Our goal is to produce estimated WG and WS raw scores for each ability level, so that we can produce norms tables for the CDI-CAT that are equivalent norms tables for the full WG and WS forms. For English, we will produce simulated CDI-CAT scores for the new norms sample, and then create CAT ability norms using those scores.

Run simulated CAT

Ability Norms

WG: Both Sexes

## GAMLSS-RS iteration 1: Global Deviance = 4685.432 
## GAMLSS-RS iteration 2: Global Deviance = 4685.16 
## GAMLSS-RS iteration 3: Global Deviance = 4685.16

age 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 99 N
12 -3.13 -2.87 -2.69 -2.55 -2.43 -2.32 -2.22 -2.12 -2.03 -1.94 -1.85 -1.75 -1.66 -1.56 -1.45 -1.33 -1.19 -1.01 -0.74 -0.25 475
13 -2.97 -2.69 -2.50 -2.35 -2.22 -2.11 -2.00 -1.90 -1.80 -1.71 -1.61 -1.51 -1.41 -1.30 -1.19 -1.06 -0.91 -0.72 -0.44 0.08 305
14 -2.80 -2.51 -2.31 -2.15 -2.02 -1.90 -1.78 -1.68 -1.58 -1.47 -1.37 -1.27 -1.16 -1.05 -0.93 -0.80 -0.64 -0.44 -0.15 0.40 263
15 -2.61 -2.31 -2.11 -1.95 -1.81 -1.68 -1.57 -1.46 -1.35 -1.25 -1.14 -1.04 -0.93 -0.81 -0.69 -0.55 -0.39 -0.18 0.12 0.69 178
16 -2.41 -2.11 -1.90 -1.74 -1.60 -1.47 -1.35 -1.24 -1.13 -1.03 -0.92 -0.81 -0.70 -0.58 -0.46 -0.31 -0.15 0.06 0.36 0.94 311
17 -2.21 -1.90 -1.69 -1.52 -1.38 -1.25 -1.14 -1.02 -0.92 -0.81 -0.70 -0.59 -0.48 -0.36 -0.24 -0.09 0.07 0.28 0.59 1.17 454
18 -1.99 -1.68 -1.48 -1.31 -1.17 -1.04 -0.92 -0.81 -0.70 -0.60 -0.49 -0.38 -0.27 -0.15 -0.02 0.12 0.29 0.49 0.80 1.38 553

WG: Males

## GAMLSS-RS iteration 1: Global Deviance = 2490.359 
## GAMLSS-RS iteration 2: Global Deviance = 2490.082 
## GAMLSS-RS iteration 3: Global Deviance = 2490.082
age 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 99 N
12 -3.22 -2.94 -2.75 -2.60 -2.47 -2.35 -2.25 -2.14 -2.04 -1.95 -1.85 -1.75 -1.65 -1.54 -1.42 -1.29 -1.14 -0.95 -0.67 -0.14 247
13 -3.05 -2.76 -2.56 -2.40 -2.27 -2.15 -2.04 -1.93 -1.83 -1.73 -1.63 -1.53 -1.42 -1.31 -1.19 -1.06 -0.90 -0.70 -0.41 0.13 151
14 -2.87 -2.57 -2.37 -2.21 -2.07 -1.95 -1.83 -1.72 -1.62 -1.52 -1.41 -1.31 -1.20 -1.08 -0.96 -0.82 -0.66 -0.46 -0.16 0.39 136
15 -2.68 -2.38 -2.17 -2.01 -1.87 -1.74 -1.63 -1.52 -1.41 -1.31 -1.20 -1.09 -0.98 -0.87 -0.74 -0.60 -0.44 -0.24 0.07 0.64 99
16 -2.49 -2.18 -1.97 -1.81 -1.67 -1.54 -1.43 -1.32 -1.21 -1.10 -1.00 -0.89 -0.78 -0.66 -0.53 -0.39 -0.23 -0.02 0.28 0.85 91
17 -2.29 -1.98 -1.78 -1.61 -1.47 -1.34 -1.23 -1.12 -1.01 -0.90 -0.80 -0.69 -0.58 -0.46 -0.33 -0.19 -0.03 0.18 0.48 1.06 146
18 -2.09 -1.79 -1.58 -1.41 -1.27 -1.15 -1.03 -0.92 -0.81 -0.71 -0.60 -0.49 -0.38 -0.26 -0.14 0.00 0.17 0.37 0.68 1.26 154

