This function is designed to calculate the descriptive statistics and summaries that are often reported on raw data when the main analyses use structural equation modelling.
Usage
SEMSummary(
formula,
data,
use = c("fiml", "pairwise.complete.obs", "complete.obs")
)Arguments
- formula
A formula of the variables to be used in the analysis. See the ‘details’ section for more information.
- data
A data frame, matrix, or list containing the variables used in the formula. This is a required argument.
- use
A character vector of how to handle missing data. Defaults to “fiml”.
Value
A list with S3 class “SEMSummary”
- names
A character vector containing the variable names.
- n
An integer vector of the length of each variable used (this includes available and missing data).
- nmissing
An integer vector of the number of missing values in each variable.
- mu
A vector of the arithmetic means of each variable (on complete data).
- stdev
A numeric vector of the standard deviations of each variable (on complete data).
- Sigma
The numeric covariance matrix for all variables.
- sSigma
The numeric correlation matrix for all variables.
- coverage
A numeric matrix giving the percentage (technically decimal) of information available for each pairwise covariance/correlation.
- pvalue
The two-sided p values for the correlation matrix. Pairwise present N used to calculate degrees of freedom.
Details
This function calculates a variety of relevant statistics on the raw data used in a SEM analysis. Because it is meant for SEM style data, for now it expects all variables to be numeric. In the future I may try to expand it to handle factor variables somehow.
Both the formula and data arguments are required. The formula should
be the right hand side only. The most common way to use it would be with
variable names separated by ‘+s’. For convenience, a ‘.’ is
expanded to mean “all variables in the data set”. For a large number
of variables or when whole datasets are being analyzed, this can be considerably
easier to write. Also it facilitates column indexing by simply passing a subset
of the data (e.g., data[, 1:10]) and using the ‘.’ expansion to
analyze the first 10 columns. The examples section demonstrate this use.
Also noteworthy is that SEMSummary is not really meant to be used
on its own. It is the computational workhorse, but it is meant to be used
with a styling or printing method to produce simple output.
APAStyler has methods for SEMSummary output.
There are several new ways to handle missing data now including listwise deletion, pairwise deletion, and using the EM algorithm, the default.
Examples
## Example using the built in iris dataset
s <- SEMSummary(~ Sepal.Length + Sepal.Width + Petal.Length, data = iris)
s # show output ... not very nice
#> $names
#> [1] "Sepal.Length" "Sepal.Width" "Petal.Length"
#>
#> $n
#> [1] 150
#>
#> $nmissing
#> Sepal.Length Sepal.Width Petal.Length
#> 0 0 0
#>
#> $mu
#> Sepal.Length Sepal.Width Petal.Length
#> 5.843333 3.057333 3.758000
#>
#> $stdev
#> Sepal.Length Sepal.Width Petal.Length
#> 0.8280661 0.4358663 1.7652982
#>
#> $Sigma
#> Sepal.Length Sepal.Width Petal.Length
#> Sepal.Length 0.6856935 -0.0424340 1.2743154
#> Sepal.Width -0.0424340 0.1899794 -0.3296564
#> Petal.Length 1.2743154 -0.3296564 3.1162779
#>
#> $sSigma
#> Sepal.Length Sepal.Width Petal.Length
#> Sepal.Length 1.0000000 -0.1175698 0.8717538
#> Sepal.Width -0.1175698 1.0000000 -0.4284401
#> Petal.Length 0.8717538 -0.4284401 1.0000000
#>
#> $coverage
#> Sepal.Length Sepal.Width Petal.Length
#> Sepal.Length 1 1 1
#> Sepal.Width 1 1 1
#> Petal.Length 1 1 1
#>
#> $pvalue
#> Sepal.Length Sepal.Width Petal.Length
#> Sepal.Length NA 1.518983e-01 0.000000e+00
#> Sepal.Width 0.1518983 NA 4.513314e-08
#> Petal.Length 0.0000000 4.513314e-08 NA
#>
#> attr(,"class")
#> [1] "SEMSummary"
## Prettier output from SEMSummary
APAStyler(s)
#> N M SD 1. 2. 3.
