cat_sim: Simulation of Computerized Adaptive Testing (CAT)
In xxIRT: Item Response Theory and Computer-Based Testing in R
Description
Usage
Arguments
Details
Value
Examples
Description
cat_sim runs a simulation of CAT. Use theta in options to set the starting
value of theta estimate.
cat_estimate_mle is the maximum likelihood estimation rule. Use
map_len to apply MAP to the first K items and use map_prior to set the
prior for MAP.
cat_estimate_eap is the expected a posteriori estimation rule,
using eap_mean and eap_sd option parameters as the prior
cat_estimate_hybrid is a hybrid estimation rule, which uses MLE for
mixed responses and EAP for all 1's or 0's responses
cat_stop_default is a three-way stopping rule. When stop_se
is set in the options, it uses the standard error stopping rule. When
stop_mi is set in the options, it uses the minimum information stopping rule. When
stop_cut is set in the options, it uses the confidence interval (set by ci_width)
stopping rule.
cat_select_maxinfo is the maximum information selection rule. Use group
(a numeric vector) to group items belonging to the same set. Use info_random to implement
the random-esque item exposure control method.
cat_select_ccat is the constrained CAT selection rule. Use
ccat_var to set the content variable in the pool. Use ccat_perc to set
the desired content distribution, with the name of each element being the content code
and tue value of each element being the percentage. Use ccat_random to add randomness
to initial item selections.
cat_select_shadow is the shadow-test selection rule. Use shadow_id
to group item sets. Use constraints to set constraints. Constraints should be in a data.frame
with four columns: var (variable name), level (variable level, NA for quantitative variable),
min (lower bound), and max (upper bound).
cat_stop_projection is the projection-based stopping rule. Use
projection_method to choose the projection method ('info' or 'diff'). Use
stop_cut to set the cut score. Use constraints to set the constraints.
Constraints should be a data.frame with columns: var (variable name),
level (variable level, NA for quantitative varialbe), min (lower bound), max (upper bound)
Usage
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cat_sim(true, pool, ...)
cat_estimate_mle(len, theta, stats, admin, pool, opts)
cat_estimate_eap(len, theta, stats, admin, pool, opts)
cat_estimate_hybrid(len, theta, stats, admin, pool, opts)
cat_stop_default(len, theta, stats, admin, pool, opts)
cat_select_maxinfo(len, theta, stats, admin, pool, opts)
cat_select_ccat(len, theta, stats, admin, pool, opts)
cat_select_shadow(len, theta, stats, admin, pool, opts)
## S3 method for class 'cat'
print(x, ...)
## S3 method for class 'cat'
plot(x, ...)
cat_stop_projection(len, theta, stats, admin, pool, opts)
Arguments
true
the true theta
pool
the item pool (data.frame)
...
option/control parameters
len
the current test length
theta
the current theta estimate
stats
a matrix of responses, theta estimate, information and std error
admin
a data frame of administered items
opts
a list of option/control parameters
x
a cat object
Details
... takes a variety of option/control parameters for the simulations from users.
min and max are mandatory for setting limits on the test length. User-defined
selection, estimation, and stopping rules are also passed to the simulator via options.
To write a new rule, the function siganiture must be: function(len, theta, stats, admin, pool, opts).
See built-in rules for examples.
Value
cat_sim returns a cat object
an estimation rule should return a theta estimate
a stopping rule should return a boolean: TRUE to stop the CAT, FALSE to continue
a selection rule should return a list of (a) the selected item and (b) the updated pool
Examples
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## Not run:
## generate a 100-item pool
num_items <- 100
pool <- with(model_3pl_gendata(1, num_items), data.frame(a=a, b=b, c=c))
pool$set_id <- sample(1:30, num_items, replace=TRUE)
pool$content <- sample(1:3, num_items, replace=TRUE)
pool$time <- round(rlnorm(num_items, mean=4.1, sd=.2))
## MLE, EAP, and hybrid estimation rule
cat_sim(1.0, pool, min=10, max=20, estimate_rule=cat_estimate_mle)
cat_sim(1.0, pool, min=10, max=20, estimate_rule=cat_estimate_eap)
cat_sim(1.0, pool, min=10, max=20, estimate_rule=cat_estimate_hybrid)
## SE, MI, and CI stopping rule
cat_sim(1.0, pool, min=10, max=20, stop_se=.3)
cat_sim(1.0, pool, min=10, max=20, stop_mi=.6)
cat_sim(1.0, pool, min=10, max=20, stop_cut=0)
cat_sim(1.0, pool, min=10, max=20, stop_cut=0, ci_width=2.58)
## maximum information selection with item sets
cat_sim(1.0, pool, min=10, max=20, group="set_id")$admin
## maximum information with item exposure control
cat_sim(1.0, pool, min=10, max=20, info_random=5)$admin
## Constrained-CAT selection rule with and without initial randomness
cat_sim(1.0, pool, min=10, max=20, select_rule=cat_select_ccat,
ccat_var="content", ccat_perc=c("1"=.2, "2"=.3, "3"=.5))
cat_sim(1.0, pool, min=10, max=20, select_rule=cat_select_ccat, ccat_random=5,
ccat_var="content", ccat_perc=c("1"=.2, "2"=.3, "3"=.5))
## Shadow-test selection rule
cons <- data.frame(var='content', level=1:3, min=c(3,3,4), max=c(3,3,4))
cons <- rbind(cons, data.frame(var='time', level=NA, min=55*10, max=65*10))
cat_sim(1.0, pool, min=10, max=10, select_rule=cat_select_shadow, constraints=cons)
## Projection-based stopping rule
cons <- data.frame(var='content', level=1:3, min=5, max=15)
cons <- rbind(cons, data.frame(var='time', level=NA, min=60*20, max=60*40))
cat_sim(1.0, pool, min=20, max=40, select_rule=cat_select_shadow, stop_rule=cat_stop_projection,
projection_method="diff", stop_cut=0, constraints=cons)
## End(Not run)
Example output
true=1, est.=-1.14, se=0.6, p=0.7, used 20 items (14 correct).
