add_ci.lmerMod: Confidence Intervals for Linear Mixed Model Predictions
In ciTools: Confidence or Prediction Intervals, Quantiles, and Probabilities for Statistical Models
Description
Usage
Arguments
Details
Value
See Also
Examples
Description
This function is one of the methods for add_ci, and is
called automatically when add_ci is used on a fit of
class lmerMod. It is recommended that one use parametric
confidence intervals when modeling with a random intercept linear
mixed model (i.e. a fit with a formula such as lmer(y ~ x +
(1|group))). Otherwise, confidence intervals may be bootstrapped
via lme4::bootMer.
Usage
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Arguments
df
A data frame of new data.
fit
An object of class lmerMod.
alpha
A real number between 0 and 1. Controls the confidence
level of the interval estimates.
names
NULL or character vector of length two. If
NULL, confidence bounds automatically will be named by
add_ci, otherwise, the lower confidence bound will be
named names[1] and the upper confidence bound will be
named names[2].
yhatName
A string. Name of the predictions vector.
type
A string. Must be "parametric" or "boot",
If type = "boot", then add_ci calls
lme4::bootMer to calculate the confidence
intervals. This method may be time consuming, but is applicable
with random slope and random intercept models. The parametric
method is fast, but currently only works well for random
intercept models.
includeRanef
A logical. Default is TRUE. Set whether
the predictions and intervals should be made conditional on the
random effects. If FALSE, random effects will not be
included.
nSims
A positive integer. Controls the number of bootstrap
replicates if type = "boot".
...
Additional arguments.
Details
Bootstrapped intervals are slower to compute, but they are the
recommended method when working with any linear mixed models more
complicated than the random intercept model.
Value
A dataframe, df, with predicted values, upper and lower
confidence bounds attached.
See Also
add_pi.lmerMod for prediction intervals
of lmerMod objects, add_probs.lmerMod for
conditional probabilities of lmerMod objects, and
add_quantile.lmerMod for response quantiles of
lmerMod objects.
Examples
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## Not run:
dat <- lme4::sleepstudy
# Fit a linear mixed model (random intercept model)
fit <- lme4::lmer(Reaction ~ Days + (1|Subject), data = lme4::sleepstudy)
# Get the fitted values for each observation in dat, and
# append CIs for those fitted values to dat
add_ci(dat, fit, alpha = 0.5)
# Try the parametric bootstrap method, and make prediction at the population level
add_ci(dat, fit, alpha = 0.5, type = "boot", includeRanef = FALSE, nSims = 100)
## End(Not run)
Example output
ciTools version 0.6.1 (C) Institute for Defense Analyses
Reaction Days Subject pred LCB0.25 UCB0.75
1 249.5600 0 308 289.2678 283.1248 295.4573
2 258.7047 1 308 299.7092 293.6721 305.6818
3 250.8006 2 308 310.2171 304.2840 316.0172
4 321.4398 3 308 320.7969 314.8716 326.5390
5 356.8519 4 308 331.2194 325.1824 336.6276
6 414.6901 5 308 341.6362 336.2246 347.9443
7 382.2038 6 308 351.9924 346.6095 358.4416
8 290.1486 7 308 362.2164 356.5761 369.1494
9 430.5853 8 308 372.5925 366.7214 379.6106
10 466.3535 9 308 383.1775 377.4736 390.2985
11 222.7339 0 309 177.8551 171.4135 185.5225
12 205.2658 1 309 188.3567 182.1316 195.7431
13 202.9778 2 309 199.0163 193.1431 206.2945
14 204.7070 3 309 209.6610 203.6499 216.7201
15 207.7161 4 309 220.1462 214.1147 226.8804
16 215.9618 5 309 230.4414 224.8506 237.1133
17 213.6303 6 309 240.9629 235.3378 247.5267
18 217.7272 7 309 251.4578 245.8656 258.1766
19 224.2957 8 309 261.7217 256.2198 268.7377
20 237.3142 9 309 272.1131 266.6316 279.3964
21 199.0539 0 310 192.2067 185.9449 199.2386
22 194.3322 1 310 202.8421 196.6238 209.5271
23 234.3200 2 310 213.4302 207.0444 219.6554
24 232.8416 3 310 223.9013 217.6611 230.3955
25 229.3074 4 310 234.1446 228.3091 240.9575
26 220.4579 5 310 244.6715 238.6616 251.4680
27 235.4208 6 310 255.1049 249.0655 262.1312
28 255.7511 7 310 265.6904 259.2002 273.0106
29 261.0125 8 310 276.2532 269.4975 283.3771
30 247.5153 9 310 286.9689 279.7617 294.1289
31 321.5426 0 330 254.6814 247.9406 262.1436
32 300.4002 1 330 264.9510 258.5398 272.1878
33 283.8565 2 330 275.7049 269.0879 282.5523
34 285.1330 3 330 286.1368 280.0427 292.7874
35 285.7973 4 330 296.6456 290.5776 303.0740
36 297.5855 5 330 307.2148 301.3441 313.3401
37 280.2396 6 330 318.1292 311.4796 324.0465
38 318.2613 7 330 328.7534 321.9510 334.5757
39 305.3495 8 330 339.3884 332.3431 345.0639
40 354.0487 9 330 349.6279 342.7789 355.7355
41 287.6079 0 331 260.1444 253.7071 266.5578
42 285.0000 1 331 270.5191 264.4807 276.9312
43 301.8206 2 331 281.2868 274.9839 287.5255
44 320.1153 3 331 291.5486 285.5566 297.9239
