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Perform principal factor factor analysis on a covariance matrix or data matrix.

Usage

factorScorePfa(x, factors = 2, covmat = NULL, cor = FALSE, 
rotation = c("varimax", "none"), 
scoresMethod = c("none", "regression", "Bartlett"))

Arguments

x

A numeric matrix or an object that can be coerced to a numeric matrix.

factors

The number of factors to be fitted.

covmat

A covariance matrix, or a covariance list as returned by cov.wt. Of course, correlation matrices are covariance matrices.

cor

A logical value indicating whether the calculation should use the covariance matrix (cor = FALSE) or the correlation matrix (cor = TRUE).

rotation

character. "none" or "varimax": it will be called with first argument the loadings matrix, and should return a list with component loadings giving the rotated loadings, or just the rotated loadings.

scoresMethod

Type of scores to produce, if any. The default is "none", "regression" gives Thompson's scores, "Bartlett" gives Bartlett's weighted least-squares scores.

Details

Other feasible usages are:

factorScorePfa(factors, covmat)

factorScorePfa(x, factors, rotation, scoresMethod)

If x is missing, then the following components of the result will be NULL: scores, ScoringCoef, meanF, corF, and n.obs.

Value

An object of class "factorScorePfa" with components:

call

The matched call.

loadings

A matrix of loadings, one column for each factor. This is of class "loadings" if rotation = "varimax": see loadings for its print method; It is a plain matrix if rotation = "none".

communality

The common variance.

uniquenesses

The uniquenesses/specific variance computed.

covariance

The robust/classical covariance matrix.

correlation

The robust/classical correlation matrix.

usedMatrix

The used matrix (running matrix). It may be the covariance or correlation matrix according to the value of cor.

reducedCorrelation

The last reduced correlation matrix.

factors

The argument factors.

method

The method: always "pfa".

scores

If requested, a matrix of scores. NULL if x is missing.

scoringCoef

The scoring coefficients. NULL if x is missing.

meanF

The sample mean of the scores. NULL if x is missing.

corF

The sample correlation matrix of the scores. NULL if x is missing.

scoresMethod

The argument scoresMethod.

n.obs

The number of observations if available. NULL if x is missing.

center

The center of the data.

eigenvalues

The eigenvalues of the usedMatrix.

References

Zhang, Y. Y. (2013), An Object Oriented Solution for Robust Factor Analysis.

Author

Ying-Ying Zhang (Robert) robertzhangyying@qq.com

Examples


data(stock611)
R611 = cor(stock611[,3:12]); R611
#>               x1           x2         x3         x4          x5           x6
#> x1   1.000000000  0.993167953 0.97034436 0.95609585 0.025163276 -0.015083014
#> x2   0.993167953  1.000000000 0.98346739 0.97164822 0.045110192 -0.004994507
#> x3   0.970344358  0.983467387 1.00000000 0.99749137 0.108682670  0.019464360
#> x4   0.956095848  0.971648219 0.99749137 1.00000000 0.133591430  0.029278642
#> x5   0.025163276  0.045110192 0.10868267 0.13359143 1.000000000  0.575741829
#> x6  -0.015083014 -0.004994507 0.01946436 0.02927864 0.575741829  1.000000000
#> x7   0.009780105  0.014165548 0.03527696 0.04429804 0.326885328  0.013993207
#> x8   0.017155253  0.036225902 0.09193857 0.11691517 0.840607798  0.298489402
#> x9   0.905256744  0.898571356 0.91651307 0.91138685 0.041581017 -0.009413168
#> x10  0.989449715  0.989605604 0.97531937 0.96400047 0.001814838 -0.046691411
#>              x7         x8           x9          x10
#> x1  0.009780105 0.01715525  0.905256744  0.989449715
#> x2  0.014165548 0.03622590  0.898571356  0.989605604
#> x3  0.035276960 0.09193857  0.916513072  0.975319373
#> x4  0.044298039 0.11691517  0.911386851  0.964000474
#> x5  0.326885328 0.84060780  0.041581017  0.001814838
#> x6  0.013993207 0.29848940 -0.009413168 -0.046691411
#> x7  1.000000000 0.35473163  0.012122296  0.007367798
#> x8  0.354731631 1.00000000  0.010355218  0.016828080
#> x9  0.012122296 0.01035522  1.000000000  0.911435130
#> x10 0.007367798 0.01682808  0.911435130  1.000000000