#> 1. Sepal.Length 150 5.84 0.83 - -0.04 1.27
#> 2. Sepal.Width 150 3.06 0.44 - -0.33
#> 3. Petal.Length 150 3.76 1.77 -
#>
#> Percentage of coverage for each pairwise covariance or correlation
#>
#> Sepal.Length Sepal.Width Petal.Length
#> Sepal.Length 1 1 1
#> Sepal.Width 1 1
#> Petal.Length 1
#### Subset the dataset and use the . expansion ####
## summary for all variables in mtcars data set
## with 11 variables, this could be a pain to write out
SEMSummary(~ ., data = mtcars)
#> $names
#> [1] "mpg" "cyl" "disp" "hp" "drat" "wt" "qsec" "vs" "am" "gear"
#> [11] "carb"
#>
#> $n
#> [1] 32
#>
#> $nmissing
#> mpg cyl disp hp drat wt qsec vs am gear carb
#> 0 0 0 0 0 0 0 0 0 0 0
#>
#> $mu
#> mpg cyl disp hp drat wt qsec
#> 20.090625 6.187500 230.721875 146.687500 3.596563 3.217250 17.848750
#> vs am gear carb
#> 0.437500 0.406250 3.687500 2.812500
#>
#> $stdev
#> mpg cyl disp hp drat wt
#> 6.0269481 1.7859216 123.9386938 68.5628685 0.5346787 0.9784574
#> qsec vs am gear carb
#> 1.7869432 0.5040161 0.4989909 0.7378041 1.6152000
#>
#> $Sigma
#> mpg cyl disp hp drat wt
#> mpg 36.324103 -9.1723790 -633.09721 -320.732056 2.19506351 -5.1166847
#> cyl -9.172379 3.1895161 199.66028 101.931452 -0.66836694 1.3673710
#> disp -633.097208 199.6602823 15360.79983 6721.158669 -47.06401915 107.6842040
#> hp -320.732056 101.9314516 6721.15867 4700.866935 -16.45110887 44.1926613
#> drat 2.195064 -0.6683669 -47.06402 -16.451109 0.28588135 -0.3727207
#> wt -5.116685 1.3673710 107.68420 44.192661 -0.37272073 0.9573790
#> qsec 4.509149 -1.8868548 -96.05168 -86.770081 0.08714073 -0.3054816
#> vs 2.017137 -0.7298387 -44.37762 -24.987903 0.11864919 -0.2736613
#> am 1.803931 -0.4657258 -36.56401 -8.320565 0.19015121 -0.3381048
#> gear 2.135685 -0.6491935 -50.80262 -6.358871 0.27598790 -0.4210806
#> carb -5.363105 1.5201613 79.06875 83.036290 -0.07840726 0.6757903
#> qsec vs am gear carb
#> mpg 4.50914919 2.01713710 1.80393145 2.1356855 -5.36310484
#> cyl -1.88685484 -0.72983871 -0.46572581 -0.6491935 1.52016129
#> disp -96.05168145 -44.37762097 -36.56401210 -50.8026210 79.06875000
#> hp -86.77008065 -24.98790323 -8.32056452 -6.3588710 83.03629032
#> drat 0.08714073 0.11864919 0.19015121 0.2759879 -0.07840726
#> wt -0.30548161 -0.27366129 -0.33810484 -0.4210806 0.67579032
#> qsec 3.19316613 0.67056452 -0.20495968 -0.2804032 -1.89411290
#> vs 0.67056452 0.25403226 0.04233871 0.0766129 -0.46370968
#> am -0.20495968 0.04233871 0.24899194 0.2923387 0.04637097
#> gear -0.28040323 0.07661290 0.29233871 0.5443548 0.32661290
#> carb -1.89411290 -0.46370968 0.04637097 0.3266129 2.60887097
#>
#> $sSigma