45 316.2773 4 331 301.8162 296.2504 308.3469
46 293.3187 5 331 312.2543 306.8751 318.6855
47 290.0750 6 331 322.8995 317.0962 328.8926
48 334.8177 7 331 333.0684 327.3393 339.5008
49 293.7469 8 331 343.3660 337.8462 350.1369
50 371.5811 9 331 353.8893 348.2208 360.9518
51 234.8606 0 332 258.4386 252.1851 266.1563
52 242.8118 1 332 269.0858 262.9635 276.3438
53 272.9613 2 332 279.6890 273.4557 286.4644
54 309.7688 3 332 289.9404 284.4897 296.4905
55 317.4629 4 332 300.3647 295.1028 307.0537
56 309.9976 5 332 310.8992 305.4133 317.7552
57 454.1619 6 332 321.6036 315.7282 328.4449
58 346.8311 7 332 332.1329 326.3317 339.0270
59 330.3003 8 332 342.7374 336.2870 349.7977
60 253.8644 9 332 353.2594 346.6700 360.4163
61 283.8424 0 333 266.7434 260.0302 274.2944
62 289.5550 1 333 277.2945 270.6303 284.7103
63 276.7693 2 333 287.6110 281.4719 295.1355
64 299.8097 3 333 298.0270 292.1946 305.4625
65 297.1710 4 333 308.4276 302.4103 315.2564
66 338.1665 5 333 318.7820 312.8254 325.8309
67 332.0265 6 333 329.4885 323.1973 336.4020
68 348.8399 7 333 340.1099 333.6899 346.7872
69 333.3600 8 333 350.9598 343.9853 357.2157
70 362.0428 9 333 361.5191 354.2948 367.9958
71 265.4731 0 334 248.2298 241.9697 255.2659
72 276.2012 1 334 258.4670 252.4375 265.1670
73 243.3647 2 334 268.5396 262.9315 275.2114
74 254.6723 3 334 279.2450 273.8533 285.7815
75 279.0244 4 334 289.6531 284.3893 296.2515
76 284.1912 5 334 299.9993 294.7500 306.7790
77 305.5248 6 334 310.5637 305.2306 317.2005
78 331.5229 7 334 320.9429 315.6149 328.1936
79 335.7469 8 334 331.5124 325.9211 338.5947
80 377.2990 9 334 341.9100 336.4053 349.0994
81 241.6083 0 335 208.8246 202.3026 216.2439
82 273.9472 1 335 219.3703 212.7203 226.1315
83 254.4907 2 335 230.0708 223.1593 236.4106
84 270.8021 3 335 240.4212 233.5042 246.9904
85 251.4519 4 335 250.9265 244.0330 257.4123
86 254.6362 5 335 261.3938 254.4131 268.2363
87 245.4523 6 335 271.8089 264.7755 278.5310
88 235.3110 7 335 282.4291 274.9959 289.2059
89 235.7541 8 335 292.9523 285.4216 299.7593
90 237.2466 9 335 303.7596 295.4639 310.4326
91 312.3666 0 337 318.1266 312.1298 324.5244
92 313.8058 1 337 328.6276 322.5916 334.8685
93 291.6112 2 337 339.2636 333.1118 345.2259
94 346.1222 3 337 349.7879 343.6621 356.0608
95 365.7324 4 337 360.5298 354.4263 366.4977
96 391.8385 5 337 371.2581 364.6000 377.1612
97 404.2601 6 337 381.6474 375.1932 387.8791
98 416.6923 7 337 392.4229 385.4383 398.5790
99 455.8643 8 337 402.9936 395.5870 409.4437
100 458.9167 9 337 413.4305 405.3490 420.1516
101 236.1032 0 349 232.1932 224.7018 238.4395
102 230.3167 1 349 242.5122 235.2059 248.7780
103 238.9256 2 349 253.1684 245.7436 259.3135
104 254.9220 3 349 263.3921 256.2307 269.8082
105 250.7103 4 349 273.8149 266.8768 280.3369
106 269.7744 5 349 284.2771 277.3528 290.8914
107 281.5648 6 349 294.6534 287.7502 301.4577
108 308.1020 7 349 304.8993 298.1462 312.1160
109 336.2806 8 349 315.4128 308.5167 322.5658
110 351.6451 9 349 326.3930 318.8858 333.2235
111 256.2968 0 350 264.8812 258.1747 270.7325
112 243.4543 1 350 275.3979 269.0410 281.0752
113 256.2046 2 350 285.7110 279.7679 291.3610
114 255.5271 3 350 296.2228 290.2334 301.8395
115 268.9165 4 350 306.4352 300.6678 311.9355
116 329.7247 5 350 316.6771 311.0507 322.7460
117 379.4445 6 350 327.1960 321.8484 333.2724
118 362.9184 7 350 337.6469 331.9481 343.7422
119 394.4872 8 350 348.1788 342.1669 354.4067
120 389.0527 9 350 358.5266 352.8671 364.9928
121 250.5265 0 351 244.5941 238.1876 250.7788
122 300.0576 1 351 255.2083 248.6591 261.1451
123 269.8939 2 351 265.7152 259.3737 271.4092
124 280.5891 3 351 276.0632 269.8235 282.1617
125 271.8274 4 351 286.5852 280.2720 292.6353
126 304.6336 5 351 297.0239 290.6922 303.3274
127 287.7466 6 351 307.5290 301.2829 314.1767
128 266.5955 7 351 317.8565 311.8221 324.7872
129 321.5418 8 351 328.3464 321.7592 335.3181
130 347.5655 9 351 339.0232 332.3639 345.9441
131 221.6771 0 352 285.3325 279.2586 291.9019
132 298.1939 1 352 295.4837 289.8796 302.3301
133 326.8785 2 352 306.0606 300.6534 312.3607
134 346.8555 3 352 316.7475 311.0867 322.5634
135 348.7402 4 352 327.0214 321.7525 333.0274
136 352.8287 5 352 337.5398 332.4332 343.4863
137 354.4266 6 352 347.8645 342.7019 353.8501
138 360.4326 7 352 358.3175 352.8176 364.4446
139 375.6406 8 352 369.1185 362.7533 374.9615
140 388.5417 9 352 379.9565 372.9895 385.6145
141 271.9235 0 369 258.4332 251.3092 264.1729
142 268.4369 1 369 269.0236 261.9558 274.7523
143 257.2424 2 369 279.0193 272.4227 285.1875
144 277.6566 3 369 289.5948 283.2098 295.4699
145 314.8222 4 369 300.1534 293.5838 305.7889
146 317.2135 5 369 310.5530 304.1309 316.0357
147 298.1353 6 369 320.7576 314.8179 326.4905
148 348.1229 7 369 331.2463 325.5022 337.1408
149 340.2800 8 369 341.6191 335.8289 347.8233
150 366.5131 9 369 352.1442 345.9868 358.6378
