Process Data by Creating Ordinal Variables

For the process_data argument. It converts continuous indicator variable to ordinal variables.

Usage

ordinal_variables(data, cut_patterns = NULL, cuts = NULL)

cut_patterns(which = NULL)

Arguments

data: A data frame.
cut_patterns: A named vector. The names are the names of the latent variables for which indicator scores will be converted. Each value must be the name of one of the built-in patterns (call cut_patterns() to list the patterns and their names). Can be used with cuts but a latent variable should appear only either in cut_patterns or cuts, not both.
cuts: A named list. The names are the names of the latent variables for which indicator scores will be converted. Each element is a vector of the thresholds for the conversion. -Inf and Inf will be automatically included during the conversion. Can be used with cut_patterns but a latent variable should appear only either in cut_patterns or cuts, not both.
which: A name of a built-in pattern.

Value

The function ordinal_variables() returns a data frame with the the converted scores.

The function cut_patterns() returns a named list of the built-in patterns if which = NULL, and a numeric vector of the thresholds of a built-in pattern if which is set to one of the names of the built-in patterns.

Details

This function is to be used in the process_data argument of power4test().

It is used for converting the continuous indicator scores generated to ordinal scores (with values 1, 2, 3, etc.).

For example, if the cut points (thresholds) are -2 and 2, then sores will be converted to three categories: (-Inf to -2], (-2 to 2], and (2 to Inf]. The intervals are closed on the right. That is, a score of -2 is in the interval (-Inf to -2], not in the interval (-2 to 2).

The conversion is implemented by cut().

There are two ways to specify the conversion. The first one is to use some built-in thresholds, based on Savalei and Rhemtulla (2013), Table 1. Call cut_patterns() with no argument to list all the built-in patterns and their names.

Alternatively, users can specify the thresholds directly through the argument cuts.

Currently, all indicators of a latent variable must be converted in the same way.

References

Savalei, V., & Rhemtulla, M. (2013). The performance of robust test statistics with categorical data. British Journal of Mathematical and Statistical Psychology, 66(2), 201–223. doi:10.1111/j.2044-8317.2012.02049.x

Examples


# Specify the model

mod <-
"
m ~ x
y ~ m + x
"

# Specify the population values

mod_es <-
"
y ~ m: l
m ~ x: m
y ~ x: n
"

# Specify the numbers of indicators and reliability coefficients

k <- c(y = 3,
       m = 4,
       x = 5)
rel <- c(y = .70,
         m = .70,
         x = .70)

# Simulate the data

out <- power4test(
         nrep = 2,
         model = mod,
         pop_es = mod_es,
         n = 200,
         number_of_indicators = k,
         reliability = rel,
         process_data = list(fun = "ordinal_variables",
                             args = list(cut_patterns = c(x = "s3"),
                                         cuts = list(m = c(-2, 0, 2)))),
         test_fun = test_parameters,
         test_args = list(op = "~"),
         parallel = FALSE,
         iseed = 1234)
#> Simulate the data:
#> Fit the model(s):
#> Do the test: test_parameters: CIs (op: ~) 