Belows is a history of the CAT:
u t se info a b c set_id content
16 1 0.4426329 0.9877031 1.025055 1.647223 -0.1127991 0.07791847 2 1
84 1 0.6805086 0.8062676 1.538302 1.520301 0.1124009 0.09169322 12 1
97 1 0.9755006 0.7620799 1.721865 1.242951 0.6639219 0.08318524 16 2
68 1 1.2613159 0.6804160 2.159986 1.379279 0.9840343 0.11069216 21 2
4 0 0.9934347 0.5234169 3.650097 1.177836 1.1098185 0.06028314 27 2
time
16 55
84 47
97 53
68 63
4 54
...
u t se info a b c set_id
88 1 1.201506 0.3270477 9.349273 1.1117415 -1.0828131 0.09423111 9
72 1 1.244813 0.3182385 9.874034 1.1315467 0.6303711 0.06165440 19
79 1 1.300769 0.3115292 10.303921 1.0262166 1.0183590 0.09599795 21
46 1 1.353064 0.3061940 10.666123 0.9831951 1.0324230 0.07288879 5
65 0 -1.135452 0.6022880 2.756713 0.9396877 1.2613025 0.04510026 23
content time
88 2 71
72 1 87
79 2 62
46 2 54
65 2 77
true=1, est.=1.1, se=0.27, p=0.7, used 20 items (14 correct).
Belows is a history of the CAT:
u t se info a b c set_id content
16 1 0.3348219 0.9038898 1.223965 1.647223 -0.1127991 0.07791847 2 1
84 1 0.5569632 0.7248393 1.903341 1.520301 0.1124009 0.09169322 12 1
58 1 0.6908327 0.6555447 2.326994 1.474747 0.1206311 0.13866093 24 2
97 1 0.8695649 0.6207522 2.595156 1.242951 0.6639219 0.08318524 16 2
68 1 1.0588729 0.5711914 3.065044 1.379279 0.9840343 0.11069216 21 2
time
16 55
84 47
58 54
97 53
68 63
...
u t se info a b c set_id content
91 0 0.9777102 0.2946393 11.51910 1.1165245 1.1804404 0.11090126 19 3
12 1 1.0555030 0.2892491 11.95242 1.0617880 1.2995275 0.06142960 30 3
79 1 1.1092831 0.2840470 12.39423 1.0262166 1.0183590 0.09599795 21 2
46 0 1.0455516 0.2750298 13.22027 0.9831951 1.0324230 0.07288879 5 2
34 1 1.0964218 0.2707877 13.63774 0.9318733 0.9552107 0.03165545 4 1
time
91 54
12 50
79 62
46 54
34 49
true=1, est.=0.97, se=0.27, p=0.65, used 20 items (13 correct).
Belows is a history of the CAT:
u t se info a b c set_id content
16 1 0.3348219 0.9038898 1.223965 1.647223 -0.1127991 0.07791847 2 1
84 1 0.5569632 0.7248393 1.903341 1.520301 0.1124009 0.09169322 12 1
58 1 0.6908327 0.6555447 2.326994 1.474747 0.1206311 0.13866093 24 2
97 1 0.8695649 0.6207522 2.595156 1.242951 0.6639219 0.08318524 16 2
68 0 0.7805161 0.5056140 3.911667 1.379279 0.9840343 0.11069216 21 2
time
16 55
84 47
58 54
97 53
68 63
...
u t se info a b c set_id content
3 1 0.8531523 0.2920034 11.72800 1.181367 0.2215912 0.11294698 16 3
90 0 0.8094693 0.2837103 12.42366 1.142360 1.3158429 0.07519694 19 1
32 1 0.8522734 0.2780630 12.93343 1.087356 0.6653296 0.18683932 6 3
91 1 0.9192257 0.2734011 13.37825 1.116525 1.1804404 0.11090126 19 3
79 1 0.9747746 0.2690344 13.81607 1.026217 1.0183590 0.09599795 21 2
time
3 85
90 65
32 48
91 54
79 62
true=1, est.=1.67, se=0.36, p=0.85, used 20 items (17 correct).
Belows is a history of the CAT:
u t se info a b c set_id content
16 1 0.4426335 0.9877036 1.025054 1.647223 -0.1127991 0.07791847 2 1
84 1 0.6805083 0.8062675 1.538302 1.520301 0.1124009 0.09169322 12 1
97 1 0.9755121 0.7620860 1.721837 1.242951 0.6639219 0.08318524 16 2
68 1 1.2613866 0.6804435 2.159812 1.379279 0.9840343 0.11069216 21 2
4 1 1.4725151 0.6390186 2.448911 1.177836 1.1098185 0.06028314 27 2
time
16 55
84 47
97 53
68 63
4 54
...
u t se info a b c set_id
12 1 0.9459471 0.3533338 8.009947 1.0617880 1.299528 0.06142960 30
100 0 1.5231581 0.3645384 7.525121 1.1921837 0.685593 0.06688831 8
91 1 -1.1391873 0.5304352 3.554146 1.1165245 1.180440 0.11090126 19
43 1 1.5925296 0.3570929 7.842193 1.0342464 -1.134937 0.06604005 12
64 1 1.6718846 0.3554301 7.915740 0.9562634 1.520666 0.08640765 16
content time
12 3 50
100 1 82
91 3 54
43 2 38
64 2 51
true=1, est.=1.38, se=0.34, p=0.71, used 14 items (10 correct).
Belows is a history of the CAT:
u t se info a b c set_id content
16 1 0.4426369 0.9877067 1.025048 1.647223 -0.1127991 0.07791847 2 1
84 1 0.6805093 0.8062682 1.538300 1.520301 0.1124009 0.09169322 12 1
97 1 0.9755031 0.7620812 1.721858 1.242951 0.6639219 0.08318524 16 2
68 1 1.2613418 0.6804261 2.159922 1.379279 0.9840343 0.11069216 21 2
4 0 0.9931541 0.5233805 3.650606 1.177836 1.1098185 0.06028314 27 2
time
16 55
84 47
97 53
68 63
4 54
...
u t se info a b c set_id content
90 0 1.293009 0.3803474 6.9125616 1.142360 1.315843 0.07519694 19 1
91 1 1.385538 0.3708402 7.2715395 1.116525 1.180440 0.11090126 19 3
86 0 1.291239 0.3462050 8.3432137 1.206985 1.605837 0.11229093 8 2
12 1 -1.089425 1.6559518 0.3646738 1.061788 1.299528 0.06142960 30 3
76 1 1.380243 0.3373238 8.7883212 1.221958 -1.232970 0.13173985 7 1
time
90 65
91 54
86 63
12 50
76 59
true=1, est.=0.96, se=0.36, p=0.6, used 10 items (6 correct).
