Data
Access the lessR data set called datMach4 for the
analysis of 351 people to the Mach IV scale. Read the optional variable
labels. Including the item contents as variable labels means that the
output of the confirmatory factor analysis contains the item content
grouped by factor.
d <- Read("Mach4", quiet=TRUE)
l <- Read("Mach4_lbl", var_labels=TRUE)
##
## >>> Suggestions
## Recommended binary format for data files: feather
## Create with Write(d, "your_file", format="feather")
## More details about your data, Enter: details() for d, or details(name)
##
## Data Types
## ------------------------------------------------------------
## character: Non-numeric data values
## ------------------------------------------------------------
##
## Variable Missing Unique
## Name Type Values Values Values First and last values
## ------------------------------------------------------------------------------------------
## 1 label character 20 0 20 Never tell anyone the real reason you did something unless it is useful to do so ... Most people forget more easily the death of a parent than the loss of their property
## ------------------------------------------------------------------------------------------
Calculate the correlations and store in here in R, a data
structure that contains the computed correlation matrix.
##
## >>> No missing data
##
##
## Note: To provide more color separation for off-diagonal
## elements, the diagonal elements of the matrix for
## computing the heat map are set to 0.
The correlation matrix for analysis is named R. The item (observed
variable) correlation matrix is the numerical input into the
confirmatory factor analysis.
View the correlation matrix.
corPrint(R, min_value=0.1)
## m01 m02 m03 m04 m05 m06 m07 m08 m09 m10 m11 m12 m13 m14 m15 m16 m17 m18 m19 m20
## m01 100 16 17 -11 -13 22 -14 -15 25 17 11 -12 19 17
## m02 100 -15 12 14 -18 -22 18 13 25
## m03 16 100 24 24 16 15 10 10 10
## m04 -15 100 14 -11 14 11 14 -18 -14 23 13 13
## m05 17 12 100 -11 -10 10 -13 23 22 -19 20 11
## m06 -11 24 -11 100 52 25 41 29 -14 -16 11 -15 24 -21
## m07 -13 24 14 -10 52 100 32 40 22 -16 -11 15 -17 21 13 -16
## m08 22 14 -11 10 100 -10 -10 10 -12 12 15
## m09 -14 -18 16 14 25 32 -10 100 25 16 -14 -13 -17 17 15 -17
## m10 -15 -22 15 11 41 40 25 100 15 -18 15 -18 11 15 -16 -12
## m11 10 14 -13 29 22 -10 16 15 100 -20 -11 26 28 -23 -17
## m12 25 18 -18 23 -14 -16 10 -14 -18 -20 100 22 -11 -15 -22 10 20
## m13 17 13 -14 22 -16 -11 -13 -11 22 100 12 16 -12 16 18
## m14 10 23 11 15 -12 15 26 -11 12 100 22 10 -13
## m15 11 25 -15 -17 -17 -18 16 100 22
## m16 10 13 -19 24 21 17 11 28 -15 22 100
## m17 -12 13 13 15 15 -22 -12 10 100 -25
## m18 19 20 -21 -16 12 -16 -23 10 16 22 100
## m19 100
## m20 17 11 15 -17 -12 -17 20 18 -13 -25 100
Exploratory Factor Analysis
Here, do the default two-factor solution with "promax"
rotation. The default correlation matrix is mycor. The
abbreviation for corEFA() is efa().
## EXPLORATORY FACTOR ANALYSIS
##
## Loadings (except -0.2 to 0.2)
## -------------------------------------
## Factor1 Factor2 Factor3 Factor4
## m06 0.828 -0.290
## m07 0.712
## m10 0.539
## m03 0.422 0.318
## m09 0.323
## m05 0.649
## m18 0.555 0.253
## m13 0.543 0.226
## m01 0.490
## m12 0.434 -0.230
## m08 0.236 -0.202
## m14 0.402 0.991 -0.401
## m04 0.426
## m20 0.237 -0.282
## m17 0.267
## m19
## m11 -0.299 0.309 -0.609
## m16 0.274 -0.455
## m02 -0.319
## m15 -0.207 0.203 -0.214
##
## Sum of Squares
## ------------------------------------------------
## Factor1 Factor2 Factor3 Factor4
## SS loadings 1.933 2.038 1.825 1.099
## Proportion Var 0.097 0.102 0.091 0.055
## Cumulative Var 0.097 0.199 0.290 0.345
##
## CONFIRMATORY FACTOR ANALYSIS CODE
##
## MeasModel <-
## " F1 =~ m01 + m02 + m03 + m04 + m05
## F2 =~ m06 + m07 + m08 + m09 + m10 + m11
## F3 =~ m12 + m13 + m14 + m15
## F4 =~ m17 + m18 + m19 + m20
## "
##
## fit <- lessR::cfa(MeasModel)
##
## library(lavaan)
## fit <- lavaan::cfa(MeasModel, data=d)
## summary(fit, fit.measures=TRUE, standardized=TRUE)
##
## Deletion threshold: min_loading = 0.2
## Deleted items: m16
Confirmatory Factor Analysis
The confirmatory factor analysis is of multiple-indicator measurement
scales, that is, each item (observed variable) is assigned to only one
factor. Solution method is centroid factor analysis.