## covmat is a matrix
fsPfa1 = factorScorePfa(factors = 3, covmat = R611); fsPfa1
#> $call
#> factorScorePfa(factors = 3, covmat = R611)
#> 
#> $loadings
#> 
#> Loadings:
#>     Factor1 Factor2 Factor3
#> X1   0.987                 
#> X2   0.992                 
#> X3   0.993                 
#> X4   0.982                 
#> X5           0.809   0.627 
#> X6           0.123   0.758 
#> X7           0.440         
#> X8           0.839   0.257 
#> X9   0.919                 
#> X10  0.992                 
#> 
#>                Factor1 Factor2 Factor3
#> SS loadings      5.739   1.582   1.041
#> Proportion Var   0.574   0.158   0.104
#> Cumulative Var   0.574   0.732   0.836
#> 
#> $communality
#>        X1        X2        X3        X4        X5        X6        X7        X8 
#> 0.9750545 0.9851462 0.9910436 0.9743261 1.0496144 0.5901617 0.1962303 0.7707067 
#>        X9       X10 
#> 0.8438532 0.9861559 
#> 
#> $uniquenesses
#>           x1           x2           x3           x4           x5           x6 
#>  0.024945502  0.014853820  0.008956431  0.025673931 -0.049614435  0.409838264 
#>           x7           x8           x9          x10 
#>  0.803769729  0.229293266  0.156146817  0.013844079 
#> 
#> $covariance
#>               x1           x2         x3         x4          x5           x6
#> x1   1.000000000  0.993167953 0.97034436 0.95609585 0.025163276 -0.015083014
#> x2   0.993167953  1.000000000 0.98346739 0.97164822 0.045110192 -0.004994507
#> x3   0.970344358  0.983467387 1.00000000 0.99749137 0.108682670  0.019464360
#> x4   0.956095848  0.971648219 0.99749137 1.00000000 0.133591430  0.029278642
#> x5   0.025163276  0.045110192 0.10868267 0.13359143 1.000000000  0.575741829
#> x6  -0.015083014 -0.004994507 0.01946436 0.02927864 0.575741829  1.000000000
#> x7   0.009780105  0.014165548 0.03527696 0.04429804 0.326885328  0.013993207
#> x8   0.017155253  0.036225902 0.09193857 0.11691517 0.840607798  0.298489402
#> x9   0.905256744  0.898571356 0.91651307 0.91138685 0.041581017 -0.009413168
#> x10  0.989449715  0.989605604 0.97531937 0.96400047 0.001814838 -0.046691411
#>              x7         x8           x9          x10
#> x1  0.009780105 0.01715525  0.905256744  0.989449715
#> x2  0.014165548 0.03622590  0.898571356  0.989605604
#> x3  0.035276960 0.09193857  0.916513072  0.975319373
#> x4  0.044298039 0.11691517  0.911386851  0.964000474
#> x5  0.326885328 0.84060780  0.041581017  0.001814838
#> x6  0.013993207 0.29848940 -0.009413168 -0.046691411
#> x7  1.000000000 0.35473163  0.012122296  0.007367798
#> x8  0.354731631 1.00000000  0.010355218  0.016828080
#> x9  0.012122296 0.01035522  1.000000000  0.911435130
#> x10 0.007367798 0.01682808  0.911435130  1.000000000
#> 
#> $correlation
#>               x1           x2         x3         x4          x5           x6
#> x1   1.000000000  0.993167953 0.97034436 0.95609585 0.025163276 -0.015083014
#> x2   0.993167953  1.000000000 0.98346739 0.97164822 0.045110192 -0.004994507
#> x3   0.970344358  0.983467387 1.00000000 0.99749137 0.108682670  0.019464360
#> x4   0.956095848  0.971648219 0.99749137 1.00000000 0.133591430  0.029278642
#> x5   0.025163276  0.045110192 0.10868267 0.13359143 1.000000000  0.575741829
#> x6  -0.015083014 -0.004994507 0.01946436 0.02927864 0.575741829  1.000000000
#> x7   0.009780105  0.014165548 0.03527696 0.04429804 0.326885328  0.013993207
#> x8   0.017155253  0.036225902 0.09193857 0.11691517 0.840607798  0.298489402
#> x9   0.905256744  0.898571356 0.91651307 0.91138685 0.041581017 -0.009413168
#> x10  0.989449715  0.989605604 0.97531937 0.96400047 0.001814838 -0.046691411
#>              x7         x8           x9          x10
#> x1  0.009780105 0.01715525  0.905256744  0.989449715
#> x2  0.014165548 0.03622590  0.898571356  0.989605604
#> x3  0.035276960 0.09193857  0.916513072  0.975319373
