in B.S.P..
The extraction column of communalities (Principal axis and varimax rotation) that is how much each variable is accounted for by the seven factors together. A small communality figure (0.186) in variable 22 shows that the seven factors taken together do not account for this variable to one appreciable extent. On the contrary, a large communality figure in rest of the variables is an indication that much of the variable is accounted for the factor.
Finally, the last row in the communality table shows the sum of square (sum of extractions eigen value) that is the relative importance of each factor in accounting for the particular set of variables. The total sum of square as shown in the table is 1, 3, 3, 9 since there are in all 24 variables this figure may be divided by 24. This will yield in 15.79 and with decimal 5.0557 @ 0.056. This is an index showing (as it is more than .03) how well factors accounts for all variables taken together. A high value of Index shows that the variables are related with each other.
JUSTIFICATION OF FACTOR ANALYSIS
According Thurnstone (Multiple factor analysis) factor analysis
may be used especially in these domains where basic and fruitful concepts are essentially lacking and where crucial experiments have been difficult to conceive. In a public sector undertaking like, ORGANISATION, where computerization is taking place very rapidly and where work culture tends to be in intervention way making of crucial experiment is just like entering into the sea without swimming ability. That is way; factor analysis is under taken in this survey.
Total Variance Explained (principal component analysis)
Initial Eigen values Extraction Sums of Squared Loadings
Component
Total % of Variance Cumulative % Total % of Variance Cumulative %
1
7.186 29.941 29.941 7.186 29.941 29.941
2
2.554 10.641 40.582 2.554 10.641 40.582
3
1.530 6.376 46.958 1.530 6.376 46.958
4
1.491 6.213 53.171 1.491 6.213 53.171
5
1.393 5.804 58.975 1.393 5.804 58.975
6
1.155 4.814 63.789 1.155 4.814 63.789
7
1.063 4.429 68.218 1.063 4.429 68.218
8
.925 3.855 72.072
9
.814 3.393 75.466
10
.761 3.172 78.638
11
.672 2.802 81.439
12
.641 2.671 84.110
13
.555 2.311 86.421
14
.514 2.142 88.563
15
.430 1.792 90.354
16
.402 1.674 92.029
17
.359 1.497 93.525
18
.315 1.313 94.838
19
.297 1.238 96.076
20
.265 1.103 97.180
21
.212 .884 98.063
22
.182 .760 98.823
23
.148 .617 99.440
24
.134 .560 100.000
Extraction Method: Principal Component Analysis.
Component Matrix
Component
1 2 3 4 5 6 7
ONE
.705 -.222 .129 6.784E-02 7.139E-02 .297 -.213
TWO
.727 -8.158E-02 -6.864E-02 .171 3.867E-02 .192 -.221
THREE
.693 -.158 7.864E-03 3.095E-02 -.123 .302 -.266
FOUR
.664 -7.000E-02 .119 -.112 -.203 -.149 -.186
FIVE
.702 -.284 -9.746E-03 9.035E-02 -.157 -.243 .195
SIX
.662 -7.790E-02 -7.276E-03 -9.095E-02 9.016E-02 -.283 5.558E-02
SEVEN
.685 7.742E-02 .124 -.478 2.593E-02 .111 2.917E-04
EIGHT
.600 8.106E-02 8.867E-02 -.581 3.030E-02 .182 .124
NINE
.568 2.520E-02 3.969E-02 -.527 -5.071E-02 3.282E-02 -4.746E-02
TEN
.467 .139 -.486 -9.732E-03 -.136 .411 .229
ELEVEN
.678 1.630E-02 -.332 .173 -1.716E-02 .153 .309
TWELVE
.605 -.104 -.417 .138 -.311 -6.671E-02 .233
THIRTEEN
.132 .779 -.237 .110 -1.956E-02 -9.326E-02 -5.190E-02
FOURTEEN
8.813E-02 9.933E-02 .204 .306 .599 .491 .199
FIFTEEN
.122 .859 -.176 6.789E-03 3.469E-02 -4.218E-02 -6.584E-02
SIXTEEN
.122 .843 -6.106E-02 6.614E-03 8.249E-02 -3.692E-02 -.135
SEVENTEE
.307 .425 .573 6.739E-02 -.359 5.801E-02 1.102E-02
EIGHTEEN
.360 .239 .481 .283 -.495 3.021E-03 .173
NINTEEN
.605 .105 .233 -6.132E-02 .412 -.194 .226
TWENTY
.488 5.077E-02 .341 .177 .344 -.179 .336
TWEONE
.602 -.137 -2.559E-02 .373 -7.773E-02 -.172 6.389E-02
TWETWO
.398 -4.175E-02 .132 .323 6.743E-02 9.136E-02 -.497
TWETHREE
.622 -3.700E-02 -.203 .233 .124 -.197 -.195
TWEFOUR
.567 -1.446E-02 -.167 -.101 .349 -.363 -.234
Extraction Method: Principal Component Analysis.
a 7 components extracted.