Belows is a history of the CAT:
u t se info a b c set_id
16 1 0.4426352 0.9877051 1.025051 1.647223 -0.1127991 0.07791847 2
84 1 0.6804697 0.8062388 1.538412 1.520301 0.1124009 0.09169322 12
97 1 0.9755266 0.7620937 1.721802 1.242951 0.6639219 0.08318524 16
68 1 1.2613315 0.6804221 2.159948 1.379279 0.9840343 0.11069216 21
4 0 0.9930084 0.5233615 3.650870 1.177836 1.1098185 0.06028314 27
100 1 1.1156673 0.4891871 4.178786 1.192184 0.6855930 0.06688831 8
42 1 1.2472206 0.4672293 4.580785 1.177062 0.9932710 0.09220206 13
63 0 1.0884965 0.4110228 5.919269 1.157707 1.1728487 0.07111505 27
35 0 1.0020819 0.3828273 6.823297 1.129563 1.4192049 0.02998260 18
72 0 0.9634069 0.3621781 7.623519 1.131547 0.6303711 0.06165440 19
content time
16 1 55
84 1 47
97 2 53
68 2 63
4 2 54
100 1 82
42 3 40
63 2 66
35 2 59
72 1 87
true=1, est.=1.01, se=0.36, p=0.73, used 11 items (8 correct).
Belows is a history of the CAT:
u t se info a b c set_id
16 1 0.4426337 0.9877038 1.025054 1.647223 -0.1127991 0.07791847 2
84 1 0.6805086 0.8062677 1.538302 1.520301 0.1124009 0.09169322 12
97 1 0.9755329 0.7620970 1.721787 1.242951 0.6639219 0.08318524 16
68 0 0.7047374 0.5479643 3.330393 1.379279 0.9840343 0.11069216 21
100 0 0.5208525 0.4732689 4.464616 1.192184 0.6855930 0.06688831 8
content time
16 1 55
84 1 47
97 2 53
68 2 63
100 1 82
...
u t se info a b c set_id content
72 1 0.7267931 0.4155111 5.792081 1.131547 0.6303711 0.06165440 19 1
62 0 0.5881922 0.3796630 6.937506 1.177431 0.6006342 0.11736218 2 2
89 1 0.6758617 0.3656451 7.479635 1.070574 0.5227013 0.05030759 26 2
42 1 0.8864438 0.3643774 7.531773 1.177062 0.9932710 0.09220206 13 3
4 1 1.0148105 0.3573531 7.830778 1.177836 1.1098185 0.06028314 27 2
time
72 87
62 57
89 51
42 40
4 54
u t se info a b c set_id
16 1 0.8379098 0.8798470 1.291771 1.6472227 -0.1127991 0.07791847 2
22 1 0.8379098 0.8798470 1.291771 1.1240637 -1.0858426 0.17126860 2
62 1 0.8379098 0.8798470 1.291771 1.1774306 0.6006342 0.11736218 2
18 1 0.9478814 0.5794128 2.978679 0.9782049 -0.7510692 0.09872854 21
68 1 0.9478814 0.5794128 2.978679 1.3792794 0.9840343 0.11069216 21
79 0 0.9478814 0.5794128 2.978679 1.0262166 1.0183590 0.09599795 21
4 1 1.4699721 0.4855306 4.241962 1.1778356 1.1098185 0.06028314 27
31 0 1.4699721 0.4855306 4.241962 0.8258244 0.7247103 0.08054818 27
63 1 1.4699721 0.4855306 4.241962 1.1577075 1.1728487 0.07111505 27
70 1 1.4699721 0.4855306 4.241962 0.9295510 0.3291351 0.13729153 27
67 0 0.8811149 0.3615718 7.649111 0.5406633 0.8735232 0.10075373 19
72 1 0.8811149 0.3615718 7.649111 1.1315467 0.6303711 0.06165440 19
90 0 0.8811149 0.3615718 7.649111 1.1423597 1.3158429 0.07519694 19
91 1 0.8811149 0.3615718 7.649111 1.1165245 1.1804404 0.11090126 19
61 1 1.3152259 0.3416435 8.567490 1.0072735 -0.2159953 0.10729972 8
86 0 1.3152259 0.3416435 8.567490 1.2069851 1.6058366 0.11229093 8
100 1 1.3152259 0.3416435 8.567490 1.1921837 0.6855930 0.06688831 8
35 1 1.4256572 0.3324214 9.049448 1.1295634 1.4192049 0.02998260 18
55 1 1.4256572 0.3324214 9.049448 1.2685049 -0.2715816 0.12383102 18
9 1 1.4553831 0.3288616 9.246423 0.9284396 0.5313580 0.06706269 4
content time
16 1 55
22 2 65
62 2 57
18 3 69
68 2 63
79 2 62
4 2 54
31 3 82
63 2 66
70 2 100
67 2 75
72 1 87
90 1 65
91 3 54
61 1 57
86 2 63
100 1 82
35 2 59
55 3 69
9 1 45
u t se info a b c set_id
16 1 0.4426330 0.9877032 1.0250548 1.6472227 -0.1127991 0.07791847 2
66 1 0.6615793 0.8597255 1.3529457 1.3130091 0.1047014 0.16347949 13
68 1 1.0980190 0.7670965 1.6994173 1.3792794 0.9840343 0.11069216 21
4 1 1.3785026 0.6859924 2.1250117 1.1778356 1.1098185 0.06028314 27
35 0 1.1518251 0.5491330 3.3162318 1.1295634 1.4192049 0.02998260 18
97 0 0.8451730 0.4788708 4.3607704 1.2429510 0.6639219 0.08318524 16
63 1 1.0321975 0.4445087 5.0610364 1.1577075 1.1728487 0.07111505 27
90 0 0.9238942 0.4170137 5.7504182 1.1423597 1.3158429 0.07519694 19
5 1 1.0129720 0.3936848 6.4521251 1.0698240 0.7153680 0.08488474 1
91 0 1.0432413 0.3745155 7.1295216 1.1165245 1.1804404 0.11090126 19
42 1 1.1437538 0.3560560 7.8879364 1.1770617 0.9932710 0.09220206 13
72 0 0.9808761 0.3388500 8.7093376 1.1315467 0.6303711 0.06165440 19
100 1 1.0501685 0.3243901 9.5030872 1.1921837 0.6855930 0.06688831 8
12 0 -1.2345311 1.9913633 0.2521732 1.0617880 1.2995275 0.06142960 30
88 1 0.9844340 0.3122466 10.2566260 1.1117415 -1.0828131 0.09423111 9
62 1 1.0331499 0.3023120 10.9418122 1.1774306 0.6006342 0.11736218 2
34 0 0.9605468 0.2938485 11.5811880 0.9318733 0.9552107 0.03165545 4
79 1 -1.2419228 0.9969713 1.0060851 1.0262166 1.0183590 0.09599795 21
43 1 1.0248125 0.2859059 12.2335819 1.0342464 -1.1349366 0.06604005 12
32 1 1.0622919 0.2801971 12.7371659 1.0873561 0.6653296 0.18683932 6
content time
16 1 55
66 2 54
68 2 63
4 2 54
35 2 59
97 2 53
63 2 66
90 1 65
5 3 71
91 3 54
42 3 40
72 1 87
100 1 82
12 3 50
88 2 71
62 2 57
34 1 49
79 2 62
43 2 38
32 3 48
true=1, est.=1.05, se=0.29, p=0.7, used 20 items (14 correct).