#> x4  0.044298039 0.11691517  0.911386851  0.964000474
#> x5  0.326885328 0.84060780  0.041581017  0.001814838
#> x6  0.013993207 0.29848940 -0.009413168 -0.046691411
#> x7  1.000000000 0.35473163  0.012122296  0.007367798
#> x8  0.354731631 1.00000000  0.010355218  0.016828080
#> x9  0.012122296 0.01035522  1.000000000  0.911435130
#> x10 0.007367798 0.01682808  0.911435130  1.000000000
#> 
#> $usedMatrix
#>               x1           x2         x3         x4          x5           x6
#> x1   1.000000000  0.993167953 0.97034436 0.95609585 0.025163276 -0.015083014
#> x2   0.993167953  1.000000000 0.98346739 0.97164822 0.045110192 -0.004994507
#> x3   0.970344358  0.983467387 1.00000000 0.99749137 0.108682670  0.019464360
#> x4   0.956095848  0.971648219 0.99749137 1.00000000 0.133591430  0.029278642
#> x5   0.025163276  0.045110192 0.10868267 0.13359143 1.000000000  0.575741829
#> x6  -0.015083014 -0.004994507 0.01946436 0.02927864 0.575741829  1.000000000
#> x7   0.009780105  0.014165548 0.03527696 0.04429804 0.326885328  0.013993207
#> x8   0.017155253  0.036225902 0.09193857 0.11691517 0.840607798  0.298489402
#> x9   0.905256744  0.898571356 0.91651307 0.91138685 0.041581017 -0.009413168
#> x10  0.989449715  0.989605604 0.97531937 0.96400047 0.001814838 -0.046691411
#>              x7         x8           x9          x10
#> x1  0.009780105 0.01715525  0.905256744  0.989449715
#> x2  0.014165548 0.03622590  0.898571356  0.989605604
#> x3  0.035276960 0.09193857  0.916513072  0.975319373
#> x4  0.044298039 0.11691517  0.911386851  0.964000474
#> x5  0.326885328 0.84060780  0.041581017  0.001814838
#> x6  0.013993207 0.29848940 -0.009413168 -0.046691411
#> x7  1.000000000 0.35473163  0.012122296  0.007367798
#> x8  0.354731631 1.00000000  0.010355218  0.016828080
#> x9  0.012122296 0.01035522  1.000000000  0.911435130
#> x10 0.007367798 0.01682808  0.911435130  1.000000000
#> 
#> $reducedCorrelation
#>               x1           x2         x3         x4          x5           x6
#> x1   0.975053749  0.993167953 0.97034436 0.95609585 0.025163276 -0.015083014
#> x2   0.993167953  0.985145619 0.98346739 0.97164822 0.045110192 -0.004994507
#> x3   0.970344358  0.983467387 0.99104353 0.99749137 0.108682670  0.019464360
#> x4   0.956095848  0.971648219 0.99749137 0.97432563 0.133591430  0.029278642
#> x5   0.025163276  0.045110192 0.10868267 0.13359143 1.049119077  0.575741829
#> x6  -0.015083014 -0.004994507 0.01946436 0.02927864 0.575741829  0.589483277
#> x7   0.009780105  0.014165548 0.03527696 0.04429804 0.326885328  0.013993207
#> x8   0.017155253  0.036225902 0.09193857 0.11691517 0.840607798  0.298489402
#> x9   0.905256744  0.898571356 0.91651307 0.91138685 0.041581017 -0.009413168
#> x10  0.989449715  0.989605604 0.97531937 0.96400047 0.001814838 -0.046691411
#>              x7         x8           x9          x10
#> x1  0.009780105 0.01715525  0.905256744  0.989449715
#> x2  0.014165548 0.03622590  0.898571356  0.989605604
#> x3  0.035276960 0.09193857  0.916513072  0.975319373
#> x4  0.044298039 0.11691517  0.911386851  0.964000474
#> x5  0.326885328 0.84060780  0.041581017  0.001814838
#> x6  0.013993207 0.29848940 -0.009413168 -0.046691411
#> x7  0.196169852 0.35473163  0.012122296  0.007367798
#> x8  0.354731631 0.77150802  0.010355218  0.016828080
#> x9  0.012122296 0.01035522  0.843854435  0.911435130
#> x10 0.007367798 0.01682808  0.911435130  0.986159101
#> 
#> $factors
#> [1] 3
#> 
#> $method
#> [1] "pfa"
#> 
#> $scores
#> NULL
#> 
#> $scoringCoef
#> NULL
#> 
#> $meanF
#> NULL
#> 
#> $corF
#> NULL
#> 
#> $scoresMethod
#> [1] "none"
#> 
#> $n.obs
#> NULL
#> 
#> $center
#> NULL
#> 
#> $eigenvalues
#>  [1] 5.7900498488 2.3189552681 1.0086871619 0.5741391921 0.1432389680
#>  [6] 0.0991672355 0.0516167794 0.0094032935 0.0039695244 0.0007727282
#> 
#> attr(,"class")
#> [1] "factorScorePfa"