#> mpg cyl disp hp drat wt
#> mpg 1.0000000 -0.8521620 -0.8475514 -0.7761684 0.68117191 -0.8676594
#> cyl -0.8521620 1.0000000 0.9020329 0.8324475 -0.69993811 0.7824958
#> disp -0.8475514 0.9020329 1.0000000 0.7909486 -0.71021393 0.8879799
#> hp -0.7761684 0.8324475 0.7909486 1.0000000 -0.44875912 0.6587479
#> drat 0.6811719 -0.6999381 -0.7102139 -0.4487591 1.00000000 -0.7124406
#> wt -0.8676594 0.7824958 0.8879799 0.6587479 -0.71244065 1.0000000
#> qsec 0.4186840 -0.5912421 -0.4336979 -0.7082234 0.09120476 -0.1747159
#> vs 0.6640389 -0.8108118 -0.7104159 -0.7230967 0.44027846 -0.5549157
#> am 0.5998324 -0.5226070 -0.5912270 -0.2432043 0.71271113 -0.6924953
#> gear 0.4802848 -0.4926866 -0.5555692 -0.1257043 0.69961013 -0.5832870
#> carb -0.5509251 0.5269883 0.3949769 0.7498125 -0.09078980 0.4276059
#> qsec vs am gear carb
#> mpg 0.41868403 0.6640389 0.59983243 0.4802848 -0.55092507
#> cyl -0.59124207 -0.8108118 -0.52260705 -0.4926866 0.52698829
#> disp -0.43369788 -0.7104159 -0.59122704 -0.5555692 0.39497686
#> hp -0.70822339 -0.7230967 -0.24320426 -0.1257043 0.74981247
#> drat 0.09120476 0.4402785 0.71271113 0.6996101 -0.09078980
#> wt -0.17471588 -0.5549157 -0.69249526 -0.5832870 0.42760594
#> qsec 1.00000000 0.7445354 -0.22986086 -0.2126822 -0.65624923
#> vs 0.74453544 1.0000000 0.16834512 0.2060233 -0.56960714
#> am -0.22986086 0.1683451 1.00000000 0.7940588 0.05753435
#> gear -0.21268223 0.2060233 0.79405876 1.0000000 0.27407284
#> carb -0.65624923 -0.5696071 0.05753435 0.2740728 1.00000000
#>
#> $coverage
#> mpg cyl disp hp drat wt qsec vs am gear carb
#> mpg 1 1 1 1 1 1 1 1 1 1 1
#> cyl 1 1 1 1 1 1 1 1 1 1 1
#> disp 1 1 1 1 1 1 1 1 1 1 1
#> hp 1 1 1 1 1 1 1 1 1 1 1
#> drat 1 1 1 1 1 1 1 1 1 1 1
#> wt 1 1 1 1 1 1 1 1 1 1 1
#> qsec 1 1 1 1 1 1 1 1 1 1 1
#> vs 1 1 1 1 1 1 1 1 1 1 1
#> am 1 1 1 1 1 1 1 1 1 1 1
#> gear 1 1 1 1 1 1 1 1 1 1 1
#> carb 1 1 1 1 1 1 1 1 1 1 1
#>
#> $pvalue
#> mpg cyl disp hp drat
#> mpg NA 6.112687e-10 9.380327e-10 1.787835e-07 1.776240e-05
#> cyl 6.112687e-10 NA 1.803002e-12 3.477861e-09 8.244636e-06
#> disp 9.380327e-10 1.803002e-12 NA 7.142679e-08 5.282022e-06
#> hp 1.787835e-07 3.477861e-09 7.142679e-08 NA 9.988772e-03
#> drat 1.776240e-05 8.244636e-06 5.282022e-06 9.988772e-03 NA
#> wt 1.293959e-10 1.217567e-07 1.222311e-11 4.145827e-05 4.784260e-06
#> qsec 1.708199e-02 3.660533e-04 1.314404e-02 5.766253e-06 6.195826e-01
#> vs 3.415937e-05 1.843018e-08 5.235012e-06 2.940896e-06 1.167553e-02
#> am 2.850207e-04 2.151207e-03 3.662114e-04 1.798309e-01 4.726790e-06
#> gear 5.400948e-03 4.173297e-03 9.635921e-04 4.930119e-01 8.360110e-06