151 225.2640 0 370 245.3301 238.7508 252.3267
152 234.5235 1 370 255.7637 249.3249 263.1909
153 238.9008 2 370 266.2529 259.9771 273.4907
154 240.4730 3 370 277.0493 270.5201 283.7240
155 267.5373 4 370 287.6103 281.2275 294.1309
156 344.1937 5 370 297.9537 291.8134 304.3273
157 281.1481 6 370 308.2526 302.0980 315.3372
158 347.5855 7 370 318.8310 312.3472 326.0458
159 365.1630 8 370 329.4624 322.7346 336.3049
160 372.2288 9 370 340.1088 332.8037 346.9413
161 269.8804 0 371 247.6461 240.3394 253.9678
162 272.4428 1 371 258.1299 251.2291 264.3176
163 277.8989 2 371 268.6032 262.1156 274.7990
164 281.7895 3 371 279.0288 272.7747 285.2247
165 279.1705 4 371 289.3000 283.3841 295.6987
166 284.5120 5 371 299.6474 293.8507 306.0975
167 259.2658 6 371 310.0876 304.4920 316.6305
168 304.6306 7 371 320.4965 315.0950 327.0402
169 350.7807 8 371 331.0530 325.6927 337.9049
170 369.4692 9 371 341.5112 336.0573 348.3466
171 269.4117 0 372 268.5214 262.2912 274.6502
172 273.4740 1 372 278.9957 272.8498 284.9580
173 297.5968 2 372 289.3419 283.0864 295.5726
174 310.6316 3 372 299.7144 293.4572 305.9781
175 287.1726 4 372 310.0917 304.0954 316.2456
176 329.6076 5 372 320.8763 314.5660 326.7115
177 334.4818 6 372 331.5243 325.3691 337.7064
178 343.2199 7 372 341.9861 335.5299 348.1539
179 369.1417 8 372 352.5127 345.8407 358.7223
180 364.1236 9 372 363.1310 356.0240 369.0624
Reaction Days Subject pred LCB0.25 UCB0.75
1 249.5600 0 308 253.5027 245.8242 260.9467
2 258.7047 1 308 263.5685 256.7850 270.7548
3 250.8006 2 308 274.3686 267.8226 280.3737
4 321.4398 3 308 285.6002 278.6498 290.6217
5 356.8519 4 308 296.5267 289.5747 301.0672
6 414.6901 5 308 306.7795 300.2963 311.9968
7 382.2038 6 308 316.9215 310.4144 322.3543
8 290.1486 7 308 326.8623 320.4549 333.8066
9 430.5853 8 308 336.9923 330.6790 344.8616
10 466.3535 9 308 347.1669 340.6084 355.4023
11 222.7339 0 309 253.5027 245.8242 260.9467
12 205.2658 1 309 263.5685 256.7850 270.7548
13 202.9778 2 309 274.3686 267.8226 280.3737
14 204.7070 3 309 285.6002 278.6498 290.6217
15 207.7161 4 309 296.5267 289.5747 301.0672
16 215.9618 5 309 306.7795 300.2963 311.9968
17 213.6303 6 309 316.9215 310.4144 322.3543
18 217.7272 7 309 326.8623 320.4549 333.8066
19 224.2957 8 309 336.9923 330.6790 344.8616
20 237.3142 9 309 347.1669 340.6084 355.4023
21 199.0539 0 310 253.5027 245.8242 260.9467
22 194.3322 1 310 263.5685 256.7850 270.7548
23 234.3200 2 310 274.3686 267.8226 280.3737
24 232.8416 3 310 285.6002 278.6498 290.6217
25 229.3074 4 310 296.5267 289.5747 301.0672
26 220.4579 5 310 306.7795 300.2963 311.9968
27 235.4208 6 310 316.9215 310.4144 322.3543
28 255.7511 7 310 326.8623 320.4549 333.8066
29 261.0125 8 310 336.9923 330.6790 344.8616
30 247.5153 9 310 347.1669 340.6084 355.4023
31 321.5426 0 330 253.5027 245.8242 260.9467
32 300.4002 1 330 263.5685 256.7850 270.7548
33 283.8565 2 330 274.3686 267.8226 280.3737
34 285.1330 3 330 285.6002 278.6498 290.6217
35 285.7973 4 330 296.5267 289.5747 301.0672
36 297.5855 5 330 306.7795 300.2963 311.9968
37 280.2396 6 330 316.9215 310.4144 322.3543
38 318.2613 7 330 326.8623 320.4549 333.8066
39 305.3495 8 330 336.9923 330.6790 344.8616
40 354.0487 9 330 347.1669 340.6084 355.4023
41 287.6079 0 331 253.5027 245.8242 260.9467
42 285.0000 1 331 263.5685 256.7850 270.7548
43 301.8206 2 331 274.3686 267.8226 280.3737
44 320.1153 3 331 285.6002 278.6498 290.6217
45 316.2773 4 331 296.5267 289.5747 301.0672
46 293.3187 5 331 306.7795 300.2963 311.9968
47 290.0750 6 331 316.9215 310.4144 322.3543
48 334.8177 7 331 326.8623 320.4549 333.8066
49 293.7469 8 331 336.9923 330.6790 344.8616
50 371.5811 9 331 347.1669 340.6084 355.4023
51 234.8606 0 332 253.5027 245.8242 260.9467
52 242.8118 1 332 263.5685 256.7850 270.7548
53 272.9613 2 332 274.3686 267.8226 280.3737
54 309.7688 3 332 285.6002 278.6498 290.6217
55 317.4629 4 332 296.5267 289.5747 301.0672
56 309.9976 5 332 306.7795 300.2963 311.9968
57 454.1619 6 332 316.9215 310.4144 322.3543
58 346.8311 7 332 326.8623 320.4549 333.8066
59 330.3003 8 332 336.9923 330.6790 344.8616
60 253.8644 9 332 347.1669 340.6084 355.4023
61 283.8424 0 333 253.5027 245.8242 260.9467
62 289.5550 1 333 263.5685 256.7850 270.7548
63 276.7693 2 333 274.3686 267.8226 280.3737
64 299.8097 3 333 285.6002 278.6498 290.6217
65 297.1710 4 333 296.5267 289.5747 301.0672
66 338.1665 5 333 306.7795 300.2963 311.9968
67 332.0265 6 333 316.9215 310.4144 322.3543
68 348.8399 7 333 326.8623 320.4549 333.8066
69 333.3600 8 333 336.9923 330.6790 344.8616
70 362.0428 9 333 347.1669 340.6084 355.4023
71 265.4731 0 334 253.5027 245.8242 260.9467
72 276.2012 1 334 263.5685 256.7850 270.7548
73 243.3647 2 334 274.3686 267.8226 280.3737
74 254.6723 3 334 285.6002 278.6498 290.6217
75 279.0244 4 334 296.5267 289.5747 301.0672
76 284.1912 5 334 306.7795 300.2963 311.9968