## covmat is a list
covx = rrcov::Cov(stock611[,3:12])
covmat = list(cov = rrcov::getCov(covx), center = rrcov::getCenter(covx), n.obs = covx@n.obs)
fsPfa2 = factorScorePfa(factors = 3, cor = TRUE, covmat = covmat); fsPfa2
#> $call
#> factorScorePfa(factors = 3, covmat = covmat, cor = TRUE)
#> 
#> $loadings
#> 
#> Loadings:
#>     Factor1 Factor2 Factor3
#> X1   0.987                 
#> X2   0.992                 
#> X3   0.993                 
#> X4   0.982                 
#> X5           0.809   0.627 
#> X6           0.123   0.758 
#> X7           0.440         
#> X8           0.839   0.257 
#> X9   0.919                 
#> X10  0.992                 
#> 
#>                Factor1 Factor2 Factor3
#> SS loadings      5.739   1.582   1.041
#> Proportion Var   0.574   0.158   0.104
#> Cumulative Var   0.574   0.732   0.836
#> 
#> $communality
#>        X1        X2        X3        X4        X5        X6        X7        X8 
#> 0.9750545 0.9851462 0.9910436 0.9743261 1.0496144 0.5901617 0.1962303 0.7707067 
#>        X9       X10 
#> 0.8438532 0.9861559 
#> 
#> $uniquenesses
#>           x1           x2           x3           x4           x5           x6 
#>  0.024945502  0.014853820  0.008956431  0.025673931 -0.049614435  0.409838264 
#>           x7           x8           x9          x10 
#>  0.803769729  0.229293266  0.156146817  0.013844079 
#> 
#> $covariance
#>                x1            x2           x3           x4           x5
#> x1   1.555244e+20  2.863371e+19 1.110191e+19 7.219175e+18 7.345648e+07
#> x2   2.863371e+19  5.344552e+18 2.085874e+18 1.360040e+18 2.441148e+07
#> x3   1.110191e+19  2.085874e+18 8.416758e+17 5.540749e+17 2.333976e+07
#> x4   7.219175e+18  1.360040e+18 5.540749e+17 3.665843e+17 1.893343e+07
#> x5   7.345648e+07  2.441148e+07 2.333976e+07 1.893343e+07 5.479330e-02
#> x6  -2.598053e+08 -1.594810e+07 2.466455e+07 2.448491e+07 1.861453e-01
#> x7   3.466949e+09  9.308800e+08 9.199586e+08 7.623881e+08 2.175023e+00
#> x8   1.107546e+09  4.335511e+08 4.366522e+08 3.664572e+08 1.018644e+00
#> x9   1.863773e+20  3.429496e+19 1.388140e+19 9.109861e+18 1.606871e+08
#> x10  4.420202e+19  8.195339e+18 3.205298e+18 2.090804e+18 1.521776e+06
#>                x6           x7           x8            x9           x10
#> x1  -2.598053e+08 3.466949e+09 1.107546e+09  1.863773e+20  4.420202e+19
#> x2  -1.594810e+07 9.308800e+08 4.335511e+08  3.429496e+19  8.195339e+18
#> x3   2.466455e+07 9.199586e+08 4.366522e+08  1.388140e+19  3.205298e+18
#> x4   2.448491e+07 7.623881e+08 3.664572e+08  9.109861e+18  2.090804e+18
#> x5   1.861453e-01 2.175023e+00 1.018644e+00  1.606871e+08  1.521776e+06
#> x6   1.907749e+00 5.493923e-01 2.134298e+00 -2.146439e+08 -2.310185e+08
#> x7   5.493923e-01 8.079963e+02 5.219995e+01  5.688682e+09  7.502250e+08
#> x8   2.134298e+00 5.219995e+01 2.679976e+01  8.850072e+08  3.120680e+08
#> x9  -2.146439e+08 5.688682e+09 8.850072e+08  2.725487e+20  5.390102e+19
#> x10 -2.310185e+08 7.502250e+08 3.120680e+08  5.390102e+19  1.283212e+19
#> 
#> $correlation
#>               x1           x2         x3         x4          x5           x6
#> x1   1.000000000  0.993167953 0.97034436 0.95609585 0.025163276 -0.015083014
#> x2   0.993167953  1.000000000 0.98346739 0.97164822 0.045110192 -0.004994507
#> x3   0.970344358  0.983467387 1.00000000 0.99749137 0.108682670  0.019464360
#> x4   0.956095848  0.971648219 0.99749137 1.00000000 0.133591430  0.029278642
#> x5   0.025163276  0.045110192 0.10868267 0.13359143 1.000000000  0.575741829
#> x6  -0.015083014 -0.004994507 0.01946436 0.02927864 0.575741829  1.000000000
#> x7   0.009780105  0.014165548 0.03527696 0.04429804 0.326885328  0.013993207
#> x8   0.017155253  0.036225902 0.09193857 0.11691517 0.840607798  0.298489402
#> x9   0.905256744  0.898571356 0.91651307 0.91138685 0.041581017 -0.009413168
#> x10  0.989449715  0.989605604 0.97531937 0.96400047 0.001814838 -0.046691411
#>              x7         x8           x9          x10
#> x1  0.009780105 0.01715525  0.905256744  0.989449715
#> x2  0.014165548 0.03622590  0.898571356  0.989605604
#> x3  0.035276960 0.09193857  0.916513072  0.975319373