#> carb 1.084446e-03 1.942340e-03 2.526789e-02 7.827810e-07 6.211834e-01
#> wt qsec vs am gear
#> mpg 1.293959e-10 1.708199e-02 3.415937e-05 2.850207e-04 5.400948e-03
#> cyl 1.217567e-07 3.660533e-04 1.843018e-08 2.151207e-03 4.173297e-03
#> disp 1.222311e-11 1.314404e-02 5.235012e-06 3.662114e-04 9.635921e-04
#> hp 4.145827e-05 5.766253e-06 2.940896e-06 1.798309e-01 4.930119e-01
#> drat 4.784260e-06 6.195826e-01 1.167553e-02 4.726790e-06 8.360110e-06
#> wt NA 3.388683e-01 9.798492e-04 1.125440e-05 4.586601e-04
#> qsec 3.388683e-01 NA 1.029669e-06 2.056621e-01 2.425344e-01
#> vs 9.798492e-04 1.029669e-06 NA 3.570439e-01 2.579439e-01
#> am 1.125440e-05 2.056621e-01 3.570439e-01 NA 5.834043e-08
#> gear 4.586601e-04 2.425344e-01 2.579439e-01 5.834043e-08 NA
#> carb 1.463861e-02 4.536949e-05 6.670496e-04 7.544526e-01 1.290291e-01
#> carb
#> mpg 1.084446e-03
#> cyl 1.942340e-03
#> disp 2.526789e-02
#> hp 7.827810e-07
#> drat 6.211834e-01
#> wt 1.463861e-02
#> qsec 4.536949e-05
#> vs 6.670496e-04
#> am 7.544526e-01
#> gear 1.290291e-01
#> carb NA
#>
#> attr(,"class")
#> [1] "SEMSummary"
## . expansion is also useful when we know column positions
## but not necessarily names
SEMSummary(~ ., data = mtcars[, c(1, 2, 3, 9, 10, 11)])
#> $names
#> [1] "mpg" "cyl" "disp" "am" "gear" "carb"
#>
#> $n
#> [1] 32
#>
#> $nmissing
#> mpg cyl disp am gear carb
#> 0 0 0 0 0 0
#>
#> $mu
#> mpg cyl disp am gear carb
#> 20.09062 6.18750 230.72188 0.40625 3.68750 2.81250
#>
#> $stdev
#> mpg cyl disp am gear carb
#> 6.0269481 1.7859216 123.9386938 0.4989909 0.7378041 1.6152000
#>
#> $Sigma
#> mpg cyl disp am gear carb
#> mpg 36.324103 -9.1723790 -633.09721 1.80393145 2.1356855 -5.36310484
#> cyl -9.172379 3.1895161 199.66028 -0.46572581 -0.6491935 1.52016129
#> disp -633.097208 199.6602823 15360.79983 -36.56401210 -50.8026210 79.06875000
#> am 1.803931 -0.4657258 -36.56401 0.24899194 0.2923387 0.04637097
#> gear 2.135685 -0.6491935 -50.80262 0.29233871 0.5443548 0.32661290
#> carb -5.363105 1.5201613 79.06875 0.04637097 0.3266129 2.60887097
#>
#> $sSigma
#> mpg cyl disp am gear carb
#> mpg 1.0000000 -0.8521620 -0.8475514 0.59983243 0.4802848 -0.55092507
#> cyl -0.8521620 1.0000000 0.9020329 -0.52260705 -0.4926866 0.52698829
#> disp -0.8475514 0.9020329 1.0000000 -0.59122704 -0.5555692 0.39497686
#> am 0.5998324 -0.5226070 -0.5912270 1.00000000 0.7940588 0.05753435
#> gear 0.4802848 -0.4926866 -0.5555692 0.79405876 1.0000000 0.27407284
#> carb -0.5509251 0.5269883 0.3949769 0.05753435 0.2740728 1.00000000
#>
#> $coverage
#> mpg cyl disp am gear carb
#> mpg 1 1 1 1 1 1
#> cyl 1 1 1 1 1 1