Belows is a history of the CAT:
u t se info a b c set_id
57 1 0.5040863 1.1691155 0.7316193 1.167261 0.002072399 0.04331153 29
58 1 0.7310156 0.8620159 1.3457658 1.474747 0.120631055 0.13866093 24
100 0 0.4331946 0.6104376 2.6835979 1.192184 0.685593032 0.06688831 8
3 0 0.1747975 0.5334140 3.5145613 1.181367 0.221591152 0.11294698 16
66 1 0.3140523 0.4734955 4.4603434 1.313009 0.104701364 0.16347949 13
content time
57 3 55
58 2 54
100 1 82
3 3 85
66 2 54
...
u t se info a b c set_id
12 0 0.9799806 0.3090876 10.467354 1.0617880 1.2995275 0.06142960 30
90 0 0.9209035 0.2965109 11.374141 1.1423597 1.3158429 0.07519694 19
48 1 0.9681386 0.2928999 11.656320 0.8578328 0.7359015 0.07589904 23
63 1 -1.2381958 1.1874893 0.709154 1.1577075 1.1728487 0.07111505 27
78 1 1.0528209 0.2868480 12.153356 1.0071481 -1.0953267 0.10696292 10
content time
12 3 50
90 1 65
48 3 56
63 2 66
78 3 52
true=1, est.=0.97, se=0.29, p=0.7, used 20 items (14 correct).
Belows is a history of the CAT:
u t se info a b c set_id
58 1 0.5366631 1.0018460 0.9963182 1.474747 0.1206311 0.13866093 24
84 1 0.7425499 0.7970060 1.5742611 1.520301 0.1124009 0.09169322 12
100 1 1.0204902 0.7522947 1.7669489 1.192184 0.6855930 0.06688831 8
72 1 1.1968025 0.7055421 2.0088809 1.131547 0.6303711 0.06165440 19
42 0 0.9184875 0.5256979 3.6184911 1.177062 0.9932710 0.09220206 13
content time
58 2 54
84 1 47
100 1 82
72 1 87
42 3 40
...
u t se info a b c set_id
53 0 1.1351705 0.3280729 9.290934 0.8268489 1.1321856 0.09914609 29
90 1 1.2314651 0.3223473 9.623916 1.1423597 1.3158429 0.07519694 19
31 1 1.2723407 0.3196381 9.787752 0.8258244 0.7247103 0.08054818 27
35 1 1.3703120 0.3153380 10.056513 1.1295634 1.4192049 0.02998260 18
19 0 0.9667661 0.2888128 11.988559 0.7524507 1.4023626 0.03018560 25
content time
53 3 49
90 1 65
31 3 82
35 2 59
19 3 53
true=1, est.=1.12, se=0.38, p=0.9, used 10 items (9 correct).
Belows is a history of the CAT:
u t se info a b c set_id
16 1 0.4426345 0.9877045 1.025052 1.647223 -0.1127991 0.07791847 2
84 1 0.6805159 0.8062731 1.538281 1.520301 0.1124009 0.09169322 12
97 1 0.9755360 0.7620987 1.721780 1.242951 0.6639219 0.08318524 16
68 0 0.7047199 0.5479619 3.330422 1.379279 0.9840343 0.11069216 21
100 1 0.8726625 0.5053337 3.916007 1.192184 0.6855930 0.06688831 8
4 1 1.0632430 0.4810182 4.321922 1.177836 1.1098185 0.06028314 27
42 1 1.1947940 0.4581087 4.764999 1.177062 0.9932710 0.09220206 13
91 1 1.3164588 0.4451357 5.046789 1.116525 1.1804404 0.11090126 19
12 1 1.4394766 0.4364443 5.249795 1.061788 1.2995275 0.06142960 30
5 1 1.1190133 0.3767953 7.043509 1.069824 0.7153680 0.08488474 1
content time shadow_id
16 1 55 16
84 1 47 84
97 2 53 97
68 2 63 68
100 1 82 100
4 2 54 4
42 3 40 42
91 3 54 91
12 3 50 12
5 3 71 5
true=1, est.=0.8, se=0.23, p=0.61, used 31 items (19 correct).
Belows is a history of the CAT:
u t se info a b c set_id content
16 1 0.4426331 0.9877033 1.025055 1.647223 -0.1127991 0.07791847 2 1
84 1 0.6805084 0.8062676 1.538302 1.520301 0.1124009 0.09169322 12 1
97 1 0.9754977 0.7620784 1.721871 1.242951 0.6639219 0.08318524 16 2
68 1 1.2613385 0.6804248 2.159930 1.379279 0.9840343 0.11069216 21 2
4 0 0.9930425 0.5233660 3.650808 1.177836 1.1098185 0.06028314 27 2
time shadow_id
16 55 16
84 47 84
97 53 97
68 63 68
4 54 4
...
u t se info a b c set_id content
69 0 0.7378440 0.2376332 17.70866 0.9257078 0.6991092 0.06719960 25 2
9 1 0.7700116 0.2344324 18.19553 0.9284396 0.5313580 0.06706269 4 1
26 0 0.7241563 0.2306811 18.79212 0.9952935 0.7347191 0.15313704 5 1
60 1 0.7493239 0.2277126 19.28528 0.9543394 0.3001219 0.06598675 26 1
12 1 0.8028694 0.2252500 19.70926 1.0617880 1.2995275 0.06142960 30 3
time shadow_id
69 57 69
9 45 9
26 60 26
60 65 60
12 50 12
xxIRT documentation built on May 1, 2019, 7:11 p.m.