#> x4  0.044298039 0.11691517  0.911386851  0.964000474
#> x5  0.326885328 0.84060780  0.041581017  0.001814838
#> x6  0.013993207 0.29848940 -0.009413168 -0.046691411
#> x7  1.000000000 0.35473163  0.012122296  0.007367798
#> x8  0.354731631 1.00000000  0.010355218  0.016828080
#> x9  0.012122296 0.01035522  1.000000000  0.911435130
#> x10 0.007367798 0.01682808  0.911435130  1.000000000
#> 
#> $usedMatrix
#>               x1           x2         x3         x4          x5           x6
#> x1   1.000000000  0.993167953 0.97034436 0.95609585 0.025163276 -0.015083014
#> x2   0.993167953  1.000000000 0.98346739 0.97164822 0.045110192 -0.004994507
#> x3   0.970344358  0.983467387 1.00000000 0.99749137 0.108682670  0.019464360
#> x4   0.956095848  0.971648219 0.99749137 1.00000000 0.133591430  0.029278642
#> x5   0.025163276  0.045110192 0.10868267 0.13359143 1.000000000  0.575741829
#> x6  -0.015083014 -0.004994507 0.01946436 0.02927864 0.575741829  1.000000000
#> x7   0.009780105  0.014165548 0.03527696 0.04429804 0.326885328  0.013993207
#> x8   0.017155253  0.036225902 0.09193857 0.11691517 0.840607798  0.298489402
#> x9   0.905256744  0.898571356 0.91651307 0.91138685 0.041581017 -0.009413168
#> x10  0.989449715  0.989605604 0.97531937 0.96400047 0.001814838 -0.046691411
#>              x7         x8           x9          x10
#> x1  0.009780105 0.01715525  0.905256744  0.989449715
#> x2  0.014165548 0.03622590  0.898571356  0.989605604
#> x3  0.035276960 0.09193857  0.916513072  0.975319373
#> x4  0.044298039 0.11691517  0.911386851  0.964000474
#> x5  0.326885328 0.84060780  0.041581017  0.001814838
#> x6  0.013993207 0.29848940 -0.009413168 -0.046691411
#> x7  1.000000000 0.35473163  0.012122296  0.007367798
#> x8  0.354731631 1.00000000  0.010355218  0.016828080
#> x9  0.012122296 0.01035522  1.000000000  0.911435130
#> x10 0.007367798 0.01682808  0.911435130  1.000000000
#> 
#> $reducedCorrelation
#>               x1           x2         x3         x4          x5           x6
#> x1   0.975053749  0.993167953 0.97034436 0.95609585 0.025163276 -0.015083014
#> x2   0.993167953  0.985145619 0.98346739 0.97164822 0.045110192 -0.004994507
#> x3   0.970344358  0.983467387 0.99104353 0.99749137 0.108682670  0.019464360
#> x4   0.956095848  0.971648219 0.99749137 0.97432563 0.133591430  0.029278642
#> x5   0.025163276  0.045110192 0.10868267 0.13359143 1.049119077  0.575741829
#> x6  -0.015083014 -0.004994507 0.01946436 0.02927864 0.575741829  0.589483277
#> x7   0.009780105  0.014165548 0.03527696 0.04429804 0.326885328  0.013993207
#> x8   0.017155253  0.036225902 0.09193857 0.11691517 0.840607798  0.298489402
#> x9   0.905256744  0.898571356 0.91651307 0.91138685 0.041581017 -0.009413168
#> x10  0.989449715  0.989605604 0.97531937 0.96400047 0.001814838 -0.046691411
#>              x7         x8           x9          x10
#> x1  0.009780105 0.01715525  0.905256744  0.989449715
#> x2  0.014165548 0.03622590  0.898571356  0.989605604
#> x3  0.035276960 0.09193857  0.916513072  0.975319373
#> x4  0.044298039 0.11691517  0.911386851  0.964000474
#> x5  0.326885328 0.84060780  0.041581017  0.001814838
#> x6  0.013993207 0.29848940 -0.009413168 -0.046691411
#> x7  0.196169852 0.35473163  0.012122296  0.007367798
#> x8  0.354731631 0.77150802  0.010355218  0.016828080
#> x9  0.012122296 0.01035522  0.843854435  0.911435130
#> x10 0.007367798 0.01682808  0.911435130  0.986159101
#> 
#> $factors
#> [1] 3
#> 
#> $method
#> [1] "pfa"
#> 
#> $scores
#> NULL
#> 
#> $scoringCoef
#> NULL
#> 
#> $meanF
#> NULL
#> 
#> $corF
#> NULL
#> 
#> $scoresMethod
#> [1] "none"
#> 
#> $n.obs
#> NULL
#> 
#> $center
#>           x1           x2           x3           x4           x5           x6 
#> 1.679190e+09 3.252545e+08 1.439706e+08 1.071863e+08 1.904953e-01 2.906124e+00 
#>           x7           x8           x9          x10 
#> 6.366363e+00 3.265233e+00 3.012056e+09 5.546872e+08 
#> 
#> $eigenvalues
#>  [1] 5.7900498488 2.3189552681 1.0086871619 0.5741391921 0.1432389680
#>  [6] 0.0991672355 0.0516167794 0.0094032935 0.0039695244 0.0007727282
#> 
#> attr(,"class")
#> [1] "factorScorePfa"