77 305.5248 6 334 316.9215 310.4144 322.3543
78 331.5229 7 334 326.8623 320.4549 333.8066
79 335.7469 8 334 336.9923 330.6790 344.8616
80 377.2990 9 334 347.1669 340.6084 355.4023
81 241.6083 0 335 253.5027 245.8242 260.9467
82 273.9472 1 335 263.5685 256.7850 270.7548
83 254.4907 2 335 274.3686 267.8226 280.3737
84 270.8021 3 335 285.6002 278.6498 290.6217
85 251.4519 4 335 296.5267 289.5747 301.0672
86 254.6362 5 335 306.7795 300.2963 311.9968
87 245.4523 6 335 316.9215 310.4144 322.3543
88 235.3110 7 335 326.8623 320.4549 333.8066
89 235.7541 8 335 336.9923 330.6790 344.8616
90 237.2466 9 335 347.1669 340.6084 355.4023
91 312.3666 0 337 253.5027 245.8242 260.9467
92 313.8058 1 337 263.5685 256.7850 270.7548
93 291.6112 2 337 274.3686 267.8226 280.3737
94 346.1222 3 337 285.6002 278.6498 290.6217
95 365.7324 4 337 296.5267 289.5747 301.0672
96 391.8385 5 337 306.7795 300.2963 311.9968
97 404.2601 6 337 316.9215 310.4144 322.3543
98 416.6923 7 337 326.8623 320.4549 333.8066
99 455.8643 8 337 336.9923 330.6790 344.8616
100 458.9167 9 337 347.1669 340.6084 355.4023
101 236.1032 0 349 253.5027 245.8242 260.9467
102 230.3167 1 349 263.5685 256.7850 270.7548
103 238.9256 2 349 274.3686 267.8226 280.3737
104 254.9220 3 349 285.6002 278.6498 290.6217
105 250.7103 4 349 296.5267 289.5747 301.0672
106 269.7744 5 349 306.7795 300.2963 311.9968
107 281.5648 6 349 316.9215 310.4144 322.3543
108 308.1020 7 349 326.8623 320.4549 333.8066
109 336.2806 8 349 336.9923 330.6790 344.8616
110 351.6451 9 349 347.1669 340.6084 355.4023
111 256.2968 0 350 253.5027 245.8242 260.9467
112 243.4543 1 350 263.5685 256.7850 270.7548
113 256.2046 2 350 274.3686 267.8226 280.3737
114 255.5271 3 350 285.6002 278.6498 290.6217
115 268.9165 4 350 296.5267 289.5747 301.0672
116 329.7247 5 350 306.7795 300.2963 311.9968
117 379.4445 6 350 316.9215 310.4144 322.3543
118 362.9184 7 350 326.8623 320.4549 333.8066
119 394.4872 8 350 336.9923 330.6790 344.8616
120 389.0527 9 350 347.1669 340.6084 355.4023
121 250.5265 0 351 253.5027 245.8242 260.9467
122 300.0576 1 351 263.5685 256.7850 270.7548
123 269.8939 2 351 274.3686 267.8226 280.3737
124 280.5891 3 351 285.6002 278.6498 290.6217
125 271.8274 4 351 296.5267 289.5747 301.0672
126 304.6336 5 351 306.7795 300.2963 311.9968
127 287.7466 6 351 316.9215 310.4144 322.3543
128 266.5955 7 351 326.8623 320.4549 333.8066
129 321.5418 8 351 336.9923 330.6790 344.8616
130 347.5655 9 351 347.1669 340.6084 355.4023
131 221.6771 0 352 253.5027 245.8242 260.9467
132 298.1939 1 352 263.5685 256.7850 270.7548
133 326.8785 2 352 274.3686 267.8226 280.3737
134 346.8555 3 352 285.6002 278.6498 290.6217
135 348.7402 4 352 296.5267 289.5747 301.0672
136 352.8287 5 352 306.7795 300.2963 311.9968
137 354.4266 6 352 316.9215 310.4144 322.3543
138 360.4326 7 352 326.8623 320.4549 333.8066
139 375.6406 8 352 336.9923 330.6790 344.8616
140 388.5417 9 352 347.1669 340.6084 355.4023
141 271.9235 0 369 253.5027 245.8242 260.9467
142 268.4369 1 369 263.5685 256.7850 270.7548
143 257.2424 2 369 274.3686 267.8226 280.3737
144 277.6566 3 369 285.6002 278.6498 290.6217
145 314.8222 4 369 296.5267 289.5747 301.0672
146 317.2135 5 369 306.7795 300.2963 311.9968
147 298.1353 6 369 316.9215 310.4144 322.3543
148 348.1229 7 369 326.8623 320.4549 333.8066
149 340.2800 8 369 336.9923 330.6790 344.8616
150 366.5131 9 369 347.1669 340.6084 355.4023
151 225.2640 0 370 253.5027 245.8242 260.9467
152 234.5235 1 370 263.5685 256.7850 270.7548
153 238.9008 2 370 274.3686 267.8226 280.3737
154 240.4730 3 370 285.6002 278.6498 290.6217
155 267.5373 4 370 296.5267 289.5747 301.0672
156 344.1937 5 370 306.7795 300.2963 311.9968
157 281.1481 6 370 316.9215 310.4144 322.3543
158 347.5855 7 370 326.8623 320.4549 333.8066
159 365.1630 8 370 336.9923 330.6790 344.8616
160 372.2288 9 370 347.1669 340.6084 355.4023
161 269.8804 0 371 253.5027 245.8242 260.9467
162 272.4428 1 371 263.5685 256.7850 270.7548
163 277.8989 2 371 274.3686 267.8226 280.3737
164 281.7895 3 371 285.6002 278.6498 290.6217
165 279.1705 4 371 296.5267 289.5747 301.0672
166 284.5120 5 371 306.7795 300.2963 311.9968
167 259.2658 6 371 316.9215 310.4144 322.3543
168 304.6306 7 371 326.8623 320.4549 333.8066
169 350.7807 8 371 336.9923 330.6790 344.8616
170 369.4692 9 371 347.1669 340.6084 355.4023
171 269.4117 0 372 253.5027 245.8242 260.9467
172 273.4740 1 372 263.5685 256.7850 270.7548
173 297.5968 2 372 274.3686 267.8226 280.3737
174 310.6316 3 372 285.6002 278.6498 290.6217
175 287.1726 4 372 296.5267 289.5747 301.0672
176 329.6076 5 372 306.7795 300.2963 311.9968
177 334.4818 6 372 316.9215 310.4144 322.3543
178 343.2199 7 372 326.8623 320.4549 333.8066
179 369.1417 8 372 336.9923 330.6790 344.8616
180 364.1236 9 372 347.1669 340.6084 355.4023
ciTools documentation built on Jan. 13, 2021, 7 a.m.