Specify the measurement model for the analysis in Lavaan notation.
Define four factors: Deceit, Trust, Cynicism, and Flattery.
MeasModel <-
"
Deceit =~ m07 + m06 + m10 + m09
Trust =~ m12 + m05 + m13 + m01
Cynicism =~ m11 + m16 + m04
Flattery =~ m15 + m02
"
Do the confirmatory factor analysis of 4-factor solution of Mach IV
scale, Hunter, Gerbing and Boster (1982). By default output goes to the
console, or, can store the output into an object, here cfa_out,
which can then be displayed as a whole, or piecemeal.
The abbreviation for corCFA() is cfa().
cfa_out <- cfa(MeasModel, R)
## FACTOR / SCALE COMPOSITION
##
## F1
## ------------------------------
## m07: There is no excuse for lying to someone else
## m06: Honesty is the best policy in all cases
## m10: When you ask someone to do something for you, it is best to give the real reasons for wanting
## it rather than giving reasons which carry more weight
## m09: All in all, it is better to be humble and honest than to be important and dishonest
##
## F2
## ------------------------------
## m12: Anyone who completely trusts anyone else is asking for trouble
## m05: It is safest to assume that all people have a vicious streak and it will come out when they
## are given a chance
## m13: The biggest difference between most criminals and other people is that the criminals are
## stupid enough to get caught
## m01: Never tell anyone the real reason you did something unless it is useful to do so
##
## F3
## ------------------------------
## m11: Most people who get ahead in the world lead clean, moral lives
## m16: It is possible to be good in all respects
## m04: Most people are basically good and kind
##
## F4
## ------------------------------
## m15: It is wise to flatter important people
## m02: The best way to handle people is to tell them what they want to hear
##
## RELIABILITY ANALYSIS
##
## Scale Alpha Omega
## -----------------------
## F1 0.691 0.701
## F2 0.515 0.517
## F3 0.402 0.421
## F4 0.400 0.400
##
## SOLUTION
##
## Fac Indi Pat Unique Factors with which an indicator correlates too
## tor cator tern ness highly, and other indicator diagnostics.
## ---------------------------------------------------------------------------
##
## F1 m07 0.743 0.448
## F1 m06 0.682 0.535
## F1 m10 0.578 0.666
## F1 m09 0.409 0.832
##
## F2 m12 0.540 0.708
## F2 m05 0.446 0.801
## F2 m13 0.435 0.810
## F2 m01 0.415 0.828
##
## F3 m11 0.549 0.698
## F3 m16 0.510 0.740
## F3 m04 0.255 0.935 F2
##
## F4 m15 0.500 0.750
## F4 m02 0.500 0.750
##
## Cyn Fla
## Dec Tru ici tte
## m07 m06 m10 m09| m12 m05 m13 m01| m11 m16 m04| m15 m02| eit st sm ry
##
## m07 55 52 40 32| -16 -10 -11 -13| 22 21 14| -17 | 74 -27 43 -26
## m06 52 47 41 25| -14 -11 -16 -11| 29 24 | -15 | 68 -28 47 -19
## m10 40 41 33 25| -18 -15| 15 11 11| -18 -22| 58 -23 28 -40
## m09 32 25 25 17| -14 -13 -14| 16 17 14| -17 -18| 41 -27 36 -35
## ----------------------------------------------------------------------------------
## m12 -16 -14 -18 -14| 29 23 22 25| -20 -15 -18| 18| -26 54 -40 26
## m05 -10 -11 | 23 20 22 17| -13 -19 | 12| -13 45 -31 21
## m13 -11 -16 -13| 22 22 19 17| -11 -14| 16 13| -20 44 -21 29
## m01 -13 -11 -15 -14| 25 17 17 17| | 11 | -22 42 -19 18
## ----------------------------------------------------------------------------------