## fsPfa3 contains scores etc.
fsPfa3 = factorScorePfa(x = stock611[,3:12], factors = 2, 
cor = TRUE, rotation = "varimax", scoresMethod = "regression"); fsPfa3
#> $call
#> factorScorePfa(x = stock611[, 3:12], factors = 2, cor = TRUE, 
#>     rotation = "varimax", scoresMethod = "regression")
#> 
#> $loadings
#> 
#> Loadings:
#>     Factor1 Factor2
#> X1   0.987         
#> X2   0.992         
#> X3   0.994         
#> X4   0.983         
#> X5           1.131 
#> X6           0.453 
#> X7           0.312 
#> X8           0.757 
#> X9   0.918         
#> X10  0.992         
#> 
#>                Factor1 Factor2
#> SS loadings      5.745   2.168
#> Proportion Var   0.575   0.217
#> Cumulative Var   0.575   0.791
#> 
#> $communality
#>         X1         X2         X3         X4         X5         X6         X7 
#> 0.97483545 0.98498499 0.99101663 0.97409584 1.28243672 0.20526961 0.09797297 
#>         X8         X9        X10 
#> 0.57415573 0.84318885 0.98555970 
#> 
#> $uniquenesses
#>           x1           x2           x3           x4           x5           x6 
#>  0.025164549  0.015015010  0.008983373  0.025904159 -0.282436723  0.794730389 
#>           x7           x8           x9          x10 
#>  0.902027030  0.425844269  0.156811145  0.014440298 
#> 
#> $covariance
#>                x1            x2           x3           x4           x5
#> x1   1.555244e+20  2.863371e+19 1.110191e+19 7.219175e+18 7.345648e+07
#> x2   2.863371e+19  5.344552e+18 2.085874e+18 1.360040e+18 2.441148e+07
#> x3   1.110191e+19  2.085874e+18 8.416758e+17 5.540749e+17 2.333976e+07
#> x4   7.219175e+18  1.360040e+18 5.540749e+17 3.665843e+17 1.893343e+07
#> x5   7.345648e+07  2.441148e+07 2.333976e+07 1.893343e+07 5.479330e-02
#> x6  -2.598053e+08 -1.594810e+07 2.466455e+07 2.448491e+07 1.861453e-01
#> x7   3.466949e+09  9.308800e+08 9.199586e+08 7.623881e+08 2.175023e+00
#> x8   1.107546e+09  4.335511e+08 4.366522e+08 3.664572e+08 1.018644e+00
#> x9   1.863773e+20  3.429496e+19 1.388140e+19 9.109861e+18 1.606871e+08
#> x10  4.420202e+19  8.195339e+18 3.205298e+18 2.090804e+18 1.521776e+06
#>                x6           x7           x8            x9           x10
#> x1  -2.598053e+08 3.466949e+09 1.107546e+09  1.863773e+20  4.420202e+19
#> x2  -1.594810e+07 9.308800e+08 4.335511e+08  3.429496e+19  8.195339e+18
#> x3   2.466455e+07 9.199586e+08 4.366522e+08  1.388140e+19  3.205298e+18
#> x4   2.448491e+07 7.623881e+08 3.664572e+08  9.109861e+18  2.090804e+18
#> x5   1.861453e-01 2.175023e+00 1.018644e+00  1.606871e+08  1.521776e+06
#> x6   1.907749e+00 5.493923e-01 2.134298e+00 -2.146439e+08 -2.310185e+08
#> x7   5.493923e-01 8.079963e+02 5.219995e+01  5.688682e+09  7.502250e+08
#> x8   2.134298e+00 5.219995e+01 2.679976e+01  8.850072e+08  3.120680e+08
#> x9  -2.146439e+08 5.688682e+09 8.850072e+08  2.725487e+20  5.390102e+19
#> x10 -2.310185e+08 7.502250e+08 3.120680e+08  5.390102e+19  1.283212e+19
#> 
#> $correlation
#>               x1           x2         x3         x4          x5           x6
#> x1   1.000000000  0.993167953 0.97034436 0.95609585 0.025163276 -0.015083014
#> x2   0.993167953  1.000000000 0.98346739 0.97164822 0.045110192 -0.004994507
#> x3   0.970344358  0.983467387 1.00000000 0.99749137 0.108682670  0.019464360
#> x4   0.956095848  0.971648219 0.99749137 1.00000000 0.133591430  0.029278642
#> x5   0.025163276  0.045110192 0.10868267 0.13359143 1.000000000  0.575741829
#> x6  -0.015083014 -0.004994507 0.01946436 0.02927864 0.575741829  1.000000000
#> x7   0.009780105  0.014165548 0.03527696 0.04429804 0.326885328  0.013993207
#> x8   0.017155253  0.036225902 0.09193857 0.11691517 0.840607798  0.298489402
#> x9   0.905256744  0.898571356 0.91651307 0.91138685 0.041581017 -0.009413168
#> x10  0.989449715  0.989605604 0.97531937 0.96400047 0.001814838 -0.046691411
#>              x7         x8           x9          x10
#> x1  0.009780105 0.01715525  0.905256744  0.989449715
#> x2  0.014165548 0.03622590  0.898571356  0.989605604
#> x3  0.035276960 0.09193857  0.916513072  0.975319373
#> x4  0.044298039 0.11691517  0.911386851  0.964000474
#> x5  0.326885328 0.84060780  0.041581017  0.001814838
#> x6  0.013993207 0.29848940 -0.009413168 -0.046691411
#> x7  1.000000000 0.35473163  0.012122296  0.007367798
#> x8  0.354731631 1.00000000  0.010355218  0.016828080
#> x9  0.012122296 0.01035522  1.000000000  0.911435130
#> x10 0.007367798 0.01682808  0.911435130  1.000000000
#> 
#> $usedMatrix
#>               x1           x2         x3         x4          x5           x6
#> x1   1.000000000  0.993167953 0.97034436 0.95609585 0.025163276 -0.015083014
#> x2   0.993167953  1.000000000 0.98346739 0.97164822 0.045110192 -0.004994507
#> x3   0.970344358  0.983467387 1.00000000 0.99749137 0.108682670  0.019464360
#> x4   0.956095848  0.971648219 0.99749137 1.00000000 0.133591430  0.029278642
#> x5   0.025163276  0.045110192 0.10868267 0.13359143 1.000000000  0.575741829
#> x6  -0.015083014 -0.004994507 0.01946436 0.02927864 0.575741829  1.000000000
#> x7   0.009780105  0.014165548 0.03527696 0.04429804 0.326885328  0.013993207
#> x8   0.017155253  0.036225902 0.09193857 0.11691517 0.840607798  0.298489402