WG: Females

## GAMLSS-RS iteration 1: Global Deviance = 2181.358 
## GAMLSS-RS iteration 2: Global Deviance = 2181.343 
## GAMLSS-RS iteration 3: Global Deviance = 2181.343
age 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 99 N
12 -3.06 -2.81 -2.64 -2.50 -2.39 -2.28 -2.19 -2.10 -2.01 -1.92 -1.83 -1.75 -1.66 -1.56 -1.46 -1.34 -1.21 -1.04 -0.79 -0.32 228
13 -2.88 -2.61 -2.43 -2.29 -2.17 -2.06 -1.96 -1.86 -1.77 -1.68 -1.59 -1.49 -1.40 -1.30 -1.19 -1.06 -0.92 -0.74 -0.48 0.02 154
14 -2.70 -2.42 -2.23 -2.08 -1.95 -1.84 -1.73 -1.63 -1.53 -1.44 -1.34 -1.24 -1.14 -1.03 -0.92 -0.79 -0.64 -0.45 -0.18 0.35 127
15 -2.50 -2.21 -2.02 -1.86 -1.73 -1.61 -1.50 -1.39 -1.29 -1.19 -1.09 -0.99 -0.88 -0.77 -0.65 -0.52 -0.36 -0.17 0.12 0.66 79
16 -2.30 -2.00 -1.80 -1.64 -1.50 -1.38 -1.27 -1.16 -1.05 -0.95 -0.85 -0.74 -0.63 -0.52 -0.39 -0.26 -0.09 0.11 0.41 0.97 79
17 -2.10 -1.79 -1.58 -1.42 -1.28 -1.15 -1.03 -0.92 -0.81 -0.71 -0.60 -0.49 -0.38 -0.26 -0.14 0.00 0.17 0.38 0.68 1.26 124
18 -1.88 -1.57 -1.36 -1.19 -1.05 -0.92 -0.80 -0.68 -0.57 -0.47 -0.36 -0.25 -0.13 -0.01 0.12 0.26 0.43 0.64 0.95 1.54 149

WS: Both Sexes

## GAMLSS-RS iteration 1: Global Deviance = 8692.072 
## GAMLSS-RS iteration 2: Global Deviance = 8689.894 
## GAMLSS-RS iteration 3: Global Deviance = 8689.891 
## GAMLSS-RS iteration 4: Global Deviance = 8689.891