R Package Documentation
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Description Usage Arguments Details Value See Also Examples
Description
This function is one of the methods for add_ci, and is
called automatically when add_ci is used on a fit of
class lmerMod. It is recommended that one use parametric
confidence intervals when modeling with a random intercept linear
mixed model (i.e. a fit with a formula such as lmer(y ~ x +
(1|group))). Otherwise, confidence intervals may be bootstrapped
via lme4::bootMer.
Usage
1 2 3 4 5 6 7 8 9 10 11 12 |
Arguments
df |
A data frame of new data. |
fit |
An object of class |
alpha |
A real number between 0 and 1. Controls the confidence level of the interval estimates. |
names |
|
yhatName |
A string. Name of the predictions vector. |
type |
A string. Must be |
includeRanef |
A logical. Default is |
nSims |
A positive integer. Controls the number of bootstrap
replicates if |
... |
Additional arguments. |
Details
Bootstrapped intervals are slower to compute, but they are the recommended method when working with any linear mixed models more complicated than the random intercept model.
Value
A dataframe, df, with predicted values, upper and lower
confidence bounds attached.
See Also
add_pi.lmerMod for prediction intervals
of lmerMod objects, add_probs.lmerMod for
conditional probabilities of lmerMod objects, and
add_quantile.lmerMod for response quantiles of
lmerMod objects.
Examples
1 2 3 4 5 6 7 8 9 10 11 | ## Not run:
dat <- lme4::sleepstudy
# Fit a linear mixed model (random intercept model)
fit <- lme4::lmer(Reaction ~ Days + (1|Subject), data = lme4::sleepstudy)
# Get the fitted values for each observation in dat, and
# append CIs for those fitted values to dat
add_ci(dat, fit, alpha = 0.5)
# Try the parametric bootstrap method, and make prediction at the population level
add_ci(dat, fit, alpha = 0.5, type = "boot", includeRanef = FALSE, nSims = 100)
## End(Not run)
|
Example output
ciTools version 0.6.1 (C) Institute for Defense Analyses
Reaction Days Subject pred LCB0.25 UCB0.75
1 249.5600 0 308 289.2678 283.1248 295.4573
2 258.7047 1 308 299.7092 293.6721 305.6818
3 250.8006 2 308 310.2171 304.2840 316.0172
4 321.4398 3 308 320.7969 314.8716 326.5390
5 356.8519 4 308 331.2194 325.1824 336.6276
6 414.6901 5 308 341.6362 336.2246 347.9443
7 382.2038 6 308 351.9924 346.6095 358.4416
8 290.1486 7 308 362.2164 356.5761 369.1494
9 430.5853 8 308 372.5925 366.7214 379.6106
10 466.3535 9 308 383.1775 377.4736 390.2985
11 222.7339 0 309 177.8551 171.4135 185.5225
12 205.2658 1 309 188.3567 182.1316 195.7431
13 202.9778 2 309 199.0163 193.1431 206.2945
14 204.7070 3 309 209.6610 203.6499 216.7201
15 207.7161 4 309 220.1462 214.1147 226.8804
16 215.9618 5 309 230.4414 224.8506 237.1133
17 213.6303 6 309 240.9629 235.3378 247.5267
18 217.7272 7 309 251.4578 245.8656 258.1766
19 224.2957 8 309 261.7217 256.2198 268.7377
20 237.3142 9 309 272.1131 266.6316 279.3964
21 199.0539 0 310 192.2067 185.9449 199.2386
22 194.3322 1 310 202.8421 196.6238 209.5271
23 234.3200 2 310 213.4302 207.0444 219.6554
24 232.8416 3 310 223.9013 217.6611 230.3955
25 229.3074 4 310 234.1446 228.3091 240.9575
26 220.4579 5 310 244.6715 238.6616 251.4680
27 235.4208 6 310 255.1049 249.0655 262.1312
28 255.7511 7 310 265.6904 259.2002 273.0106
29 261.0125 8 310 276.2532 269.4975 283.3771
30 247.5153 9 310 286.9689 279.7617 294.1289
31 321.5426 0 330 254.6814 247.9406 262.1436
32 300.4002 1 330 264.9510 258.5398 272.1878
33 283.8565 2 330 275.7049 269.0879 282.5523
34 285.1330 3 330 286.1368 280.0427 292.7874
35 285.7973 4 330 296.6456 290.5776 303.0740
36 297.5855 5 330 307.2148 301.3441 313.3401
37 280.2396 6 330 318.1292 311.4796 324.0465
38 318.2613 7 330 328.7534 321.9510 334.5757
39 305.3495 8 330 339.3884 332.3431 345.0639
40 354.0487 9 330 349.6279 342.7789 355.7355
41 287.6079 0 331 260.1444 253.7071 266.5578
42 285.0000 1 331 270.5191 264.4807 276.9312
43 301.8206 2 331 281.2868 274.9839 287.5255
44 320.1153 3 331 291.5486 285.5566 297.9239
45 316.2773 4 331 301.8162 296.2504 308.3469
46 293.3187 5 331 312.2543 306.8751 318.6855
47 290.0750 6 331 322.8995 317.0962 328.8926
48 334.8177 7 331 333.0684 327.3393 339.5008
49 293.7469 8 331 343.3660 337.8462 350.1369
50 371.5811 9 331 353.8893 348.2208 360.9518
51 234.8606 0 332 258.4386 252.1851 266.1563
52 242.8118 1 332 269.0858 262.9635 276.3438
53 272.9613 2 332 279.6890 273.4557 286.4644
54 309.7688 3 332 289.9404 284.4897 296.4905
55 317.4629 4 332 300.3647 295.1028 307.0537
56 309.9976 5 332 310.8992 305.4133 317.7552
57 454.1619 6 332 321.6036 315.7282 328.4449