#> x9   0.905256744  0.898571356 0.91651307 0.91138685 0.041581017 -0.009413168
#> x10  0.989449715  0.989605604 0.97531937 0.96400047 0.001814838 -0.046691411
#>              x7         x8           x9          x10
#> x1  0.009780105 0.01715525  0.905256744  0.989449715
#> x2  0.014165548 0.03622590  0.898571356  0.989605604
#> x3  0.035276960 0.09193857  0.916513072  0.975319373
#> x4  0.044298039 0.11691517  0.911386851  0.964000474
#> x5  0.326885328 0.84060780  0.041581017  0.001814838
#> x6  0.013993207 0.29848940 -0.009413168 -0.046691411
#> x7  1.000000000 0.35473163  0.012122296  0.007367798
#> x8  0.354731631 1.00000000  0.010355218  0.016828080
#> x9  0.012122296 0.01035522  1.000000000  0.911435130
#> x10 0.007367798 0.01682808  0.911435130  1.000000000
#> 
#> $reducedCorrelation
#>               x1           x2         x3         x4          x5           x6
#> x1   0.974837883  0.993167953 0.97034436 0.95609585 0.025163276 -0.015083014
#> x2   0.993167953  0.984984347 0.98346739 0.97164822 0.045110192 -0.004994507
#> x3   0.970344358  0.983467387 0.99102095 0.99749137 0.108682670  0.019464360
#> x4   0.956095848  0.971648219 0.99749137 0.97410839 0.133591430  0.029278642
#> x5   0.025163276  0.045110192 0.10868267 0.13359143 1.277471757  0.575741829
#> x6  -0.015083014 -0.004994507 0.01946436 0.02927864 0.575741829  0.205466836
#> x7   0.009780105  0.014165548 0.03527696 0.04429804 0.326885328  0.013993207
#> x8   0.017155253  0.036225902 0.09193857 0.11691517 0.840607798  0.298489402
#> x9   0.905256744  0.898571356 0.91651307 0.91138685 0.041581017 -0.009413168
#> x10  0.989449715  0.989605604 0.97531937 0.96400047 0.001814838 -0.046691411
#>              x7         x8           x9          x10
#> x1  0.009780105 0.01715525  0.905256744  0.989449715
#> x2  0.014165548 0.03622590  0.898571356  0.989605604
#> x3  0.035276960 0.09193857  0.916513072  0.975319373
#> x4  0.044298039 0.11691517  0.911386851  0.964000474
#> x5  0.326885328 0.84060780  0.041581017  0.001814838
#> x6  0.013993207 0.29848940 -0.009413168 -0.046691411
#> x7  0.098164353 0.35473163  0.012122296  0.007367798
#> x8  0.354731631 0.57603192  0.010355218  0.016828080
#> x9  0.012122296 0.01035522  0.843191079  0.911435130
#> x10 0.007367798 0.01682808  0.911435130  0.985564105
#> 
#> $factors
#> [1] 2
#> 
#> $method
#> [1] "pfa"
#> 
#> $scores
#>          Factor1       Factor2
#> 1   -0.106792384 -0.7235262275
#> 2   -0.129543790  1.7540249047
#> 3   -0.185957366 -0.9085174391
#> 4   -0.117112604 -1.7738845047
#> 5   -0.142945564 -1.5322906094
#> 6   -0.129254370 -4.7173034885
#> 7   -0.125484499 -0.8181458299
#> 8   -0.159680012 -5.4611567296
#> 9   -0.120291888 -2.4118547391
#> 10  -0.116724852 -6.1914650063
#> 11  -0.128582277  0.0175848472
#> 12  -0.135314227 -6.1686647194
#> 13  -0.127766372 -1.0093301327
#> 14  -0.132398003 -1.8342255233
#> 15  -0.135960582 -2.3765596775
#> 16  -0.122383712 -0.9699068442
#> 17  -0.139279527 -4.6733697191
#> 18  -0.116235822 -6.7374295033
#> 19  -0.111026362  1.2663702888
#> 20  -0.115609052 -1.1555301737
#> 21  -0.138400158 -3.4200477090
#> 22  -0.121974479 -4.0257998665
#> 23  -0.124375792 -2.5486745508
#> 24  -0.169579548 -2.2140323848
#> 25  -0.146102694 -4.0408315782
#> 26  -0.111272335 -4.3621509426
#> 27  -0.118206193 -3.4685879605
#> 28  -0.120914468 -1.6511771327
#> 29  -0.119663924 -2.0028644678
#> 30  -0.101710733 -2.0176887131
#> 31  -0.104055212 -1.9973922102
#> 32  -0.140059106 -1.6899285282
#> 33  -0.111984226 -3.8788683285
#> 34  -0.099350324 -1.5744602830
#> 35  -0.075158573 -1.9643378598
#> 36  -0.085495119 -1.5818743147
#> 37  -0.115549999 -2.4999246590
#> 38  -0.109285928 -2.1204116729
#> 39  -0.123625580 -2.8399581201
#> 40  -0.083527486 -2.1181221325
#> 41  -0.122431235 -0.7806133640
#> 42  -0.117318874 -2.3998585852
#> 43  -0.126522668 -0.4069132698
#> 44   0.004181504 -0.8240013312
#> 45  -0.127841687 -1.0482477124
#> 46  -0.154590671 -1.0311549003
#> 47  -0.107756972 -0.7581043729
#> 48  -0.108302945 -0.5391470656
#> 49  -0.113842684 -1.8775324640
#> 50  -0.114891272 -0.7422763230
#> 51  -0.108509649 -0.5682489532
#> 52  -0.121775592 -0.6362957180
#> 53  -0.110449419 -1.1562880815
#> 54  -0.104402020 -1.2436433426
#> 55  -0.106469517 -0.8418712964
#> 56   0.081886507 -0.7356547146
#> 57  -0.066362067 -0.2958614201
#> 58  -0.122708148 -1.1613864453
#> 59   0.508499126  0.8805356736
#> 60  -0.120894823 -0.6398031161
#> 61  -0.111154532 -0.5184594530
#> 62  -0.054075741 -0.6767324183
#> 63  -0.071815085 -0.4410627265
#> 64  -0.111378582 -0.7995555512
#> 65  -0.118716516 -0.9448062808
#> 66  -0.196417018 -0.9969556865
#> 67  -0.117590149 -0.7237045335
#> 68  -0.129736729 -0.7205912413
#> 69  -0.091832448 -1.9514457367
#> 70  -0.068176729 -1.2614531161
#> 71  -0.113331684 -0.4389830997
#> 72  -0.100117784 -1.1320854138
#> 73  -0.128148175 -0.0984283709
#> 74   0.086032675  0.5673735891
#> 75   0.023720738 -2.2215735357
#> 76  -0.123070182 -0.6398622757
#> 77  -0.108480332 -1.2568127809
#> 78  -0.128130123 -0.4353268346
#> 79   1.024200494  0.4655085076
#> 80  -0.088096014 -1.6533161322
#> 81  -0.010923867 -0.9465751013
#> 82  -0.130412403 -0.2093952465