age 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 99 N
16 -1.96 -1.72 -1.55 -1.42 -1.31 -1.21 -1.12 -1.03 -0.94 -0.86 -0.77 -0.69 -0.60 -0.51 -0.40 -0.29 -0.16 0.00 0.25 0.70 311
17 -1.83 -1.57 -1.40 -1.26 -1.15 -1.04 -0.94 -0.85 -0.76 -0.67 -0.59 -0.50 -0.40 -0.31 -0.20 -0.08 0.05 0.22 0.48 0.96 454
18 -1.69 -1.42 -1.25 -1.10 -0.98 -0.87 -0.77 -0.67 -0.58 -0.49 -0.40 -0.30 -0.21 -0.11 0.00 0.12 0.27 0.45 0.71 1.21 553
19 -1.55 -1.28 -1.09 -0.95 -0.82 -0.70 -0.60 -0.50 -0.40 -0.31 -0.21 -0.12 -0.02 0.09 0.20 0.33 0.48 0.66 0.94 1.45 224
20 -1.41 -1.13 -0.94 -0.79 -0.66 -0.54 -0.43 -0.33 -0.23 -0.13 -0.03 0.07 0.17 0.28 0.40 0.53 0.68 0.87 1.15 1.69 208
21 -1.27 -0.98 -0.79 -0.63 -0.50 -0.38 -0.27 -0.16 -0.06 0.04 0.14 0.24 0.35 0.46 0.58 0.71 0.87 1.07 1.36 1.90 184
22 -1.13 -0.84 -0.64 -0.48 -0.34 -0.22 -0.11 0.00 0.10 0.21 0.31 0.41 0.52 0.63 0.75 0.89 1.05 1.25 1.54 2.09 197
23 -0.99 -0.69 -0.49 -0.33 -0.19 -0.07 0.04 0.15 0.26 0.36 0.46 0.57 0.68 0.79 0.91 1.05 1.21 1.41 1.71 2.27 264
24 -0.86 -0.56 -0.36 -0.19 -0.06 0.07 0.18 0.29 0.40 0.50 0.61 0.71 0.82 0.94 1.06 1.20 1.36 1.57 1.87 2.43 431
25 -0.73 -0.43 -0.23 -0.06 0.08 0.20 0.32 0.43 0.54 0.64 0.75 0.85 0.96 1.08 1.21 1.35 1.51 1.71 2.02 2.59 253
26 -0.61 -0.30 -0.10 0.07 0.21 0.34 0.45 0.56 0.67 0.78 0.88 0.99 1.10 1.22 1.35 1.49 1.65 1.86 2.16 2.74 239
27 -0.47 -0.17 0.04 0.20 0.35 0.47 0.59 0.70 0.81 0.92 1.02 1.13 1.24 1.36 1.49 1.63 1.79 2.00 2.31 2.88 256
28 -0.33 -0.02 0.18 0.35 0.49 0.62 0.73 0.85 0.95 1.06 1.17 1.27 1.39 1.50 1.63 1.77 1.94 2.14 2.45 3.03 205
29 -0.18 0.13 0.33 0.50 0.64 0.77 0.88 0.99 1.10 1.21 1.32 1.42 1.54 1.65 1.78 1.92 2.09 2.29 2.60 3.18 248
30 -0.03 0.28 0.49 0.65 0.79 0.92 1.04 1.15 1.26 1.36 1.47 1.58 1.69 1.81 1.93 2.07 2.24 2.45 2.75 3.33 335
31 0.13 0.43 0.64 0.80 0.95 1.07 1.19 1.30 1.41 1.52 1.62 1.73 1.84 1.96 2.09 2.23 2.39 2.60 2.91 3.48 NA
32 0.28 0.59 0.79 0.96 1.10 1.23 1.34 1.46 1.56 1.67 1.78 1.88 2.00 2.11 2.24 2.38 2.55 2.75 3.06 3.64 NA
33 0.43 0.74 0.95 1.11 1.25 1.38 1.50 1.61 1.72 1.82 1.93 2.04 2.15 2.27 2.39 2.54 2.70 2.91 3.21 3.79 NA
34 0.59 0.89 1.10 1.27 1.41 1.53 1.65 1.76 1.87 1.98 2.08 2.19 2.30 2.42 2.55 2.69 2.85 3.06 3.37 3.94 NA
35 0.74 1.05 1.25 1.42 1.56 1.69 1.80 1.92 2.02 2.13 2.24 2.34 2.46 2.57 2.70 2.84 3.01 3.21 3.52 4.10 NA
36 0.89 1.20 1.41 1.57 1.71 1.84 1.96 2.07 2.18 2.28 2.39 2.50 2.61 2.73 2.85 3.00 3.16 3.37 3.68 4.25 NA