58 346.8311 7 332 332.1329 326.3317 339.0270
59 330.3003 8 332 342.7374 336.2870 349.7977
60 253.8644 9 332 353.2594 346.6700 360.4163
61 283.8424 0 333 266.7434 260.0302 274.2944
62 289.5550 1 333 277.2945 270.6303 284.7103
63 276.7693 2 333 287.6110 281.4719 295.1355
64 299.8097 3 333 298.0270 292.1946 305.4625
65 297.1710 4 333 308.4276 302.4103 315.2564
66 338.1665 5 333 318.7820 312.8254 325.8309
67 332.0265 6 333 329.4885 323.1973 336.4020
68 348.8399 7 333 340.1099 333.6899 346.7872
69 333.3600 8 333 350.9598 343.9853 357.2157
70 362.0428 9 333 361.5191 354.2948 367.9958
71 265.4731 0 334 248.2298 241.9697 255.2659
72 276.2012 1 334 258.4670 252.4375 265.1670
73 243.3647 2 334 268.5396 262.9315 275.2114
74 254.6723 3 334 279.2450 273.8533 285.7815
75 279.0244 4 334 289.6531 284.3893 296.2515
76 284.1912 5 334 299.9993 294.7500 306.7790
77 305.5248 6 334 310.5637 305.2306 317.2005
78 331.5229 7 334 320.9429 315.6149 328.1936
79 335.7469 8 334 331.5124 325.9211 338.5947
80 377.2990 9 334 341.9100 336.4053 349.0994
81 241.6083 0 335 208.8246 202.3026 216.2439
82 273.9472 1 335 219.3703 212.7203 226.1315
83 254.4907 2 335 230.0708 223.1593 236.4106
84 270.8021 3 335 240.4212 233.5042 246.9904
85 251.4519 4 335 250.9265 244.0330 257.4123
86 254.6362 5 335 261.3938 254.4131 268.2363
87 245.4523 6 335 271.8089 264.7755 278.5310
88 235.3110 7 335 282.4291 274.9959 289.2059
89 235.7541 8 335 292.9523 285.4216 299.7593
90 237.2466 9 335 303.7596 295.4639 310.4326
91 312.3666 0 337 318.1266 312.1298 324.5244
92 313.8058 1 337 328.6276 322.5916 334.8685
93 291.6112 2 337 339.2636 333.1118 345.2259
94 346.1222 3 337 349.7879 343.6621 356.0608
95 365.7324 4 337 360.5298 354.4263 366.4977
96 391.8385 5 337 371.2581 364.6000 377.1612
97 404.2601 6 337 381.6474 375.1932 387.8791
98 416.6923 7 337 392.4229 385.4383 398.5790
99 455.8643 8 337 402.9936 395.5870 409.4437
100 458.9167 9 337 413.4305 405.3490 420.1516
101 236.1032 0 349 232.1932 224.7018 238.4395
102 230.3167 1 349 242.5122 235.2059 248.7780
103 238.9256 2 349 253.1684 245.7436 259.3135
104 254.9220 3 349 263.3921 256.2307 269.8082
105 250.7103 4 349 273.8149 266.8768 280.3369
106 269.7744 5 349 284.2771 277.3528 290.8914
107 281.5648 6 349 294.6534 287.7502 301.4577
108 308.1020 7 349 304.8993 298.1462 312.1160
109 336.2806 8 349 315.4128 308.5167 322.5658
110 351.6451 9 349 326.3930 318.8858 333.2235
111 256.2968 0 350 264.8812 258.1747 270.7325
112 243.4543 1 350 275.3979 269.0410 281.0752
113 256.2046 2 350 285.7110 279.7679 291.3610
114 255.5271 3 350 296.2228 290.2334 301.8395
115 268.9165 4 350 306.4352 300.6678 311.9355
116 329.7247 5 350 316.6771 311.0507 322.7460
117 379.4445 6 350 327.1960 321.8484 333.2724
118 362.9184 7 350 337.6469 331.9481 343.7422
119 394.4872 8 350 348.1788 342.1669 354.4067
120 389.0527 9 350 358.5266 352.8671 364.9928
121 250.5265 0 351 244.5941 238.1876 250.7788
122 300.0576 1 351 255.2083 248.6591 261.1451
123 269.8939 2 351 265.7152 259.3737 271.4092
124 280.5891 3 351 276.0632 269.8235 282.1617
125 271.8274 4 351 286.5852 280.2720 292.6353
126 304.6336 5 351 297.0239 290.6922 303.3274
127 287.7466 6 351 307.5290 301.2829 314.1767
128 266.5955 7 351 317.8565 311.8221 324.7872
129 321.5418 8 351 328.3464 321.7592 335.3181
130 347.5655 9 351 339.0232 332.3639 345.9441
131 221.6771 0 352 285.3325 279.2586 291.9019
132 298.1939 1 352 295.4837 289.8796 302.3301
133 326.8785 2 352 306.0606 300.6534 312.3607
134 346.8555 3 352 316.7475 311.0867 322.5634
135 348.7402 4 352 327.0214 321.7525 333.0274
136 352.8287 5 352 337.5398 332.4332 343.4863
137 354.4266 6 352 347.8645 342.7019 353.8501
138 360.4326 7 352 358.3175 352.8176 364.4446
139 375.6406 8 352 369.1185 362.7533 374.9615
140 388.5417 9 352 379.9565 372.9895 385.6145
141 271.9235 0 369 258.4332 251.3092 264.1729
142 268.4369 1 369 269.0236 261.9558 274.7523
143 257.2424 2 369 279.0193 272.4227 285.1875
144 277.6566 3 369 289.5948 283.2098 295.4699
145 314.8222 4 369 300.1534 293.5838 305.7889
146 317.2135 5 369 310.5530 304.1309 316.0357
147 298.1353 6 369 320.7576 314.8179 326.4905
148 348.1229 7 369 331.2463 325.5022 337.1408
149 340.2800 8 369 341.6191 335.8289 347.8233
150 366.5131 9 369 352.1442 345.9868 358.6378
151 225.2640 0 370 245.3301 238.7508 252.3267
152 234.5235 1 370 255.7637 249.3249 263.1909
153 238.9008 2 370 266.2529 259.9771 273.4907
154 240.4730 3 370 277.0493 270.5201 283.7240
155 267.5373 4 370 287.6103 281.2275 294.1309
156 344.1937 5 370 297.9537 291.8134 304.3273
157 281.1481 6 370 308.2526 302.0980 315.3372
158 347.5855 7 370 318.8310 312.3472 326.0458
159 365.1630 8 370 329.4624 322.7346 336.3049