#> disp 1 1 1 1 1 1
#> am 1 1 1 1 1 1
#> gear 1 1 1 1 1 1
#> carb 1 1 1 1 1 1
#>
#> $pvalue
#> mpg cyl disp am gear
#> mpg NA 6.112687e-10 9.380327e-10 2.850207e-04 5.400948e-03
#> cyl 6.112687e-10 NA 1.803002e-12 2.151207e-03 4.173297e-03
#> disp 9.380327e-10 1.803002e-12 NA 3.662114e-04 9.635921e-04
#> am 2.850207e-04 2.151207e-03 3.662114e-04 NA 5.834043e-08
#> gear 5.400948e-03 4.173297e-03 9.635921e-04 5.834043e-08 NA
#> carb 1.084446e-03 1.942340e-03 2.526789e-02 7.544526e-01 1.290291e-01
#> carb
#> mpg 0.001084446
#> cyl 0.001942340
#> disp 0.025267886
#> am 0.754452554
#> gear 0.129029084
#> carb NA
#>
#> attr(,"class")
#> [1] "SEMSummary"
## clean up
rm(s)
## sample data
Xmiss <- as.matrix(iris[, -5])
# make q0% missing completely at random
set.seed(10)
Xmiss[sample(length(Xmiss), length(Xmiss) * .10)] <- NA
Xmiss <- as.data.frame(Xmiss)
SEMSummary(~ ., data = Xmiss, use = "fiml")
#> $names
#> [1] "Sepal.Length" "Sepal.Width" "Petal.Length" "Petal.Width"
#>
#> $n
#> [1] 150
#>
#> $nmissing
#> Sepal.Length Sepal.Width Petal.Length Petal.Width
#> 15 8 21 16
#>
#> $mu
#> Sepal.Length Sepal.Width Petal.Length Petal.Width
#> 5.859048 3.063777 3.744655 1.199088
#>
#> $stdev
#> Sepal.Length Sepal.Width Petal.Length Petal.Width
#> 0.8315335 0.4326462 1.7393932 0.7630092
#>
#> $Sigma
#> Sepal.Length Sepal.Width Petal.Length Petal.Width
#> Sepal.Length 0.69144798 -0.04277193 1.255775 0.5177624
#> Sepal.Width -0.04277193 0.18718270 -0.325356 -0.1222384
#> Petal.Length 1.25577465 -0.32535602 3.025489 1.2796561
#> Petal.Width 0.51776245 -0.12223835 1.279656 0.5821831
#>
#> $sSigma
#> Sepal.Length Sepal.Width Petal.Length Petal.Width
#> Sepal.Length 1.0000000 -0.1188902 0.8682288 0.8160580
#> Sepal.Width -0.1188902 1.0000000 -0.4323428 -0.3702924
#> Petal.Length 0.8682288 -0.4323428 1.0000000 0.9641969
#> Petal.Width 0.8160580 -0.3702924 0.9641969 1.0000000
#>
#> $coverage
#> Sepal.Length Sepal.Width Petal.Length Petal.Width
#> Sepal.Length 0.9000000 0.8466667 0.7733333 0.8000000
#> Sepal.Width 0.8466667 0.9466667 0.8266667 0.8400000
#> Petal.Length 0.7733333 0.8266667 0.8600000 0.7600000
#> Petal.Width 0.8000000 0.8400000 0.7600000 0.8933333
#>
#> $pvalue
#> Sepal.Length Sepal.Width Petal.Length Petal.Width
#> Sepal.Length NA 1.830888e-01 0.000000e+00 0.000000e+00
#> Sepal.Width 0.1830888 NA 5.321816e-07 1.973922e-05
#> Petal.Length 0.0000000 5.321816e-07 NA 0.000000e+00
#> Petal.Width 0.0000000 1.973922e-05 0.000000e+00 NA
#>
#> attr(,"class")
#> [1] "SEMSummary"
## pairwise
APAStyler(SEMSummary(~ ., data = Xmiss, use = "pair"),
type = "cor")
#> N M SD 1. 2. 3. 4.