## m11 22 29 15 16| -20 -13 -11 | 30 28 14| | 34 -29 55
## m16 21 24 11 17| -15 -19 | 28 26 13| | 30 -25 51
## m04 14 11 14| -18 -14 | 14 13 | -15| 20 -27 25 -16
## ----------------------------------------------------------------------------------
## m15 -17 -15 -18 -17| 16 11| | 25 25| -28 24 50
## m02 -22 -18| 18 12 13 | -15| 25 25| -22 27 -13 50
## ----------------------------------------------------------------------------------
## Deceit 74 68 58 41| -26 -13 -20 -22| 34 30 20| -28 -22| 100 -44 64 -50
## Trust -27 -28 -23 -27| 54 45 44 42| -29 -25 -27| 24 27| -44 100 -61 51
## Cynicism 43 47 28 36| -40 -31 -21 -19| 55 51 25| -13| 64 -61 100 -16
## Flattery -26 -19 -40 -35| 26 21 29 18| -16| 50 50| -50 51 -16 100
##
## RESIDUALS
##
## m07 m06 m10 m09| m12 m05 m13 m01| m11 m16 m04| m15 m02|
##
## m07 | | | 09|
## m06 | | 05 | 13|
## m10 | 09 | -05 -08 | -08|
## m09 | -05 -07| 07| -07 -08|
## -------------------------------------------------------------
## m12 | | -10| -06 |
## m05 09 | | -05 | |
## m13 -05| | 11 -07| |
## m01 -07| | | |
## -------------------------------------------------------------
## m11 05 -05 | | | 05|
## m16 -08 | -05 11 | | |
## m04 07| -10 -07 | | -13|
## -------------------------------------------------------------
## m15 -07| -06 | | |
## m02 09 13 -08 -08| | 05 -13| |
## -------------------------------------------------------------
##
## Sum of Average
## Squares Abs Value
## ------- ---------
## m07 0.017 0.030
## m06 0.024 0.032
## m10 0.031 0.044
## m09 0.028 0.042
## m12 0.020 0.034
## m05 0.017 0.029
## m13 0.027 0.040
## m01 0.014 0.028
## m11 0.015 0.030
## m16 0.026 0.036
## m04 0.038 0.039
## m15 0.015 0.028
## m02 0.061 0.056
##
## Total sum of squares for all items: 0.333
##
## Root mean square residual for all items: 0.577
##
## Average absolute residual w/o the diagonal: 0.036
##
##
##
## LAVAAN SPECIFICATION
##
## MeasModel <-
## "
## Deceit =~ m07 + m06 + m10 + m09
## Trust =~ m12 + m05 + m13 + m01
## Cynicism =~ m11 + m16 + m04
## Flattery =~ m15 + m02
## "
##
## library(lavaan)
## fit <- lavaan::cfa(MeasModel, data=d, std.ov=TRUE, std.lv=TRUE)
## summary(fit, fit.measures=TRUE)
##
## --------
## The preceding code fits the model from data frame: d
## To access the correlation matrix directly without the data
## replace the parameter data with the parameters
## sample.cov and sample.nobs
## These names refer to the name of the input correlation matrix and sample size
##
Or, view pieces. See the names of all the output components. The
output includes:
- Heat map: Ordered correlation matrix, items within factors
- Item content: Items within factors
- Reliability analysis: Coefficient alpha and omega
- Solution: Factor pattern coefficients, indicator diagnostics
- Residual matrix: Items within factors
- Item Diagnostics: Sum of squares and average sum of squares by
item
- Lavaan code: Run the model in Lavaan for maximum likelihood
solution
## [1] "call" "out_title_scales" "out_labels"
## [4] "out_title_rel" "out_reliability" "out_title_solution"
## [7] "out_indicators" "out_solution" "out_title_residuals"
## [10] "out_residuals" "out_res_stats" "out_title_lavaan"
## [13] "out_lavaan" "out_Rmd" "ff.cor"
## [16] "if.cor" "diag.cor" "alpha"
## [19] "omega" "pred" "resid"
Here just view just the scale reliabilities.