dat <- pool_sim_data(out)
head(dat, 50)
#>             y1           y2          y3 m1 m2 m3 m4 x1 x2 x3 x4 x5
#> 1   0.01052630 -0.992532325 -1.12858280  1  1  2  2  1  2  1  3  2
#> 2   0.94959134 -0.550501576  0.71633641  4  2  2  2  2  2  2  2  1
#> 3  -0.86172905  0.369667531 -0.74777555  3  4  3  2  2  2  2  2  2
#> 4   0.16065430  0.930350881  0.04865838  1  2  2  2  2  2  1  2  2
#> 5   0.36428103  0.280704629  0.88255101  3  3  2  3  1  2  1  2  2
#> 6   0.47454562  1.193414924 -0.81892507  3  3  3  3  2  2  2  2  2
#> 7   1.84947779  0.192314739  1.72345307  3  3  3  2  2  1  2  2  3
#> 8   1.46300684  0.187227098  0.18509161  2  2  2  2  2  2  2  1  1
#> 9  -1.07128820  0.213832606 -0.71610120  2  2  2  2  2  2  2  2  2
#> 10 -0.16787023 -1.192830517 -0.59227042  2  3  2  2  1  2  2  2  2
#> 11 -0.52480153  0.538197321  0.90971320  2  3  2  2  1  1  2  2  2
#> 12 -0.47321651 -0.051951968  0.60136010  2  1  2  2  1  3  2  2  2
#> 13  0.90104149  0.065799515 -0.36006259  2  2  3  2  2  2  2  2  2
#> 14 -1.01343165 -1.692283852 -1.44158610  2  3  2  2  2  2  3  1  2
#> 15 -1.06075451  1.804756880  0.14617995  3  3  3  4  1  2  2  2  3
#> 16 -0.22584750  0.009541832  0.20346814  3  3  2  3  2  3  2  2  2
#> 17  1.01902557 -0.130757360 -0.46949887  3  3  3  2  3  2  2  2  3
#> 18 -0.56502372 -0.735528452 -2.45120322  3  2  3  2  2  2  2  2  2
#> 19 -1.01022070 -0.809507916 -0.59213953  3  3  2  2  2  2  3  2  3
#> 20  0.64497818  0.441692748  0.25057198  4  3  3  3  2  2  3  2  1
#> 21  1.22553574 -0.419440215  0.45720513  3  2  2  2  2  2  2  2  2
#> 22  0.52006346  0.945972594 -0.36778692  2  2  3  2  2  2  2  3  3
#> 23  0.47989941  0.413242189  1.06458100  3  3  2  2  2  1  2  2  2
#> 24  0.83837396  1.334289107  0.27753312  3  3  3  3  3  3  2  2  2
#> 25  0.45873786  1.066181596 -0.29502525  2  2  3  1  2  2  2  3  2
#> 26  0.46840197  0.044822336 -1.10683996  2  1  2  2  2  3  2  3  1
#> 27  1.34943533  1.906682546  3.00702248  3  3  2  3  2  2  2  2  2
#> 28 -0.20840506 -0.327936980  0.61388164  2  2  3  2  2  2  2  2  2
#> 29  0.22589651 -1.330356124 -0.69540289  2  2  2  2  2  2  1  1  2
#> 30 -0.45918773 -0.128768664 -1.03451723  3  2  2  3  1  2  3  1  2
#> 31  1.13580785 -0.133853226  0.82626211  3  3  2  3  1  2  1  1  2
#> 32  0.28465082 -0.380563660 -1.57508921  3  3  2  3  2  1  1  1  1
#> 33 -2.08318854 -1.291915129 -1.72575951  1  2  2  2  1  2  1  1  2
#> 34  0.15287649  0.306684498 -0.74724547  2  2  1  3  1  2  2  2  2
#> 35 -1.45578006  0.144219309 -1.12064300  2  1  1  2  2  1  2  3  2
#> 36 -1.92471062 -0.019276706 -1.50393445  2  2  2  3  2  2  3  3  3
#> 37 -2.32469913 -0.690198223 -1.41211190  2  2  2  3  3  2  2  3  3
#> 38 -0.45449874 -0.348604457 -0.57666311  2  2  2  2  3  2  3  3  1
#> 39 -0.22685258 -0.633981183 -0.73922466  3  2  3  3  2  2  2  2  2
#> 40  1.14393646  0.137734893  0.69951719  2  2  2  2  1  1  2  3  2
#> 41  0.76074030 -0.681440535  0.68772460  3  3  3  3  2  3  3  2  2
#> 42 -0.61874796 -0.016490482 -1.02900539  2  3  2  2  2  2  2  1  2
#> 43 -0.79195229 -1.200898358 -1.30236735  3  2  2  2  1  1  1  3  1
#> 44 -0.16069150  0.529614698  0.62540536  2  2  2  2  2  1  2  1  1
#> 45 -0.08074066 -0.231264615  1.43307962  2  2  3  2  2  2  1  1  1
#> 46 -0.88273770 -1.057467169  1.16472866  2  2  3  3  2  1  3  2  3
#> 47  0.36822771  0.482098562  1.08300171  2  3  3  2  2  2  2  2  3
#> 48 -0.12661242 -1.218748112 -0.21361696  2  2  2  2  3  2  1  2  3
#> 49 -0.50786225  0.691200009 -1.27590161  3  2  2  2  3  3  2  2  1
#> 50  0.23234577 -1.170596984 -0.34671738  2  3  2  3  2  3  2  3  2

# The built-in patterns

cut_patterns()
#> $s2
#> [1] 0
#> 
#> $s3
#> [1] -0.83  0.83
#> 
#> $s4
#> [1] -1.25  0.00  1.25
#> 
#> $s5
#> [1] -1.5 -0.5  0.5  1.5
#> 
#> $s6
#> [1] -1.60 -0.83  0.00  0.83  1.60
#> 
#> $s7
#> [1] -1.79 -1.07 -0.36  0.36  1.07  1.79
#> 
#> $ma2
#> [1] 0.36
#> 
#> $ma3
#> [1] -0.50  0.76
#> 
#> $ma4
#> [1] -0.31  0.79  1.66
#> 
#> $ma5
#> [1] -0.70  0.39  1.16  2.05
#> 
#> $ma6
#> [1] -1.05  0.08  0.81  1.44  2.33
#> 
#> $ma7
#> [1] -1.43 -0.43  0.38  0.94  1.44  2.54
#> 
#> $ea2
#> [1] 1.04
#> 
#> $ea3
#> [1] 0.58 1.13
#> 
#> $ea4
#> [1] 0.28 0.71 1.23
#> 
#> $ea5
#> [1] 0.05 0.44 0.84 1.34
#> 
#> $ea6
#> [1] -0.13  0.25  0.61  0.99  1.48
#> 
#> $ea7
#> [1] -0.25  0.13  0.47  0.81  1.18  1.64
#> 
#> $`-ma2`
#> [1] -0.36
#> 
#> $`-ma3`
#> [1] -0.76  0.50
#> 
#> $`-ma4`
#> [1] -1.66 -0.79  0.31
#> 
#> $`-ma5`
#> [1] -2.05 -1.16 -0.39  0.70
#> 
#> $`-ma6`
#> [1] -2.33 -1.44 -0.81 -0.08  1.05
#> 
#> $`-ma7`
#> [1] -2.54 -1.44 -0.94 -0.38  0.43  1.43
#> 
#> $`-ea2`
#> [1] -1.04
#> 
#> $`-ea3`
#> [1] -1.13 -0.58
#> 
#> $`-ea4`
#> [1] -1.23 -0.71 -0.28
#> 
#> $`-ea5`
#> [1] -1.34 -0.84 -0.44 -0.05
#> 
#> $`-ea6`
#> [1] -1.48 -0.99 -0.61 -0.25  0.13
#> 
#> $`-ea7`
#> [1] -1.64 -1.18 -0.81 -0.47 -0.13  0.25
#>