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Descripción: FACTOR CAMION USADO EN EL DISEÑO DE PAVIMENTOS
Factor Analysis (DATA REDUCTION TECHNIQUE)
It is not bothered/affected bothered/affected by type of DV and IV
All statements are interval/scale/ratio in nature ie all data has to be numeric in nature
We do not check correlation
When we run FA, to check adequacy of samples, we should have 5 t imes number of responses as compared to variables
Analyse data reduction factor
OUTPUT: 1. Total Variance Explained
Initial Eigenvalues
Compon ent
Total
% of Variance
Extraction Sums of Squared Loadings
Cumulative %
Total
% of Variance
Rotation Su
Cumulative %
Total
1
3.883
38.828
38.828
3.883
38.828
38.828
3.841
2
2.777
27.770
66.598
2.777
27.770
66.598
2.429
3
1.375
13.747
80.346
1.375
13.747
80.346
1.764
4
.945
9.449
89.795
5
.479
4.793
94.588
6
.292
2.923
97.511
7
.117
1.166
98.677
8
.068
.680
99.356
9
.037
.374
99.730
10
.027
.270
100.000
Extraction Method: Principal Component Analysis.
Three factors are explaining variation upto 80.346% 2.
Rotated Component Matrixa
Component 1 I use a 2-wheeler because it is affordable. It gives me a sense of freedom to own a 2-wheeler.
2
3
.126
.313
.780
-.181
-.639
-.107
-.116
.604
.594
.970
-.064
-.006
.964
.131
.063
Low maintenance cost makes a 2-wheeler very economical in the long run. A 2-wheeler is essentially a man’s vehicle.
I feel very powerful when I am on my 2-wheeler.
%
Some of my friends who .945
-.140
.030
.971
.024
.106
-.262
.848
.101
.010
.881
-.044
.063
-.149
.874
don’t have their own vehicle
are jealous of me. I feel good whenever I see the ad for 2-wheeler on T.V., in a magazine or on a hoarding. My vehicle gives me a comfortable ride. I think 2-wheelers are a safe way to travel. Three people should be legally allowed to travel on a 2-wheeler. Extraction Method: Principal Component Analysis. Rotation Method: Varimax with Kaiser Normalization. a. Rotation converged in 5 iterations.
Depending on size of the data, we decide threshold values 05/0.4/0.7 ,more data, less var iation In this data, we choose .7 Interpretation:
The highlighted values are factor loading of variables 4,5,6,7. Factor loading more than 0.7 are c onsidered for analysis We name this factor as “Pride of ownership”
Factor2: combine 8 and 9 which has high loading of 0.85 and 0.87 we call it “Functional values/utility”
Factor3: High loading on var 1,10 we name it “Economical”
3.
BARTLETS TEST OF SPERICITY: We want to prove that correlation is insignificant. Variables can be interrelated but not factors( this is the reason we combine variables in above highlighted table) Ho: correlation is significant H1: Correlation is insignificant
KMO table KMO and Bartlett's Test
Kaiser-Meyer-Olkin Measure of Sampling Adequacy. Bartlett's Test of Sphericity
Approx. Chi-Square df Sig.
.618 164.098 45 .000
P value is less than 0.05 indicates the rejection of hypothesis that correlation matrix of the variables is insignificant. The sample size is five times the number of variables(10), so the sampling adequacy required for factor analysis is also justified, which is not true in this c ase as it has only 20 observations
KMO test is for sampling adequacy. Please note that the KMO statistics is 0.618 indicates that factor analysis can be used for this data KMO ANALYSIS IS MORE THAN 0.5 MEANS THAT DATA IS A DEQUATE AND FA CAN BE USED.
EXCEL— Eigen value for factor 1,2 and 3 is being calculated as sum of square of factor 1,2 and 3 in Component matrix table in output which is same as in the eigen values table Total Variance Explained
Initial Eigenvalues
Compon ent
Total
% of Variance
Extraction Sums of Squared Loadings Cumulative %
Total
% of Variance
Rotation Sums of Squared Loa
Cumulative %
Total
% of Variance
1
3.883
38.828
38.828
3.883
38.828
38.828
3.841
38.409
2
2.777
27.770
66.598
2.777
27.770
66.598
2.429
24.294
3
1.375
13.747
80.346
1.375
13.747
80.346
1.764
17.643
4
.945
9.449
89.795
5
.479
4.793
94.588
6
.292
2.923
97.511
7
.117
1.166
98.677
8
.068
.680
99.356
9
.037
.374
99.730
10
.027
.270
100.000
Extraction Method: Principal Component Analysis.
3.88 is eigen value for factor 1 and so on… % of var explained by factor 1 =eigen value of factor 1 x 100 sum total of all eigen values CALCULATION OF COMMUNALITY: explanation of original variable variance Communality is denoted by
ℎ
2
Comm for 1st variable is 0.72 which means 72% of variance or information content of the first variable is explained by 3 factors.