R Package Documentation
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Description Usage Arguments Details Value Examples
Description
cat_sim runs a simulation of CAT. Use theta in options to set the starting
value of theta estimate.
cat_estimate_mle is the maximum likelihood estimation rule. Use
map_len to apply MAP to the first K items and use map_prior to set the
prior for MAP.
cat_estimate_eap is the expected a posteriori estimation rule,
using eap_mean and eap_sd option parameters as the prior
cat_estimate_hybrid is a hybrid estimation rule, which uses MLE for
mixed responses and EAP for all 1's or 0's responses
cat_stop_default is a three-way stopping rule. When stop_se
is set in the options, it uses the standard error stopping rule. When
stop_mi is set in the options, it uses the minimum information stopping rule. When
stop_cut is set in the options, it uses the confidence interval (set by ci_width)
stopping rule.
cat_select_maxinfo is the maximum information selection rule. Use group
(a numeric vector) to group items belonging to the same set. Use info_random to implement
the random-esque item exposure control method.
cat_select_ccat is the constrained CAT selection rule. Use
ccat_var to set the content variable in the pool. Use ccat_perc to set
the desired content distribution, with the name of each element being the content code
and tue value of each element being the percentage. Use ccat_random to add randomness
to initial item selections.
cat_select_shadow is the shadow-test selection rule. Use shadow_id
to group item sets. Use constraints to set constraints. Constraints should be in a data.frame
with four columns: var (variable name), level (variable level, NA for quantitative variable),
min (lower bound), and max (upper bound).
cat_stop_projection is the projection-based stopping rule. Use
projection_method to choose the projection method ('info' or 'diff'). Use
stop_cut to set the cut score. Use constraints to set the constraints.
Constraints should be a data.frame with columns: var (variable name),
level (variable level, NA for quantitative varialbe), min (lower bound), max (upper bound)
Usage
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 | cat_sim(true, pool, ...)
cat_estimate_mle(len, theta, stats, admin, pool, opts)
cat_estimate_eap(len, theta, stats, admin, pool, opts)
cat_estimate_hybrid(len, theta, stats, admin, pool, opts)
cat_stop_default(len, theta, stats, admin, pool, opts)
cat_select_maxinfo(len, theta, stats, admin, pool, opts)
cat_select_ccat(len, theta, stats, admin, pool, opts)
cat_select_shadow(len, theta, stats, admin, pool, opts)
## S3 method for class 'cat'
print(x, ...)
## S3 method for class 'cat'
plot(x, ...)
cat_stop_projection(len, theta, stats, admin, pool, opts)
|
Arguments
true |
the true theta |
pool |
the item pool (data.frame) |
... |
option/control parameters |
len |
the current test length |
theta |
the current theta estimate |
stats |
a matrix of responses, theta estimate, information and std error |
admin |
a data frame of administered items |
opts |
a list of option/control parameters |
x |
a |
Details
... takes a variety of option/control parameters for the simulations from users.
min and max are mandatory for setting limits on the test length. User-defined
selection, estimation, and stopping rules are also passed to the simulator via options.
To write a new rule, the function siganiture must be: function(len, theta, stats, admin, pool, opts).
See built-in rules for examples.
Value
cat_sim returns a cat object
an estimation rule should return a theta estimate
a stopping rule should return a boolean: TRUE to stop the CAT, FALSE to continue
a selection rule should return a list of (a) the selected item and (b) the updated pool
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 | ## Not run:
## generate a 100-item pool
num_items <- 100
pool <- with(model_3pl_gendata(1, num_items), data.frame(a=a, b=b, c=c))
pool$set_id <- sample(1:30, num_items, replace=TRUE)
pool$content <- sample(1:3, num_items, replace=TRUE)
pool$time <- round(rlnorm(num_items, mean=4.1, sd=.2))
## MLE, EAP, and hybrid estimation rule
cat_sim(1.0, pool, min=10, max=20, estimate_rule=cat_estimate_mle)
cat_sim(1.0, pool, min=10, max=20, estimate_rule=cat_estimate_eap)
cat_sim(1.0, pool, min=10, max=20, estimate_rule=cat_estimate_hybrid)
## SE, MI, and CI stopping rule
cat_sim(1.0, pool, min=10, max=20, stop_se=.3)
cat_sim(1.0, pool, min=10, max=20, stop_mi=.6)
cat_sim(1.0, pool, min=10, max=20, stop_cut=0)
cat_sim(1.0, pool, min=10, max=20, stop_cut=0, ci_width=2.58)
## maximum information selection with item sets
cat_sim(1.0, pool, min=10, max=20, group="set_id")$admin
## maximum information with item exposure control
cat_sim(1.0, pool, min=10, max=20, info_random=5)$admin
## Constrained-CAT selection rule with and without initial randomness
cat_sim(1.0, pool, min=10, max=20, select_rule=cat_select_ccat,
ccat_var="content", ccat_perc=c("1"=.2, "2"=.3, "3"=.5))
cat_sim(1.0, pool, min=10, max=20, select_rule=cat_select_ccat, ccat_random=5,
ccat_var="content", ccat_perc=c("1"=.2, "2"=.3, "3"=.5))
## Shadow-test selection rule
cons <- data.frame(var='content', level=1:3, min=c(3,3,4), max=c(3,3,4))
cons <- rbind(cons, data.frame(var='time', level=NA, min=55*10, max=65*10))
cat_sim(1.0, pool, min=10, max=10, select_rule=cat_select_shadow, constraints=cons)
## Projection-based stopping rule
cons <- data.frame(var='content', level=1:3, min=5, max=15)
cons <- rbind(cons, data.frame(var='time', level=NA, min=60*20, max=60*40))
cat_sim(1.0, pool, min=20, max=40, select_rule=cat_select_shadow, stop_rule=cat_stop_projection,
projection_method="diff", stop_cut=0, constraints=cons)
## End(Not run)
|
Example output
true=1, est.=-1.14, se=0.6, p=0.7, used 20 items (14 correct).