#> 83  -0.056423899 -0.6345118384
#> 84  -0.089432859 -0.6669086291
#> 85  -0.128975476 -0.4673238294
#> 86  -0.111207890 -0.6092130520
#> 87  -0.124230600 -1.2804165477
#> 88  -0.124599725 -0.4975076208
#> 89  -0.125378979 -0.3123390581
#> 90  -0.128369593 -0.4447294413
#> 91  -0.113879333 -0.9224554828
#> 92  -0.151969099  2.7723489817
#> 93  -0.106170153 -1.0694680445
#> 94  -0.126347126 -0.1434736985
#> 95  -0.117456342 -0.7312043564
#> 96  -0.104129892 -0.0476003872
#> 97   0.036358357 -2.1905359280
#> 98  -0.122304951 -0.5166212934
#> 99  -0.126537595 -0.4788364059
#> 100 -0.075538846 -0.5548726437
#> 101 -0.101472255 -0.5642440466
#> 102 -0.083713952 -0.3678541961
#> 103 -0.039449620 -0.5987372576
#> 104 -0.102217083 -0.0718113351
#> 105 -0.108961555 -0.3762842436
#> 106 -0.112115338 -1.0429435950
#> 107 -0.115628843 -0.4745283909
#> 108 -0.034589539  0.0810353677
#> 109 -0.114411447 -0.8458110364
#> 110 -0.077988712 -1.0286683200
#> 111 -0.081679063 -0.6851636176
#> 112 -0.097741177 -0.8681569992
#> 113  0.652910026  1.2466099712
#> 114 -0.086237891 -0.6557991057
#> 115 -0.123932143 -0.2175359171
#> 116 -0.096979424 -0.9035179708
#> 117 -0.049214648  0.5205754957
#> 118 -0.110814882 -0.9646239623
#> 119 -0.115983380 -0.6557278007
#> 120 -0.102819041 -1.0360191679
#> 121 -0.110583761  0.0175650261
#> 122 -0.107250070 -0.6499942755
#> 123 -0.106585802 -0.8377568366
#> 124 -0.094961482 -0.4669685955
#> 125 -0.128148449  0.1674167150
#> 126 -0.120945857 -0.5150467738
#> 127 -0.107504751  0.0053232806
#> 128 -0.127300306 -0.3883270311
#> 129  0.371260667  0.1580877918
#> 130 -0.095713548 -0.7720565385
#> 131 -0.079142005 -1.4520795745
#> 132 -0.080259977 -0.5919088205
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#> 538 -0.047784891  0.3676324033
#> 539  2.474780775  0.6304450740
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#> 550 -0.074497972  0.4655908816
#> 551 -0.082119035  0.5333983559
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#> 553  0.167194200  1.8270098536
#> 554  0.031891037  1.1292786883
#> 555 -0.070096700  1.6284131305
#> 556 -0.063560949  0.5122348790
#> 557 -0.003210012  3.3008398742
#> 558 -0.060663761  4.0388583608
#> 559 -0.091867158  1.7767677677
#> 560 -0.081730119 -0.0430215941
#> 561 -0.127781244  0.4497442514
#> 562  0.309197384  0.8373744177
#> 563 -0.100389242  2.8068008660
#> 564 -0.073765306  1.5546606177
#> 565 -0.049118677  1.5080537900
#> 566 -0.011274628  0.0392835822
#> 567 -0.030481003  0.4419516188
#> 568 -0.038854943  0.8470799666
#> 569  0.495590300  2.1500511578
#> 570 -0.014528032  0.5481164955
#> 571  0.762255932  0.0797676646
#> 572  0.579219157  2.5450624777
#> 573 -0.078211175  1.6567556966
#> 574 -0.004174512  1.1910342449
#> 575 -0.124848908  1.3678026502
#> 576  1.234422462  3.2967937826
#> 577 -0.074001470  0.9315102903
#> 578 -0.090444274  1.7626872549
#> 579 -0.017598028  2.6231251823
#> 580  0.091312998  1.1590163732
#> 581  0.672964870  0.4947663323
#> 582 -0.044146721 -0.8200086763
#> 583  0.533036253  7.1718041737
#> 584  0.085602272  1.1331520290
#> 585 -0.042755984  0.2475069185
#> 586 -0.099117842  0.0740987473
#> 587 -0.101146686  0.0129776071
#> 588  0.408891103  3.2716598560
#> 589  0.974862182  3.2708419729
#> 590 -0.016024262  2.6160434700
#> 591 -0.104204258  0.0493829633
#> 592  0.052458516  2.6146025707
#> 593  0.460706469  0.1410043073
#> 594  0.174262135  1.7516766644
#> 595  0.125015093  1.6006622466
#> 596 -0.090199497 -0.2900569163
#> 597 -0.092246420  0.2353736950
#> 598 -0.082785744  3.7084703736
#> 599 -0.062012026 -0.1334813583
#> 600 -0.114230994 -1.5174365731
#> 601 -0.051541688  1.0097712189
#> 602 -0.038491237  0.4382067918
#> 603 -0.086059309  0.2201204585
#> 604  0.350393718 -1.2902436828
#> 605  0.064801239  1.4382888905
#> 606 -0.099327744  7.3859949186
#> 607 -0.108939112 -0.6929816617
#> 608 -0.106409291  2.3863414791
#> 609 -0.063042981 -0.3405280769
#> 610 -0.141954509  1.8227776161
#> 611 -0.131970065  1.2242320419
#> 
#> $scoringCoef
#>                 x1          x2        x3         x4         x5           x6
#> Factor1  0.1542090 -0.53298976  2.542032 -1.5150207 -0.0107372  0.008643302
#> Factor2 -0.7468658  0.02288815 -1.195907  0.3787577  2.5796211 -0.613008768
#>                   x7           x8          x9       x10
#> Factor1  0.002632769  0.001954781 -0.04985304 0.3936587
#> Factor2 -0.093687621 -1.143722733 -0.21967488 1.6608499
#> 
#> $meanF
#>       Factor1       Factor2 
#>  1.669877e-16 -1.898463e-15 
#> 
#> $corF
#>            Factor1    Factor2
#> Factor1  1.0000000 -0.0022317
#> Factor2 -0.0022317  1.0000000
#> 
#> $scoresMethod
#> [1] "regression"
#> 
#> $n.obs
#> [1] 611
#> 
#> $center
#>           x1           x2           x3           x4           x5           x6 
#> 1.679190e+09 3.252545e+08 1.439706e+08 1.071863e+08 1.904953e-01 2.906124e+00 
#>           x7           x8           x9          x10 
#> 6.366363e+00 3.265233e+00 3.012056e+09 5.546872e+08 
#> 
#> $eigenvalues
#>  [1] 5.7900498488 2.3189552681 1.0086871619 0.5741391921 0.1432389680
#>  [6] 0.0991672355 0.0516167794 0.0094032935 0.0039695244 0.0007727282
#> 
#> attr(,"class")
#> [1] "factorScorePfa"