WS: Males

## GAMLSS-RS iteration 1: Global Deviance = 4566.97 
## GAMLSS-RS iteration 2: Global Deviance = 4565.456 
## GAMLSS-RS iteration 3: Global Deviance = 4565.453 
## GAMLSS-RS iteration 4: Global Deviance = 4565.453
age 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 99 N
16 -2.09 -1.84 -1.67 -1.54 -1.42 -1.32 -1.22 -1.13 -1.05 -0.96 -0.87 -0.78 -0.69 -0.60 -0.50 -0.38 -0.25 -0.08 0.17 0.64 73
17 -1.94 -1.69 -1.51 -1.37 -1.26 -1.15 -1.05 -0.96 -0.87 -0.78 -0.69 -0.60 -0.51 -0.41 -0.30 -0.19 -0.05 0.13 0.38 0.86 95
18 -1.80 -1.53 -1.36 -1.21 -1.09 -0.98 -0.88 -0.79 -0.69 -0.60 -0.51 -0.42 -0.32 -0.22 -0.11 0.01 0.15 0.33 0.59 1.09 133
19 -1.66 -1.38 -1.20 -1.06 -0.93 -0.82 -0.71 -0.62 -0.52 -0.43 -0.33 -0.24 -0.14 -0.03 0.08 0.20 0.35 0.53 0.80 1.31 104
20 -1.51 -1.24 -1.05 -0.90 -0.77 -0.65 -0.55 -0.45 -0.35 -0.25 -0.16 -0.06 0.04 0.15 0.27 0.39 0.54 0.73 1.01 1.53 103
21 -1.37 -1.09 -0.90 -0.74 -0.61 -0.50 -0.39 -0.28 -0.18 -0.08 0.02 0.12 0.22 0.33 0.45 0.58 0.73 0.92 1.21 1.74 93
22 -1.24 -0.95 -0.75 -0.60 -0.46 -0.34 -0.23 -0.12 -0.02 0.08 0.18 0.28 0.39 0.50 0.62 0.75 0.91 1.11 1.40 1.94 89
23 -1.11 -0.81 -0.61 -0.45 -0.32 -0.20 -0.08 0.03 0.13 0.23 0.34 0.44 0.55 0.66 0.78 0.92 1.08 1.28 1.58 2.13 133
24 -0.99 -0.69 -0.48 -0.32 -0.18 -0.06 0.06 0.17 0.27 0.38 0.48 0.59 0.70 0.82 0.94 1.08 1.24 1.45 1.75 2.31 239
25 -0.87 -0.57 -0.36 -0.19 -0.05 0.08 0.19 0.30 0.41 0.52 0.63 0.73 0.85 0.96 1.09 1.23 1.40 1.60 1.91 2.49 127
26 -0.76 -0.45 -0.24 -0.07 0.08 0.20 0.32 0.44 0.55 0.66 0.76 0.87 0.99 1.11 1.24 1.38 1.55 1.76 2.07 2.66 128
27 -0.65 -0.33 -0.11 0.06 0.20 0.33 0.46 0.57 0.68 0.79 0.90 1.02 1.13 1.25 1.39 1.53 1.70 1.92 2.24 2.83 131
28 -0.53 -0.21 0.01 0.19 0.33 0.47 0.59 0.71 0.82 0.93 1.05 1.16 1.28 1.40 1.53 1.68 1.86 2.07 2.40 3.00 115
29 -0.40 -0.08 0.14 0.32 0.47 0.61 0.73 0.85 0.96 1.08 1.19 1.31 1.42 1.55 1.68 1.84 2.01 2.23 2.56 3.17 133
30 -0.27 0.06 0.28 0.46 0.61 0.75 0.87 0.99 1.11 1.22 1.34 1.45 1.57 1.70 1.84 1.99 2.17 2.39 2.72 3.34 177
31 -0.15 0.19 0.41 0.59 0.75 0.89 1.01 1.14 1.25 1.37 1.48 1.60 1.72 1.85 1.99 2.14 2.32 2.55 2.88 3.51 NA
32 -0.02 0.32 0.55 0.73 0.89 1.03 1.16 1.28 1.40 1.51 1.63 1.75 1.87 2.00 2.14 2.30 2.48 2.71 3.04 3.68 NA
33 0.11 0.45 0.68 0.87 1.02 1.17 1.30 1.42 1.54 1.66 1.78 1.90 2.02 2.15 2.29 2.45 2.63 2.87 3.21 3.85 NA
34 0.24 0.59 0.82 1.00 1.16 1.31 1.44 1.56 1.69 1.80 1.92 2.05 2.17 2.30 2.45 2.61 2.79 3.02 3.37 4.02 NA
35 0.37 0.72 0.95 1.14 1.30 1.45 1.58 1.71 1.83 1.95 2.07 2.19 2.32 2.45 2.60 2.76 2.95 3.18 3.53 4.19 NA
36 0.50 0.85 1.09 1.28 1.44 1.59 1.72 1.85 1.97 2.10 2.22 2.34 2.47 2.61 2.75 2.91 3.10 3.34 3.70 4.36 NA