Belows is a history of the CAT:
u t se info a b c set_id content
16 1 0.4426329 0.9877031 1.025055 1.647223 -0.1127991 0.07791847 2 1
84 1 0.6805086 0.8062676 1.538302 1.520301 0.1124009 0.09169322 12 1
97 1 0.9755006 0.7620799 1.721865 1.242951 0.6639219 0.08318524 16 2
68 1 1.2613159 0.6804160 2.159986 1.379279 0.9840343 0.11069216 21 2
4 0 0.9934347 0.5234169 3.650097 1.177836 1.1098185 0.06028314 27 2
time
16 55
84 47
97 53
68 63
4 54
...
u t se info a b c set_id
88 1 1.201506 0.3270477 9.349273 1.1117415 -1.0828131 0.09423111 9
72 1 1.244813 0.3182385 9.874034 1.1315467 0.6303711 0.06165440 19
79 1 1.300769 0.3115292 10.303921 1.0262166 1.0183590 0.09599795 21
46 1 1.353064 0.3061940 10.666123 0.9831951 1.0324230 0.07288879 5
65 0 -1.135452 0.6022880 2.756713 0.9396877 1.2613025 0.04510026 23
content time
88 2 71
72 1 87
79 2 62
46 2 54
65 2 77
true=1, est.=1.1, se=0.27, p=0.7, used 20 items (14 correct).
Belows is a history of the CAT:
u t se info a b c set_id content
16 1 0.3348219 0.9038898 1.223965 1.647223 -0.1127991 0.07791847 2 1
84 1 0.5569632 0.7248393 1.903341 1.520301 0.1124009 0.09169322 12 1
58 1 0.6908327 0.6555447 2.326994 1.474747 0.1206311 0.13866093 24 2
97 1 0.8695649 0.6207522 2.595156 1.242951 0.6639219 0.08318524 16 2
68 1 1.0588729 0.5711914 3.065044 1.379279 0.9840343 0.11069216 21 2
time
16 55
84 47
58 54
97 53
68 63
...
u t se info a b c set_id content
91 0 0.9777102 0.2946393 11.51910 1.1165245 1.1804404 0.11090126 19 3
12 1 1.0555030 0.2892491 11.95242 1.0617880 1.2995275 0.06142960 30 3
79 1 1.1092831 0.2840470 12.39423 1.0262166 1.0183590 0.09599795 21 2
46 0 1.0455516 0.2750298 13.22027 0.9831951 1.0324230 0.07288879 5 2
34 1 1.0964218 0.2707877 13.63774 0.9318733 0.9552107 0.03165545 4 1
time
91 54
12 50
79 62
46 54
34 49
true=1, est.=0.97, se=0.27, p=0.65, used 20 items (13 correct).
Belows is a history of the CAT:
u t se info a b c set_id content
16 1 0.3348219 0.9038898 1.223965 1.647223 -0.1127991 0.07791847 2 1
84 1 0.5569632 0.7248393 1.903341 1.520301 0.1124009 0.09169322 12 1
58 1 0.6908327 0.6555447 2.326994 1.474747 0.1206311 0.13866093 24 2
97 1 0.8695649 0.6207522 2.595156 1.242951 0.6639219 0.08318524 16 2
68 0 0.7805161 0.5056140 3.911667 1.379279 0.9840343 0.11069216 21 2
time
16 55
84 47
58 54
97 53
68 63
...
u t se info a b c set_id content
3 1 0.8531523 0.2920034 11.72800 1.181367 0.2215912 0.11294698 16 3
90 0 0.8094693 0.2837103 12.42366 1.142360 1.3158429 0.07519694 19 1
32 1 0.8522734 0.2780630 12.93343 1.087356 0.6653296 0.18683932 6 3
91 1 0.9192257 0.2734011 13.37825 1.116525 1.1804404 0.11090126 19 3
79 1 0.9747746 0.2690344 13.81607 1.026217 1.0183590 0.09599795 21 2
time
3 85
90 65
32 48
91 54
79 62
true=1, est.=1.67, se=0.36, p=0.85, used 20 items (17 correct).
Belows is a history of the CAT:
u t se info a b c set_id content
16 1 0.4426335 0.9877036 1.025054 1.647223 -0.1127991 0.07791847 2 1
84 1 0.6805083 0.8062675 1.538302 1.520301 0.1124009 0.09169322 12 1
97 1 0.9755121 0.7620860 1.721837 1.242951 0.6639219 0.08318524 16 2
68 1 1.2613866 0.6804435 2.159812 1.379279 0.9840343 0.11069216 21 2
4 1 1.4725151 0.6390186 2.448911 1.177836 1.1098185 0.06028314 27 2
time
16 55
84 47
97 53
68 63
4 54
...
u t se info a b c set_id
12 1 0.9459471 0.3533338 8.009947 1.0617880 1.299528 0.06142960 30
100 0 1.5231581 0.3645384 7.525121 1.1921837 0.685593 0.06688831 8
91 1 -1.1391873 0.5304352 3.554146 1.1165245 1.180440 0.11090126 19
43 1 1.5925296 0.3570929 7.842193 1.0342464 -1.134937 0.06604005 12
64 1 1.6718846 0.3554301 7.915740 0.9562634 1.520666 0.08640765 16
content time
12 3 50
100 1 82
91 3 54
43 2 38
64 2 51
true=1, est.=1.38, se=0.34, p=0.71, used 14 items (10 correct).
Belows is a history of the CAT:
u t se info a b c set_id content
16 1 0.4426369 0.9877067 1.025048 1.647223 -0.1127991 0.07791847 2 1
84 1 0.6805093 0.8062682 1.538300 1.520301 0.1124009 0.09169322 12 1
97 1 0.9755031 0.7620812 1.721858 1.242951 0.6639219 0.08318524 16 2
68 1 1.2613418 0.6804261 2.159922 1.379279 0.9840343 0.11069216 21 2
4 0 0.9931541 0.5233805 3.650606 1.177836 1.1098185 0.06028314 27 2
time
16 55
84 47
97 53
68 63
4 54
...
u t se info a b c set_id content
90 0 1.293009 0.3803474 6.9125616 1.142360 1.315843 0.07519694 19 1
91 1 1.385538 0.3708402 7.2715395 1.116525 1.180440 0.11090126 19 3
86 0 1.291239 0.3462050 8.3432137 1.206985 1.605837 0.11229093 8 2
12 1 -1.089425 1.6559518 0.3646738 1.061788 1.299528 0.06142960 30 3
76 1 1.380243 0.3373238 8.7883212 1.221958 -1.232970 0.13173985 7 1
time
90 65
91 54
86 63
12 50
76 59
true=1, est.=0.96, se=0.36, p=0.6, used 10 items (6 correct).
