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Conditional Selection Rate

Source: R/02_TestItemFunctions.R
CSR.Rd

Calculate the Conditional Selection Rate (CSR) for polytomous data. CSR measures the proportion of respondents who selected a specific category in item K, given that they selected a particular category in item J.

Usage

CSR(U, na = NULL, Z = NULL, w = NULL)

Arguments

U

Either an object of class "exametrika" or raw data. When raw data is given, it is converted to the exametrika class with the dataFormat function.

na

Values to be treated as missing values.

Z

Missing indicator matrix of type matrix or data.frame. Values of 1 indicate observed responses, while 0 indicates missing data.

w

Item weight vector specifying the relative importance of each item.

Value

A list of Joint Selection Rate matrices for each item pair.

Details

The function returns a nested list structure CSR, where CSR[[j]][[k]] contains a matrix of conditional probabilities. In this matrix, the element at row l and column m represents P(K=m|J=l), which is the probability of selecting category m for item K, given that category l was selected for item J.

Mathematically, for each cell (l,m) in the CSR[[j]][[k]] matrix: CSR[[j]][[k]][l,m] = P(Item K = category m | Item J = category l)

This is calculated as the number of respondents who selected both category l for item J and category m for item K, divided by the total number of respondents who selected category l for item J.

Examples

# example code
# Calculate CSR using sample dataset J5S1000
CSR(J5S1000)
#> [[1]]
#> [[1]][[1]]
#>         V1-Cat1 V1-Cat2 V1-Cat3 V1-Cat4
#> V1-Cat1       1       0       0       0
#> V1-Cat2       0       1       0       0
#> V1-Cat3       0       0       1       0
#> V1-Cat4       0       0       0       1
#> 
#> [[1]][[2]]
#>           V2-Cat1   V2-Cat2   V2-Cat3
#> V1-Cat1 0.4299517 0.4009662 0.1690821
#> V1-Cat2 0.2635135 0.5337838 0.2027027
#> V1-Cat3 0.2581818 0.4763636 0.2654545
#> V1-Cat4 0.1853659 0.4292683 0.3853659
#> 
#> [[1]][[3]]
#>           V3-Cat1   V3-Cat2   V3-Cat3   V3-Cat4
#> V1-Cat1 0.3205742 0.3349282 0.2057416 0.1387560
#> V1-Cat2 0.2040134 0.2775920 0.2608696 0.2575251
#> V1-Cat3 0.1684982 0.2783883 0.3150183 0.2380952
#> V1-Cat4 0.1250000 0.2355769 0.2644231 0.3750000
#> 
#> [[1]][[4]]
#>           V4-Cat1   V4-Cat2   V4-Cat3
#> V1-Cat1 0.4182692 0.4086538 0.1730769
#> V1-Cat2 0.3010033 0.4414716 0.2575251
#> V1-Cat3 0.2028986 0.5108696 0.2862319
#> V1-Cat4 0.1256039 0.4541063 0.4202899
#> 
#> [[1]][[5]]
#>           V5-Cat1   V5-Cat2   V5-Cat3   V5-Cat4
#> V1-Cat1 0.3492823 0.3062201 0.2200957 0.1244019
#> V1-Cat2 0.2709030 0.2976589 0.2474916 0.1839465
#> V1-Cat3 0.2072727 0.2472727 0.3272727 0.2181818
#> V1-Cat4 0.1153846 0.2163462 0.3317308 0.3365385
#> 
#> 
#> [[2]]
#> [[2]][[1]]
#>           V1-Cat1   V1-Cat2   V1-Cat3   V1-Cat4
#> V2-Cat1 0.3224638 0.2826087 0.2572464 0.1376812
#> V2-Cat2 0.1804348 0.3434783 0.2847826 0.1913043
#> V2-Cat3 0.1417004 0.2429150 0.2955466 0.3198381
#> 
#> [[2]][[2]]
#>         V2-Cat1 V2-Cat2 V2-Cat3
#> V2-Cat1       1       0       0
#> V2-Cat2       0       1       0
#> V2-Cat3       0       0       1
#> 
#> [[2]][[3]]
#>           V3-Cat1   V3-Cat2   V3-Cat3   V3-Cat4
#> V2-Cat1 0.2877698 0.3453237 0.2086331 0.1582734
#> V2-Cat2 0.1782609 0.2913043 0.2826087 0.2478261
#> V2-Cat3 0.1491935 0.1935484 0.2903226 0.3669355
#> 
#> [[2]][[4]]
#>            V4-Cat1   V4-Cat2   V4-Cat3
#> V2-Cat1 0.42599278 0.4584838 0.1155235
#> V2-Cat2 0.25379610 0.4598698 0.2863341
#> V2-Cat3 0.08835341 0.4618474 0.4497992
#> 
#> [[2]][[5]]
#>           V5-Cat1   V5-Cat2   V5-Cat3   V5-Cat4
#> V2-Cat1 0.3309353 0.2877698 0.2482014 0.1330935
#> V2-Cat2 0.2359307 0.3030303 0.2662338 0.1948052