#> 1. Sepal.Length 135 5.89 0.81 - -0.18 0.86 0.81
#> 2. Sepal.Width 142 3.07 0.44 - -0.43 -0.43
#> 3. Petal.Length 129 3.82 1.74 - 0.97
#> 4. Petal.Width 134 1.19 0.77 -
#>
#> Percentage of coverage for each pairwise covariance or correlation
#>
#> Sepal.Length Sepal.Width Petal.Length Petal.Width
#> Sepal.Length 0.9 0.85 0.77 0.8
#> Sepal.Width 0.95 0.83 0.84
#> Petal.Length 0.86 0.76
#> Petal.Width 0.89
## same as cor()
cor(Xmiss, use = "pairwise.complete.obs")
#> Sepal.Length Sepal.Width Petal.Length Petal.Width
#> Sepal.Length 1.0000000 -0.1832230 0.8646983 0.8119316
#> Sepal.Width -0.1832230 1.0000000 -0.4291999 -0.4293565
#> Petal.Length 0.8646983 -0.4291999 1.0000000 0.9650212
#> Petal.Width 0.8119316 -0.4293565 0.9650212 1.0000000
## complete cases only
SEMSummary(~ ., data = Xmiss, use = "comp")
#> $names
#> [1] "Sepal.Length" "Sepal.Width" "Petal.Length" "Petal.Width"
#>
#> $n
#> [1] 150
#>
#> $nmissing
#> Sepal.Length Sepal.Width Petal.Length Petal.Width
#> 15 8 21 16
#>
#> $mu
#> Sepal.Length Sepal.Width Petal.Length Petal.Width
#> 5.853608 3.037113 3.802062 1.229897
#>
#> $stdev
#> Sepal.Length Sepal.Width Petal.Length Petal.Width
#> 0.7987049 0.4194042 1.7165845 0.7479367
#>
#> $Sigma
#> Sepal.Length Sepal.Width Petal.Length Petal.Width
#> Sepal.Length 0.63792955 -0.05919781 1.1747841 0.4824431
#> Sepal.Width -0.05919781 0.17589991 -0.3682023 -0.1415378
#> Petal.Length 1.17478415 -0.36820232 2.9466624 1.2399377
#> Petal.Width 0.48244308 -0.14153780 1.2399377 0.5594094
#>
#> $sSigma
#> Sepal.Length Sepal.Width Petal.Length Petal.Width
#> Sepal.Length 1.0000000 -0.1767203 0.8568534 0.8075973
#> Sepal.Width -0.1767203 1.0000000 -0.5114327 -0.4512059
#> Petal.Length 0.8568534 -0.5114327 1.0000000 0.9657613
#> Petal.Width 0.8075973 -0.4512059 0.9657613 1.0000000
#>
#> $coverage
#> Sepal.Length Sepal.Width Petal.Length Petal.Width
#> Sepal.Length 0.9000000 0.8466667 0.7733333 0.8000000
#> Sepal.Width 0.8466667 0.9466667 0.8266667 0.8400000
#> Petal.Length 0.7733333 0.8266667 0.8600000 0.7600000
#> Petal.Width 0.8000000 0.8400000 0.7600000 0.8933333
#>
#> $pvalue
#> Sepal.Length Sepal.Width Petal.Length Petal.Width
#> Sepal.Length NA 4.686510e-02 0.000000e+00 0.000000e+00
#> Sepal.Width 0.0468651 NA 1.278788e-09 1.142829e-07
#> Petal.Length 0.0000000 1.278788e-09 NA 0.000000e+00
#> Petal.Width 0.0000000 1.142829e-07 0.000000e+00 NA
#>
#> attr(,"class")
#> [1] "SEMSummary"
## clean up
rm(Xmiss)