## Scale Alpha Omega
## -----------------------
## F1 0.691 0.701
## F2 0.515 0.517
## F3 0.402 0.421
## F4 0.400 0.400
Can also just analysis item content, without the factor analysis.
cfa(MeasModel, labels="only")
##
## F1
## ------------------------------
## m07: There is no excuse for lying to someone else
## m06: Honesty is the best policy in all cases
## m10: When you ask someone to do something for you, it is best to give the real reasons for wanting it rather than giving reasons which carry more weight
## m09: All in all, it is better to be humble and honest than to be important and dishonest
##
## F2
## ------------------------------
## m12: Anyone who completely trusts anyone else is asking for trouble
## m05: It is safest to assume that all people have a vicious streak and it will come out when they are given a chance
## m13: The biggest difference between most criminals and other people is that the criminals are stupid enough to get caught
## m01: Never tell anyone the real reason you did something unless it is useful to do so
##
## F3
## ------------------------------
## m11: Most people who get ahead in the world lead clean, moral lives
## m16: It is possible to be good in all respects
## m04: Most people are basically good and kind
##
## F4
## ------------------------------
## m15: It is wise to flatter important people
## m02: The best way to handle people is to tell them what they want to hear
##
Generate R Markdown instructions of the confirmation factor analysis
with the option: Rmd. Output file in this example will be
m4.Rmd, a simple text file that can be edited with any text editor
including RStudio, from which it can be knit to generate dynamic output
such as to a Word document.
c <- cfa(MeasModel, R, Rmd="m4")
Re-order the Correlation Matrix
Hierarchical Cluster Analysis
Re-order the correlation matrix and display its heat map according to
a hierarchical cluster analysis, indicated by the default parameter of
the order parameter, hclust. Default input
correlation matrix is the mycor structure, from which
R will be extracted automatically.
The optional n_clusters parameter indicates to display
corresponding cluster membership according to the specified number of
clusters from the hierarchical tree. Although a four-factor solution,
choose five clusters to allow for a “garbage” cluster.
corReorder(R, n_clusters=5)
##
## 5 Cluster Solution
## -------------------
## m01 m05 m08 m12 m13 m18 m20 m02 m15 m03 m06 m07 m09 m10 m04 m11 m14 m16 m17 m19
## 1 1 1 1 1 1 1 2 2 3 3 3 3 3 4 4 4 4 5 5
## m02 m15 m08 m20 m18 m01 m12 m05 m13 m17 m19 m03
## m02 1.00 0.25 0.14 0.08 0.08 0.07 0.18 0.12 0.13 -0.05 -0.03 0.00
## m15 0.25 1.00 0.06 0.04 0.22 0.11 0.08 0.09 0.16 -0.02 -0.01 -0.01
## m08 0.14 0.06 1.00 0.15 0.12 0.22 0.10 0.10 0.09 -0.06 0.04 0.06
## m20 0.08 0.04 0.15 1.00 0.09 0.17 0.20 0.11 0.18 -0.25 -0.03 -0.05
## m18 0.08 0.22 0.12 0.09 1.00 0.19 0.10 0.20 0.16 -0.08 0.00 0.09
## m01 0.07 0.11 0.22 0.17 0.19 1.00 0.25 0.17 