#> V2-Cat3 0.1290323 0.1854839 0.3467742 0.3387097
#> 
#> 
#> [[3]]
#> [[3]][[1]]
#>           V1-Cat1   V1-Cat2   V1-Cat3   V1-Cat4
#> V3-Cat1 0.3350000 0.3050000 0.2300000 0.1300000
#> V3-Cat2 0.2517986 0.2985612 0.2733813 0.1762590
#> V3-Cat3 0.1641221 0.2977099 0.3282443 0.2099237
#> V3-Cat4 0.1164659 0.3092369 0.2610442 0.3132530
#> 
#> [[3]][[2]]
#>           V2-Cat1   V2-Cat2   V2-Cat3
#> V3-Cat1 0.4020101 0.4120603 0.1859296
#> V3-Cat2 0.3453237 0.4820144 0.1726619
#> V3-Cat3 0.2230769 0.5000000 0.2769231
#> V3-Cat4 0.1767068 0.4578313 0.3654618
#> 
#> [[3]][[3]]
#>         V3-Cat1 V3-Cat2 V3-Cat3 V3-Cat4
#> V3-Cat1       1       0       0       0
#> V3-Cat2       0       1       0       0
#> V3-Cat3       0       0       1       0
#> V3-Cat4       0       0       0       1
#> 
#> [[3]][[4]]
#>           V4-Cat1   V4-Cat2   V4-Cat3
#> V3-Cat1 0.4455446 0.3960396 0.1584158
#> V3-Cat2 0.3082437 0.4982079 0.1935484
#> V3-Cat3 0.1692308 0.4769231 0.3538462
#> V3-Cat4 0.1587302 0.4404762 0.4007937
#> 
#> [[3]][[5]]
#>           V5-Cat1   V5-Cat2   V5-Cat3   V5-Cat4
#> V3-Cat1 0.3415842 0.2623762 0.2326733 0.1633663
#> V3-Cat2 0.2928571 0.2714286 0.2785714 0.1571429
#> V3-Cat3 0.2068966 0.2681992 0.2528736 0.2720307
#> V3-Cat4 0.1274900 0.2669323 0.3545817 0.2509960
#> 
#> 
#> [[4]]
#> [[4]][[1]]
#>           V1-Cat1   V1-Cat2   V1-Cat3   V1-Cat4
#> V4-Cat1 0.3359073 0.3474903 0.2162162 0.1003861
#> V4-Cat2 0.1880531 0.2920354 0.3119469 0.2079646
#> V4-Cat3 0.1290323 0.2759857 0.2831541 0.3118280
#> 
#> [[4]][[2]]
#>           V2-Cat1   V2-Cat2    V2-Cat3
#> V4-Cat1 0.4591440 0.4552529 0.08560311
#> V4-Cat2 0.2797357 0.4669604 0.25330396
#> V4-Cat3 0.1159420 0.4782609 0.40579710
#> 
#> [[4]][[3]]
#>           V3-Cat1   V3-Cat2   V3-Cat3   V3-Cat4
#> V4-Cat1 0.3461538 0.3307692 0.1692308 0.1538462
#> V4-Cat2 0.1762115 0.3061674 0.2731278 0.2444934
#> V4-Cat3 0.1146953 0.1935484 0.3297491 0.3620072
#> 
#> [[4]][[4]]
#>         V4-Cat1 V4-Cat2 V4-Cat3
#> V4-Cat1       1       0       0
#> V4-Cat2       0       1       0
#> V4-Cat3       0       0       1
#> 
#> [[4]][[5]]
#>           V5-Cat1   V5-Cat2   V5-Cat3   V5-Cat4
#> V4-Cat1 0.3601533 0.2835249 0.2375479 0.1187739
#> V4-Cat2 0.2263736 0.2945055 0.2769231 0.2021978
#> V4-Cat3 0.1397849 0.2043011 0.3333333 0.3225806
#> 
#> 
#> [[5]]
#> [[5]][[1]]
#>           V1-Cat1   V1-Cat2   V1-Cat3   V1-Cat4
#> V5-Cat1 0.3106383 0.3446809 0.2425532 0.1021277
#> V5-Cat2 0.2406015 0.3345865 0.2556391 0.1691729
#> V5-Cat3 0.1648746 0.2652330 0.3225806 0.2473118
#> V5-Cat4 0.1232227 0.2606635 0.2843602 0.3317536
#> 
#> [[5]][[2]]
#>           V2-Cat1   V2-Cat2   V2-Cat3
#> V5-Cat1 0.3948498 0.4678112 0.1373391
#> V5-Cat2 0.3007519 0.5263158 0.1729323
#> V5-Cat3 0.2482014 0.4424460 0.3093525
#> V5-Cat4 0.1753555 0.4265403 0.3981043
#> 
#> [[5]][[3]]
#>           V3-Cat1   V3-Cat2   V3-Cat3   V3-Cat4
#> V5-Cat1 0.2911392 0.3459916 0.2278481 0.1350211
#> V5-Cat2 0.1992481 0.2857143 0.2631579 0.2518797
#> V5-Cat3 0.1678571 0.2785714 0.2357143 0.3178571
#> V5-Cat4 0.1563981 0.2085308 0.3364929 0.2985782
#> 
#> [[5]][[4]]
#>           V4-Cat1   V4-Cat2   V4-Cat3
#> V5-Cat1 0.3983051 0.4364407 0.1652542
#> V5-Cat2 0.2792453 0.5056604 0.2150943
#> V5-Cat3 0.2206406 0.4483986 0.3309609
#> V5-Cat4 0.1455399 0.4319249 0.4225352
#> 
#> [[5]][[5]]
#>         V5-Cat1 V5-Cat2 V5-Cat3 V5-Cat4
#> V5-Cat1       1       0       0       0
#> V5-Cat2       0       1       0       0
#> V5-Cat3       0       0       1       0
#> V5-Cat4       0       0       0       1
#> 
#> 

# Extract the conditional selection rates from item 1 to item 2
csr_1_2 <- CSR(J5S1000)[[1]][[2]]
# This shows the probability of selecting each category in item 2
# given that a specific category was selected in item 1