160 372.2288 9 370 340.1088 332.8037 346.9413
161 269.8804 0 371 247.6461 240.3394 253.9678
162 272.4428 1 371 258.1299 251.2291 264.3176
163 277.8989 2 371 268.6032 262.1156 274.7990
164 281.7895 3 371 279.0288 272.7747 285.2247
165 279.1705 4 371 289.3000 283.3841 295.6987
166 284.5120 5 371 299.6474 293.8507 306.0975
167 259.2658 6 371 310.0876 304.4920 316.6305
168 304.6306 7 371 320.4965 315.0950 327.0402
169 350.7807 8 371 331.0530 325.6927 337.9049
170 369.4692 9 371 341.5112 336.0573 348.3466
171 269.4117 0 372 268.5214 262.2912 274.6502
172 273.4740 1 372 278.9957 272.8498 284.9580
173 297.5968 2 372 289.3419 283.0864 295.5726
174 310.6316 3 372 299.7144 293.4572 305.9781
175 287.1726 4 372 310.0917 304.0954 316.2456
176 329.6076 5 372 320.8763 314.5660 326.7115
177 334.4818 6 372 331.5243 325.3691 337.7064
178 343.2199 7 372 341.9861 335.5299 348.1539
179 369.1417 8 372 352.5127 345.8407 358.7223
180 364.1236 9 372 363.1310 356.0240 369.0624
Reaction Days Subject pred LCB0.25 UCB0.75
1 249.5600 0 308 253.5027 245.8242 260.9467
2 258.7047 1 308 263.5685 256.7850 270.7548
3 250.8006 2 308 274.3686 267.8226 280.3737
4 321.4398 3 308 285.6002 278.6498 290.6217
5 356.8519 4 308 296.5267 289.5747 301.0672
6 414.6901 5 308 306.7795 300.2963 311.9968
7 382.2038 6 308 316.9215 310.4144 322.3543
8 290.1486 7 308 326.8623 320.4549 333.8066
9 430.5853 8 308 336.9923 330.6790 344.8616
10 466.3535 9 308 347.1669 340.6084 355.4023
11 222.7339 0 309 253.5027 245.8242 260.9467
12 205.2658 1 309 263.5685 256.7850 270.7548
13 202.9778 2 309 274.3686 267.8226 280.3737
14 204.7070 3 309 285.6002 278.6498 290.6217
15 207.7161 4 309 296.5267 289.5747 301.0672
16 215.9618 5 309 306.7795 300.2963 311.9968
17 213.6303 6 309 316.9215 310.4144 322.3543
18 217.7272 7 309 326.8623 320.4549 333.8066
19 224.2957 8 309 336.9923 330.6790 344.8616
20 237.3142 9 309 347.1669 340.6084 355.4023
21 199.0539 0 310 253.5027 245.8242 260.9467
22 194.3322 1 310 263.5685 256.7850 270.7548
23 234.3200 2 310 274.3686 267.8226 280.3737
24 232.8416 3 310 285.6002 278.6498 290.6217
25 229.3074 4 310 296.5267 289.5747 301.0672
26 220.4579 5 310 306.7795 300.2963 311.9968
27 235.4208 6 310 316.9215 310.4144 322.3543
28 255.7511 7 310 326.8623 320.4549 333.8066
29 261.0125 8 310 336.9923 330.6790 344.8616
30 247.5153 9 310 347.1669 340.6084 355.4023
31 321.5426 0 330 253.5027 245.8242 260.9467
32 300.4002 1 330 263.5685 256.7850 270.7548
33 283.8565 2 330 274.3686 267.8226 280.3737
34 285.1330 3 330 285.6002 278.6498 290.6217
35 285.7973 4 330 296.5267 289.5747 301.0672
36 297.5855 5 330 306.7795 300.2963 311.9968
37 280.2396 6 330 316.9215 310.4144 322.3543
38 318.2613 7 330 326.8623 320.4549 333.8066
39 305.3495 8 330 336.9923 330.6790 344.8616
40 354.0487 9 330 347.1669 340.6084 355.4023
41 287.6079 0 331 253.5027 245.8242 260.9467
42 285.0000 1 331 263.5685 256.7850 270.7548
43 301.8206 2 331 274.3686 267.8226 280.3737
44 320.1153 3 331 285.6002 278.6498 290.6217
45 316.2773 4 331 296.5267 289.5747 301.0672
46 293.3187 5 331 306.7795 300.2963 311.9968
47 290.0750 6 331 316.9215 310.4144 322.3543
48 334.8177 7 331 326.8623 320.4549 333.8066
49 293.7469 8 331 336.9923 330.6790 344.8616
50 371.5811 9 331 347.1669 340.6084 355.4023
51 234.8606 0 332 253.5027 245.8242 260.9467
52 242.8118 1 332 263.5685 256.7850 270.7548
53 272.9613 2 332 274.3686 267.8226 280.3737
54 309.7688 3 332 285.6002 278.6498 290.6217
55 317.4629 4 332 296.5267 289.5747 301.0672
56 309.9976 5 332 306.7795 300.2963 311.9968
57 454.1619 6 332 316.9215 310.4144 322.3543
58 346.8311 7 332 326.8623 320.4549 333.8066
59 330.3003 8 332 336.9923 330.6790 344.8616
60 253.8644 9 332 347.1669 340.6084 355.4023
61 283.8424 0 333 253.5027 245.8242 260.9467
62 289.5550 1 333 263.5685 256.7850 270.7548
63 276.7693 2 333 274.3686 267.8226 280.3737
64 299.8097 3 333 285.6002 278.6498 290.6217
65 297.1710 4 333 296.5267 289.5747 301.0672
66 338.1665 5 333 306.7795 300.2963 311.9968
67 332.0265 6 333 316.9215 310.4144 322.3543
68 348.8399 7 333 326.8623 320.4549 333.8066
69 333.3600 8 333 336.9923 330.6790 344.8616
70 362.0428 9 333 347.1669 340.6084 355.4023
71 265.4731 0 334 253.5027 245.8242 260.9467
72 276.2012 1 334 263.5685 256.7850 270.7548
73 243.3647 2 334 274.3686 267.8226 280.3737
74 254.6723 3 334 285.6002 278.6498 290.6217
75 279.0244 4 334 296.5267 289.5747 301.0672
76 284.1912 5 334 306.7795 300.2963 311.9968
77 305.5248 6 334 316.9215 310.4144 322.3543
78 331.5229 7 334 326.8623 320.4549 333.8066
79 335.7469 8 334 336.9923 330.6790 344.8616
80 377.2990 9 334 347.1669 340.6084 355.4023