0.17 -0.12 0.08 0.16
## m12 0.18 0.08 0.10 0.20 0.10 0.25 1.00 0.23 0.22 -0.22 -0.06 0.04
## m05 0.12 0.09 0.10 0.11 0.20 0.17 0.23 1.00 0.22 -0.06 -0.08 0.06
## m13 0.13 0.16 0.09 0.18 0.16 0.17 0.22 0.22 1.00 -0.12 -0.01 -0.06
## m17 -0.05 -0.02 -0.06 -0.25 -0.08 -0.12 -0.22 -0.06 -0.12 1.00 0.09 0.07
## m19 -0.03 -0.01 0.04 -0.03 0.00 0.08 -0.06 -0.08 -0.01 0.09 1.00 0.02
## m03 0.00 -0.01 0.06 -0.05 0.09 0.16 0.04 0.06 -0.06 0.07 0.02 1.00
## m09 -0.18 -0.17 -0.10 -0.17 -0.09 -0.14 -0.14 -0.09 -0.13 0.15 0.02 0.16
## m10 -0.22 -0.18 -0.07 -0.12 -0.16 -0.15 -0.18 -0.02 -0.08 0.15 -0.01 0.15
## m06 -0.04 -0.15 -0.05 -0.07 -0.21 -0.11 -0.14 -0.11 -0.16 0.05 0.02 0.24
## m07 -0.09 -0.17 -0.09 -0.07 -0.16 -0.13 -0.16 -0.10 -0.11 0.13 0.02 0.24
## m11 0.01 -0.02 -0.10 -0.17 -0.23 -0.09 -0.20 -0.13 -0.11 0.03 0.01 0.10
## m16 -0.03 -0.01 -0.06 -0.01 -0.07 -0.08 -0.15 -0.19 -0.03 0.06 0.00 0.10
## m04 -0.15 -0.01 -0.11 -0.09 -0.05 -0.08 -0.18 -0.09 -0.14 0.13 0.02 0.07
## m14 -0.02 0.01 -0.12 -0.13 0.06 -0.03 -0.11 0.06 0.12 0.10 0.08 0.10
## m09 m10 m06 m07 m11 m16 m04 m14
## m02 -0.18 -0.22 -0.04 -0.09 0.01 -0.03 -0.15 -0.02
## m15 -0.17 -0.18 -0.15 -0.17 -0.02 -0.01 -0.01 0.01
## m08 -0.10 -0.07 -0.05 -0.09 -0.10 -0.06 -0.11 -0.12
## m20 -0.17 -0.12 -0.07 -0.07 -0.17 -0.01 -0.09 -0.13
## m18 -0.09 -0.16 -0.21 -0.16 -0.23 -0.07 -0.05 0.06
## m01 -0.14 -0.15 -0.11 -0.13 -0.09 -0.08 -0.08 -0.03
## m12 -0.14 -0.18 -0.14 -0.16 -0.20 -0.15 -0.18 -0.11
## m05 -0.09 -0.02 -0.11 -0.10 -0.13 -0.19 -0.09 0.06
## m13 -0.13 -0.08 -0.16 -0.11 -0.11 -0.03 -0.14 0.12
## m17 0.15 0.15 0.05 0.13 0.03 0.06 0.13 0.10
## m19 0.02 -0.01 0.02 0.02 0.01 0.00 0.02 0.08
## m03 0.16 0.15 0.24 0.24 0.10 0.10 0.07 0.10
## m09 1.00 0.25 0.25 0.32 0.16 0.17 0.14 0.06
## m10 0.25 1.00 0.41 0.40 0.15 0.11 0.11 0.15
## m06 0.25 0.41 1.00 0.52 0.29 0.24 0.09 0.11
## m07 0.32 0.40 0.52 1.00 0.22 0.21 0.14 0.15
## m11 0.16 0.15 0.29 0.22 1.00 0.28 0.14 0.26
## m16 0.17 0.11 0.24 0.21 0.28 1.00 0.13 0.22
## m04 0.14 0.11 0.09 0.14 0.14 0.13 1.00 0.23
## m14 0.06 0.15 0.11 0.15 0.26 0.22 0.23 1.00
Use the hclust_type parameter to specify the type of
cluster analysis provided by base R beyond the default of
"complete". Other possibilities include
"ward.D", "ward.D2", "single",
"average".
Manual Reorder
The variables in the correlation matrix can be re-ordered manually,
including sub-setting the matrix. Do so with the vars
parameter, specifying the index (ordinal positioning) of each variable
in the re-ordered matrix.
Here, subset six variables from the original correlation matrix.
Specifying the vars parameter automatically sets
order to manual, so no need to separately
specify.
R2 <- corReorder(R, vars=c(6,7,9,10,15,2))
## m06 m07 m09 m10 m15 m02
## m06 1.00 0.52 0.25 0.41 -0.15 -0.04
## m07 0.52 1.00 0.32 0.40 -0.17 -0.09
## m09 0.25 0.32 1.00 0.25 -0.17 -0.18
## m10 0.41 0.40 0.25 1.00 -0.18 -0.22
## m15 -0.15 -0.17 -0.17 -0.18 1.00 0.25
## m02 -0.04 -0.09 -0.18 -0.22 0.25 1.00