WS: Females

## GAMLSS-RS iteration 1: Global Deviance = 4021.191 
## GAMLSS-RS iteration 2: Global Deviance = 4020.332 
## GAMLSS-RS iteration 3: Global Deviance = 4020.331
age 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 99 N
16 -1.81 -1.57 -1.41 -1.28 -1.17 -1.07 -0.98 -0.89 -0.81 -0.72 -0.64 -0.56 -0.47 -0.38 -0.28 -0.17 -0.04 0.12 0.36 0.81 68
17 -1.67 -1.43 -1.26 -1.12 -1.01 -0.91 -0.81 -0.72 -0.63 -0.55 -0.46 -0.37 -0.28 -0.18 -0.08 0.03 0.17 0.34 0.58 1.05 89
18 -1.54 -1.28 -1.11 -0.97 -0.85 -0.74 -0.64 -0.55 -0.46 -0.37 -0.28 -0.19 -0.09 0.01 0.11 0.23 0.37 0.55 0.81 1.29 117
19 -1.41 -1.14 -0.96 -0.81 -0.69 -0.58 -0.48 -0.38 -0.28 -0.19 -0.10 0.00 0.09 0.20 0.31 0.43 0.58 0.76 1.03 1.53 120
20 -1.27 -0.99 -0.81 -0.66 -0.53 -0.42 -0.31 -0.21 -0.11 -0.02 0.08 0.17 0.27 0.38 0.49 0.62 0.77 0.96 1.23 1.75 105
21 -1.12 -0.84 -0.65 -0.50 -0.37 -0.26 -0.15 -0.05 0.05 0.15 0.25 0.35 0.45 0.56 0.67 0.80 0.95 1.14 1.42 1.95 91
22 -0.97 -0.69 -0.50 -0.34 -0.21 -0.10 0.01 0.12 0.22 0.31 0.41 0.51 0.62 0.72 0.84 0.97 1.13 1.32 1.60 2.14 108
23 -0.82 -0.53 -0.34 -0.19 -0.06 0.06 0.17 0.27 0.37 0.47 0.57 0.67 0.78 0.89 1.00 1.13 1.29 1.48 1.77 2.30 131
24 -0.67 -0.38 -0.19 -0.04 0.10 0.21 0.32 0.43 0.53 0.63 0.73 0.83 0.93 1.04 1.16 1.29 1.44 1.63 1.92 2.46 192
25 -0.52 -0.23 -0.04 0.11 0.25 0.36 0.47 0.58 0.68 0.78 0.87 0.98 1.08 1.19 1.31 1.44 1.59 1.78 2.07 2.61 126
26 -0.37 -0.09 0.11 0.26 0.39 0.51 0.62 0.72 0.82 0.92 1.02 1.12 1.23 1.34 1.45 1.59 1.74 1.93 2.22 2.75 111
27 -0.22 0.06 0.25 0.41 0.54 0.66 0.77 0.87 0.97 1.07 1.17 1.27 1.37 1.48 1.60 1.73 1.89 2.08 2.36 2.90 125
28 -0.08 0.21 0.40 0.56 0.69 0.81 0.92 1.02 1.12 1.22 1.32 1.42 1.52 1.63 1.75 1.88 2.03 2.23 2.51 3.05 90
29 0.08 0.36 0.55 0.71 0.84 0.96 1.07 1.17 1.27 1.37 1.47 1.57 1.67 1.78 1.90 2.03 2.19 2.38 2.66 3.20 115
30 0.23 0.51 0.71 0.86 0.99 1.11 1.22 1.32 1.42 1.52 1.62 1.72 1.83 1.94 2.05 2.18 2.34 2.53 2.82 3.35 158
31 0.38 0.67 0.86 1.01 1.14 1.26 1.37 1.48 1.58 1.68 1.77 1.87 1.98 2.09 2.21 2.34 2.49 2.68 2.97 3.51 NA
32 0.53 0.82 1.01 1.17 1.30 1.42 1.52 1.63 1.73 1.83 1.93 2.03 2.13 2.24 2.36 2.49 2.64 2.84 3.12 3.66 NA
33 0.69 0.97 1.17 1.32 1.45 1.57 1.68 1.78 1.88 1.98 2.08 2.18 2.28 2.39 2.51 2.64 2.80 2.99 3.27 3.81 NA
34 0.84 1.12 1.32 1.47 1.60 1.72 1.83 1.93 2.03 2.13 2.23 2.33 2.44 2.55 2.66 2.80 2.95 3.14 3.43 3.96 NA
35 0.99 1.28 1.47 1.62 1.76 1.87 1.98 2.09 2.19 2.29 2.38 2.49 2.59 2.70 2.82 2.95 3.10 3.29 3.58 4.12 NA
36 1.14 1.43 1.62 1.78 1.91 2.03 2.14 2.24 2.34 2.44 2.54 2.64 2.74 2.85 2.97 3.10 3.25 3.45 3.73 4.27 NA