Total Variance Explained (principal axis method)
Initial Eigen values Extraction Sums of Squared Loadings Rotation Sums of Squared Loadings
Factor
Total % of Variance Cumulative % Total % of Variance Cumulative % Total % of Variance Cumulative %
1
7.186 29.941 29.941 6.759 28.161 28.161 3.170 13.208 13.208
2
2.554 10.641 40.582 2.201 9.171 37.333 2.298 9.574 22.782
3
1.530 6.376 46.958 1.116 4.652 41.984 2.099 8.745 31.527
4
1.491 6.213 53.171 1.079 4.497 46.481 1.989 8.288 39.815
5
1.393 5.804 58.975 .914 3.810 50.291 1.746 7.276 47.092
6
1.155 4.814 63.789 .695 2.897 53.188 1.302 5.424 52.516
7
1.063 4.429 68.218 .598 2.490 55.678 .759 3.163 55.678
8
.925 3.855 72.072
9
.814 3.393 75.466
10
.761 3.172 78.638
11
.672 2.802 81.439
12
.641 2.671 84.110
13
.555 2.311 86.421
14
.514 2.142 88.563
15
.430 1.792 90.354
16
.402 1.674 92.029
17
.359 1.497 93.525
18
.315 1.313 94.838
19
.297 1.238 96.076
20
.265 1.103 97.180
21
.212 .884 98.063
22
.182 .760 98.823
23
.148 .617 99.440
24
.134 .560 100.000
Extraction Method: Principal Axis Factoring.
Communalities
Sum of squares
Initial Extraction
ONE
.662 .745
TWO
.652 .624
THREE
.612 .583
FOUR
.526 .519
FIVE
.676 .622
SIX
.546 .446
SEVEN
.671 .670
EIGHT
.631 .745
NINE
.571 .449
TEN
.545 .551
ELEVEN
.597 .599
TWELVE
.641 .654
THIRTEEN
.541 .544
FOURTEEN
.347 .341
FIFTEEN
.684 .741
SIXTEEN
.632 .666
SEVENTEE
.556 .535
EIGHTEEN
.531 .680
NINTEEN
.594 .624
TWENTY
.396 .456
TWEONE
.479 .441
TWETWO
.323 .186
TWETHREE
.538 .438
TWEFOUR
.526 .506
1339 (decimal ommitted
Extraction Method: Principal Axis Factoring.
Rotated Factor Matrix (varimax with kaizer normalisation)
Factor
1 2 3 4 5 6 7
ONE
.762 .284 -.122 .102 .100 8.242E-02 .204
TWO
.691 .183 4.612E-02 .182 .249 5.044E-02 .113
THREE
.645 .300 -5.781E-02 4.383E-02 .242 .118 2.001E-02
FOUR
.511 .320 1.519E-02 .247 6.728E-02 .173 -.244
FIVE
.408 .188 -.198 .457 .324 .168 -.197
SIX
.346 .310 7.941E-03 .437 .172 3.313E-02 -9.096E-02
SEVEN
.288 .719 7.399E-02 .197 .119 .104 2.326E-04
EIGHT
.116 .822 3.975E-02 .135 .175 7.299E-02 3.801E-02
NINE
.212 .588 3.643E-02 .174 .120 4.478E-02 -.101
TEN
.158 .241 .162 -3.728E-02 .654 -2.442E-02 .111
ELEVEN
.360 .156 8.887E-02 .271 .595 3.119E-02 9.070E-02
TWELVE
.290 .112 -8.084E-03 .226 .654 6.563E-02 -.273
THIRTEEN
-1.028E-02 -1.702E-02 .720 3.671E-02 .130 7.946E-02 -2.471E-02
FOURTEEN
9.349E-02 -4.310E-02 4.918E-02 9.062E-02 -8.131E-03 -8.854E-03 .565
FIFTEEN
-4.424E-02 6.631E-02 .850 1.007E-02 7.373E-02 7.338E-02 3.484E-02
SIXTEEN
6.954E-03 6.919E-02 .801 3.299E-02 -4.722E-02 9.974E-02 7.575E-02
SEVENTEE
.153 .175 .256 4.061E-02 -.104 .634 8.817E-04
EIGHTEEN
.136 3.366E-02 7.541E-02 .113 .131 .790 -1.283E-02
NINTEEN
.180 .321 9.309E-02 .633 4.220E-02 9.394E-02 .260
TWENTY
.132 .143 3.955E-03 .543 7.633E-02 .215 .267
TWEONE
.431 -8.419E-03 -4.419E-02 .377 .283 .167 -5.210E-02
TWETWO
.369 2.818E-02 1.499E-02 .157 6.523E-02 .112 8.613E-02
TWETHREE
.451 7.401E-02 9.441E-02 .390 .250 -3.520E-02 -6.479E-02
TWEFOUR
.375 .231 .140 .480 3.894E-02 -.223 -.103
Extraction Method: Principal Axis Factoring. Rotation Method: Varimax with Kaiser Normalization.
a Rotation converged in 21 iterations.
Factorization of variables according to rotated factor matrics
Factor-1
HRD at ORGANISATION comes to our help in solving people’s problem.
We use this service for debottlenecking typical personal administrative difficulties
HRD at Organisation is an essential business partner contributing to profitability.
The HRD function is managed by people who appear to know their business.
Factor-2:
The software (faculty skills, programme contents and usefulness, methods) is of sufficient standards.
Our HRD function appears to be well prepared for meeting our future needs.
HRD at Organisation appears to be involved in number of games and welfare activities.
Factor-3
HRD at Organisation appears to be committed to bridge the differences between Management & Employees expectations
My team leader always encourages me to take part in HRD activities.
HRD practices take care for Recognition/ Awards/ Rewards for best work done by the employees.
Factor-4
Our workforce is fully enabled to develop and utilize its full potential, aligned with the company’s objective.
ORGANISATION’s high production & productivity and excellent performances are the results of HRD practices.
HRD activities are effective way of communication.
We find the HRD function open to feedback from us.
The infrastructure available with HRD is adequate.
Factor-5
The staff of HRD function practice what they preach.
HRD function at Organisation serves non-executive, executives and fresh entrants in a balanced way.
The staff in HRD is positive and has a helpful attitude for others.
Factor-6
HRIS creates more transparency in the system.
HRD at Organisation appears to be involved in number welfare activities.
A Practical Introduction to Factor Analysis of Management