Belows is a history of the CAT:
u t se info a b c set_id
16 1 0.4426352 0.9877051 1.025051 1.647223 -0.1127991 0.07791847 2
84 1 0.6804697 0.8062388 1.538412 1.520301 0.1124009 0.09169322 12
97 1 0.9755266 0.7620937 1.721802 1.242951 0.6639219 0.08318524 16
68 1 1.2613315 0.6804221 2.159948 1.379279 0.9840343 0.11069216 21
4 0 0.9930084 0.5233615 3.650870 1.177836 1.1098185 0.06028314 27
100 1 1.1156673 0.4891871 4.178786 1.192184 0.6855930 0.06688831 8
42 1 1.2472206 0.4672293 4.580785 1.177062 0.9932710 0.09220206 13
63 0 1.0884965 0.4110228 5.919269 1.157707 1.1728487 0.07111505 27
35 0 1.0020819 0.3828273 6.823297 1.129563 1.4192049 0.02998260 18
72 0 0.9634069 0.3621781 7.623519 1.131547 0.6303711 0.06165440 19
content time
16 1 55
84 1 47
97 2 53
68 2 63
4 2 54
100 1 82
42 3 40
63 2 66
35 2 59
72 1 87
true=1, est.=1.01, se=0.36, p=0.73, used 11 items (8 correct).
Belows is a history of the CAT:
u t se info a b c set_id
16 1 0.4426337 0.9877038 1.025054 1.647223 -0.1127991 0.07791847 2
84 1 0.6805086 0.8062677 1.538302 1.520301 0.1124009 0.09169322 12
97 1 0.9755329 0.7620970 1.721787 1.242951 0.6639219 0.08318524 16
68 0 0.7047374 0.5479643 3.330393 1.379279 0.9840343 0.11069216 21
100 0 0.5208525 0.4732689 4.464616 1.192184 0.6855930 0.06688831 8
content time
16 1 55
84 1 47
97 2 53
68 2 63
100 1 82
...
u t se info a b c set_id content
72 1 0.7267931 0.4155111 5.792081 1.131547 0.6303711 0.06165440 19 1
62 0 0.5881922 0.3796630 6.937506 1.177431 0.6006342 0.11736218 2 2
89 1 0.6758617 0.3656451 7.479635 1.070574 0.5227013 0.05030759 26 2
42 1 0.8864438 0.3643774 7.531773 1.177062 0.9932710 0.09220206 13 3
4 1 1.0148105 0.3573531 7.830778 1.177836 1.1098185 0.06028314 27 2
time
72 87
62 57
89 51
42 40
4 54
u t se info a b c set_id
16 1 0.8379098 0.8798470 1.291771 1.6472227 -0.1127991 0.07791847 2
22 1 0.8379098 0.8798470 1.291771 1.1240637 -1.0858426 0.17126860 2
62 1 0.8379098 0.8798470 1.291771 1.1774306 0.6006342 0.11736218 2
18 1 0.9478814 0.5794128 2.978679 0.9782049 -0.7510692 0.09872854 21
68 1 0.9478814 0.5794128 2.978679 1.3792794 0.9840343 0.11069216 21
79 0 0.9478814 0.5794128 2.978679 1.0262166 1.0183590 0.09599795 21
4 1 1.4699721 0.4855306 4.241962 1.1778356 1.1098185 0.06028314 27
31 0 1.4699721 0.4855306 4.241962 0.8258244 0.7247103 0.08054818 27
63 1 1.4699721 0.4855306 4.241962 1.1577075 1.1728487 0.07111505 27
70 1 1.4699721 0.4855306 4.241962 0.9295510 0.3291351 0.13729153 27
67 0 0.8811149 0.3615718 7.649111 0.5406633 0.8735232 0.10075373 19
72 1 0.8811149 0.3615718 7.649111 1.1315467 0.6303711 0.06165440 19
90 0 0.8811149 0.3615718 7.649111 1.1423597 1.3158429 0.07519694 19
91 1 0.8811149 0.3615718 7.649111 1.1165245 1.1804404 0.11090126 19
61 1 1.3152259 0.3416435 8.567490 1.0072735 -0.2159953 0.10729972 8
86 0 1.3152259 0.3416435 8.567490 1.2069851 1.6058366 0.11229093 8
100 1 1.3152259 0.3416435 8.567490 1.1921837 0.6855930 0.06688831 8
35 1 1.4256572 0.3324214 9.049448 1.1295634 1.4192049 0.02998260 18
55 1 1.4256572 0.3324214 9.049448 1.2685049 -0.2715816 0.12383102 18
9 1 1.4553831 0.3288616 9.246423 0.9284396 0.5313580 0.06706269 4
content time
16 1 55
22 2 65
62 2 57
18 3 69
68 2 63
79 2 62
4 2 54
31 3 82
63 2 66
70 2 100
67 2 75
72 1 87
90 1 65
91 3 54
61 1 57
86 2 63
100 1 82
35 2 59
55 3 69
9 1 45
u t se info a b c set_id
16 1 0.4426330 0.9877032 1.0250548 1.6472227 -0.1127991 0.07791847 2
66 1 0.6615793 0.8597255 1.3529457 1.3130091 0.1047014 0.16347949 13
68 1 1.0980190 0.7670965 1.6994173 1.3792794 0.9840343 0.11069216 21
4 1 1.3785026 0.6859924 2.1250117 1.1778356 1.1098185 0.06028314 27
35 0 1.1518251 0.5491330 3.3162318 1.1295634 1.4192049 0.02998260 18
97 0 0.8451730 0.4788708 4.3607704 1.2429510 0.6639219 0.08318524 16
63 1 1.0321975 0.4445087 5.0610364 1.1577075 1.1728487 0.07111505 27
90 0 0.9238942 0.4170137 5.7504182 1.1423597 1.3158429 0.07519694 19
5 1 1.0129720 0.3936848 6.4521251 1.0698240 0.7153680 0.08488474 1
91 0 1.0432413 0.3745155 7.1295216 1.1165245 1.1804404 0.11090126 19
42 1 1.1437538 0.3560560 7.8879364 1.1770617 0.9932710 0.09220206 13
72 0 0.9808761 0.3388500 8.7093376 1.1315467 0.6303711 0.06165440 19
100 1 1.0501685 0.3243901 9.5030872 1.1921837 0.6855930 0.06688831 8
12 0 -1.2345311 1.9913633 0.2521732 1.0617880 1.2995275 0.06142960 30
88 1 0.9844340 0.3122466 10.2566260 1.1117415 -1.0828131 0.09423111 9
62 1 1.0331499 0.3023120 10.9418122 1.1774306 0.6006342 0.11736218 2
34 0 0.9605468 0.2938485 11.5811880 0.9318733 0.9552107 0.03165545 4
79 1 -1.2419228 0.9969713 1.0060851 1.0262166 1.0183590 0.09599795 21
43 1 1.0248125 0.2859059 12.2335819 1.0342464 -1.1349366 0.06604005 12
32 1 1.0622919 0.2801971 12.7371659 1.0873561 0.6653296 0.18683932 6
content time
16 1 55
66 2 54
68 2 63
4 2 54
35 2 59
97 2 53
63 2 66
90 1 65
5 3 71
91 3 54
42 3 40
72 1 87
100 1 82
12 3 50
88 2 71
62 2 57
34 1 49
79 2 62
43 2 38
32 3 48
true=1, est.=1.05, se=0.29, p=0.7, used 20 items (14 correct).