81 241.6083 0 335 253.5027 245.8242 260.9467
82 273.9472 1 335 263.5685 256.7850 270.7548
83 254.4907 2 335 274.3686 267.8226 280.3737
84 270.8021 3 335 285.6002 278.6498 290.6217
85 251.4519 4 335 296.5267 289.5747 301.0672
86 254.6362 5 335 306.7795 300.2963 311.9968
87 245.4523 6 335 316.9215 310.4144 322.3543
88 235.3110 7 335 326.8623 320.4549 333.8066
89 235.7541 8 335 336.9923 330.6790 344.8616
90 237.2466 9 335 347.1669 340.6084 355.4023
91 312.3666 0 337 253.5027 245.8242 260.9467
92 313.8058 1 337 263.5685 256.7850 270.7548
93 291.6112 2 337 274.3686 267.8226 280.3737
94 346.1222 3 337 285.6002 278.6498 290.6217
95 365.7324 4 337 296.5267 289.5747 301.0672
96 391.8385 5 337 306.7795 300.2963 311.9968
97 404.2601 6 337 316.9215 310.4144 322.3543
98 416.6923 7 337 326.8623 320.4549 333.8066
99 455.8643 8 337 336.9923 330.6790 344.8616
100 458.9167 9 337 347.1669 340.6084 355.4023
101 236.1032 0 349 253.5027 245.8242 260.9467
102 230.3167 1 349 263.5685 256.7850 270.7548
103 238.9256 2 349 274.3686 267.8226 280.3737
104 254.9220 3 349 285.6002 278.6498 290.6217
105 250.7103 4 349 296.5267 289.5747 301.0672
106 269.7744 5 349 306.7795 300.2963 311.9968
107 281.5648 6 349 316.9215 310.4144 322.3543
108 308.1020 7 349 326.8623 320.4549 333.8066
109 336.2806 8 349 336.9923 330.6790 344.8616
110 351.6451 9 349 347.1669 340.6084 355.4023
111 256.2968 0 350 253.5027 245.8242 260.9467
112 243.4543 1 350 263.5685 256.7850 270.7548
113 256.2046 2 350 274.3686 267.8226 280.3737
114 255.5271 3 350 285.6002 278.6498 290.6217
115 268.9165 4 350 296.5267 289.5747 301.0672
116 329.7247 5 350 306.7795 300.2963 311.9968
117 379.4445 6 350 316.9215 310.4144 322.3543
118 362.9184 7 350 326.8623 320.4549 333.8066
119 394.4872 8 350 336.9923 330.6790 344.8616
120 389.0527 9 350 347.1669 340.6084 355.4023
121 250.5265 0 351 253.5027 245.8242 260.9467
122 300.0576 1 351 263.5685 256.7850 270.7548
123 269.8939 2 351 274.3686 267.8226 280.3737
124 280.5891 3 351 285.6002 278.6498 290.6217
125 271.8274 4 351 296.5267 289.5747 301.0672
126 304.6336 5 351 306.7795 300.2963 311.9968
127 287.7466 6 351 316.9215 310.4144 322.3543
128 266.5955 7 351 326.8623 320.4549 333.8066
129 321.5418 8 351 336.9923 330.6790 344.8616
130 347.5655 9 351 347.1669 340.6084 355.4023
131 221.6771 0 352 253.5027 245.8242 260.9467
132 298.1939 1 352 263.5685 256.7850 270.7548
133 326.8785 2 352 274.3686 267.8226 280.3737
134 346.8555 3 352 285.6002 278.6498 290.6217
135 348.7402 4 352 296.5267 289.5747 301.0672
136 352.8287 5 352 306.7795 300.2963 311.9968
137 354.4266 6 352 316.9215 310.4144 322.3543
138 360.4326 7 352 326.8623 320.4549 333.8066
139 375.6406 8 352 336.9923 330.6790 344.8616
140 388.5417 9 352 347.1669 340.6084 355.4023
141 271.9235 0 369 253.5027 245.8242 260.9467
142 268.4369 1 369 263.5685 256.7850 270.7548
143 257.2424 2 369 274.3686 267.8226 280.3737
144 277.6566 3 369 285.6002 278.6498 290.6217
145 314.8222 4 369 296.5267 289.5747 301.0672
146 317.2135 5 369 306.7795 300.2963 311.9968
147 298.1353 6 369 316.9215 310.4144 322.3543
148 348.1229 7 369 326.8623 320.4549 333.8066
149 340.2800 8 369 336.9923 330.6790 344.8616
150 366.5131 9 369 347.1669 340.6084 355.4023
151 225.2640 0 370 253.5027 245.8242 260.9467
152 234.5235 1 370 263.5685 256.7850 270.7548
153 238.9008 2 370 274.3686 267.8226 280.3737
154 240.4730 3 370 285.6002 278.6498 290.6217
155 267.5373 4 370 296.5267 289.5747 301.0672
156 344.1937 5 370 306.7795 300.2963 311.9968
157 281.1481 6 370 316.9215 310.4144 322.3543
158 347.5855 7 370 326.8623 320.4549 333.8066
159 365.1630 8 370 336.9923 330.6790 344.8616
160 372.2288 9 370 347.1669 340.6084 355.4023
161 269.8804 0 371 253.5027 245.8242 260.9467
162 272.4428 1 371 263.5685 256.7850 270.7548
163 277.8989 2 371 274.3686 267.8226 280.3737
164 281.7895 3 371 285.6002 278.6498 290.6217
165 279.1705 4 371 296.5267 289.5747 301.0672
166 284.5120 5 371 306.7795 300.2963 311.9968
167 259.2658 6 371 316.9215 310.4144 322.3543
168 304.6306 7 371 326.8623 320.4549 333.8066
169 350.7807 8 371 336.9923 330.6790 344.8616
170 369.4692 9 371 347.1669 340.6084 355.4023
171 269.4117 0 372 253.5027 245.8242 260.9467
172 273.4740 1 372 263.5685 256.7850 270.7548
173 297.5968 2 372 274.3686 267.8226 280.3737
174 310.6316 3 372 285.6002 278.6498 290.6217
175 287.1726 4 372 296.5267 289.5747 301.0672
176 329.6076 5 372 306.7795 300.2963 311.9968
177 334.4818 6 372 316.9215 310.4144 322.3543
178 343.2199 7 372 326.8623 320.4549 333.8066
179 369.1417 8 372 336.9923 330.6790 344.8616
180 364.1236 9 372 347.1669 340.6084 355.4023
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