Belows is a history of the CAT:
u t se info a b c set_id
57 1 0.5040863 1.1691155 0.7316193 1.167261 0.002072399 0.04331153 29
58 1 0.7310156 0.8620159 1.3457658 1.474747 0.120631055 0.13866093 24
100 0 0.4331946 0.6104376 2.6835979 1.192184 0.685593032 0.06688831 8
3 0 0.1747975 0.5334140 3.5145613 1.181367 0.221591152 0.11294698 16
66 1 0.3140523 0.4734955 4.4603434 1.313009 0.104701364 0.16347949 13
content time
57 3 55
58 2 54
100 1 82
3 3 85
66 2 54
...
u t se info a b c set_id
12 0 0.9799806 0.3090876 10.467354 1.0617880 1.2995275 0.06142960 30
90 0 0.9209035 0.2965109 11.374141 1.1423597 1.3158429 0.07519694 19
48 1 0.9681386 0.2928999 11.656320 0.8578328 0.7359015 0.07589904 23
63 1 -1.2381958 1.1874893 0.709154 1.1577075 1.1728487 0.07111505 27
78 1 1.0528209 0.2868480 12.153356 1.0071481 -1.0953267 0.10696292 10
content time
12 3 50
90 1 65
48 3 56
63 2 66
78 3 52
true=1, est.=0.97, se=0.29, p=0.7, used 20 items (14 correct).
Belows is a history of the CAT:
u t se info a b c set_id
58 1 0.5366631 1.0018460 0.9963182 1.474747 0.1206311 0.13866093 24
84 1 0.7425499 0.7970060 1.5742611 1.520301 0.1124009 0.09169322 12
100 1 1.0204902 0.7522947 1.7669489 1.192184 0.6855930 0.06688831 8
72 1 1.1968025 0.7055421 2.0088809 1.131547 0.6303711 0.06165440 19
42 0 0.9184875 0.5256979 3.6184911 1.177062 0.9932710 0.09220206 13
content time
58 2 54
84 1 47
100 1 82
72 1 87
42 3 40
...
u t se info a b c set_id
53 0 1.1351705 0.3280729 9.290934 0.8268489 1.1321856 0.09914609 29
90 1 1.2314651 0.3223473 9.623916 1.1423597 1.3158429 0.07519694 19
31 1 1.2723407 0.3196381 9.787752 0.8258244 0.7247103 0.08054818 27
35 1 1.3703120 0.3153380 10.056513 1.1295634 1.4192049 0.02998260 18
19 0 0.9667661 0.2888128 11.988559 0.7524507 1.4023626 0.03018560 25
content time
53 3 49
90 1 65
31 3 82
35 2 59
19 3 53
true=1, est.=1.12, se=0.38, p=0.9, used 10 items (9 correct).
Belows is a history of the CAT:
u t se info a b c set_id
16 1 0.4426345 0.9877045 1.025052 1.647223 -0.1127991 0.07791847 2
84 1 0.6805159 0.8062731 1.538281 1.520301 0.1124009 0.09169322 12
97 1 0.9755360 0.7620987 1.721780 1.242951 0.6639219 0.08318524 16
68 0 0.7047199 0.5479619 3.330422 1.379279 0.9840343 0.11069216 21
100 1 0.8726625 0.5053337 3.916007 1.192184 0.6855930 0.06688831 8
4 1 1.0632430 0.4810182 4.321922 1.177836 1.1098185 0.06028314 27
42 1 1.1947940 0.4581087 4.764999 1.177062 0.9932710 0.09220206 13
91 1 1.3164588 0.4451357 5.046789 1.116525 1.1804404 0.11090126 19
12 1 1.4394766 0.4364443 5.249795 1.061788 1.2995275 0.06142960 30
5 1 1.1190133 0.3767953 7.043509 1.069824 0.7153680 0.08488474 1
content time shadow_id
16 1 55 16
84 1 47 84
97 2 53 97
68 2 63 68
100 1 82 100
4 2 54 4
42 3 40 42
91 3 54 91
12 3 50 12
5 3 71 5
true=1, est.=0.8, se=0.23, p=0.61, used 31 items (19 correct).
Belows is a history of the CAT:
u t se info a b c set_id content
16 1 0.4426331 0.9877033 1.025055 1.647223 -0.1127991 0.07791847 2 1
84 1 0.6805084 0.8062676 1.538302 1.520301 0.1124009 0.09169322 12 1
97 1 0.9754977 0.7620784 1.721871 1.242951 0.6639219 0.08318524 16 2
68 1 1.2613385 0.6804248 2.159930 1.379279 0.9840343 0.11069216 21 2
4 0 0.9930425 0.5233660 3.650808 1.177836 1.1098185 0.06028314 27 2
time shadow_id
16 55 16
84 47 84
97 53 97
68 63 68
4 54 4
...
u t se info a b c set_id content
69 0 0.7378440 0.2376332 17.70866 0.9257078 0.6991092 0.06719960 25 2
9 1 0.7700116 0.2344324 18.19553 0.9284396 0.5313580 0.06706269 4 1
26 0 0.7241563 0.2306811 18.79212 0.9952935 0.7347191 0.15313704 5 1
60 1 0.7493239 0.2277126 19.28528 0.9543394 0.3001219 0.06598675 26 1
12 1 0.8028694 0.2252500 19.70926 1.0617880 1.2995275 0.06142960 30 3
time shadow_id
69 57 69
9 45 9
26 60 26
60 65 60
12 50 12
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