CTT VS IRT Analysis

Case

• A rural subsample of 8445 w1 omen from the Bangladesh Fertility Survey of 1989 (Huqand Cleland, 1990).

• The dimension of interest is women’s mobility and social freedom.

• Described in: Bartholomew, D., Steel, F., Moustaki, I. and Galbraith, J. (2002) The Analysis and Interpretation of Multivariate Data for Social Scientists. London: Chapman and Hall.

• Data is available within R software package “ltm”

1PL - RASCH

library(ltm)

## Loading required package: MASS

## Loading required package: msm

## Loading required package: polycor

head(Mobility)

##   Item 1 Item 2 Item 3 Item 4 Item 5 Item 6 Item 7 Item 8
## 1      1      1      1      1      0      0      0      0
## 2      0      0      0      0      0      0      0      0
## 3      0      0      0      0      0      0      0      0
## 4      0      0      0      0      0      0      0      0
## 5      0      0      0      0      0      0      0      0
## 6      0      0      0      0      0      0      0      0

my1pl<-rasch(Mobility)
summary(my1pl)

## 
## Call:
## rasch(data = Mobility)
## 
## Model Summary:
##    log.Lik      AIC      BIC
##  -23416.48 46850.96 46914.33
## 
## Coefficients:
##                 value std.err   z.vals
## Dffclt.Item 1 -1.0101  0.0201 -50.1740
## Dffclt.Item 2  0.5562  0.0177  31.4822
## Dffclt.Item 3 -0.8258  0.0188 -43.8296
## Dffclt.Item 4  0.3877  0.0170  22.7803
## Dffclt.Item 5  1.8517  0.0300  61.8094
## Dffclt.Item 6  1.4935  0.0253  58.9716
## Dffclt.Item 7  2.0434  0.0330  61.9871
## Dffclt.Item 8  1.6861  0.0277  60.9246
## Dscrmn         2.4985  0.0353  70.7925
## 
## Integration:
## method: Gauss-Hermite
## quadrature points: 21 
## 
## Optimization:
## Convergence: 0 
## max(|grad|): 0.09 
## quasi-Newton: BFGS

#Now plot ICC and IIC for 1pl model.
plot(my1pl, type = "ICC")

plot(my1pl, type = "IIC", items=0)

2PL

my2pl <- ltm(Mobility ~ z1)
summary(my2pl)

## 
## Call:
## ltm(formula = Mobility ~ z1)
## 
## Model Summary:
##    log.Lik      AIC      BIC
##  -23141.71 46315.43 46428.09
## 
## Coefficients:
##                 value std.err   z.vals
## Dffclt.Item 1 -1.0836  0.0280 -38.7067
## Dffclt.Item 2  0.6314  0.0206  30.6227
## Dffclt.Item 3 -1.0249  0.0313 -32.7756
## Dffclt.Item 4  0.4003  0.0168  23.8700
## Dffclt.Item 5  1.6302  0.0290  56.3001
## Dffclt.Item 6  1.4018  0.0260  53.8161
## Dffclt.Item 7  1.6988  0.0323  52.6558
## Dffclt.Item 8  1.5846  0.0298  53.1201
## Dscrmn.Item 1  2.1087  0.0915  23.0466
## Dscrmn.Item 2  2.0580  0.0675  30.4949
## Dscrmn.Item 3  1.5086  0.0573  26.3384
## Dscrmn.Item 4  3.0100  0.1245  24.1866
## Dscrmn.Item 5  3.9761  0.2116  18.7936
## Dscrmn.Item 6  3.1384  0.1294  24.2557
## Dscrmn.Item 7  5.8162  0.4526  12.8517
## Dscrmn.Item 8  3.0220  0.1273  23.7312
## 
## Integration:
## method: Gauss-Hermite
## quadrature points: 21 
## 
## Optimization:
## Convergence: 0 
## max(|grad|): 0.17 
## quasi-Newton: BFGS

#Now plot ICC and IIC for 2pl model.
plot(my2pl, type = "ICC")

plot(my2pl, type = "IIC", items=0)

3PL

my3pl <- tpm(Mobility)
summary(my3pl)

## 
## Call:
## tpm(data = Mobility)
## 
## Model Summary:
##    log.Lik      AIC      BIC
##  -23079.63 46207.26 46376.25
## 
## Coefficients:
##                 value std.err   z.vals
## Gussng.Item 1  0.0003  0.0046   0.0738
## Gussng.Item 2  0.0000  0.0000   0.0011
## Gussng.Item 3  0.1703  0.0769   2.2148
## Gussng.Item 4  0.0144  0.0073   1.9735
## Gussng.Item 5  0.0010  0.0006   1.5186
## Gussng.Item 6  0.0109  0.0026   4.2529
## Gussng.Item 7  0.0000     NaN      NaN
## Gussng.Item 8  0.0098  0.0016   6.2617
## Dffclt.Item 1 -1.0535  0.0287 -36.7111
## Dffclt.Item 2  0.6417  0.0207  30.9792
## Dffclt.Item 3 -0.7342  0.1390  -5.2831
## Dffclt.Item 4  0.4311  0.0203  21.2520
## Dffclt.Item 5  1.6204  0.0274  59.2193
## Dffclt.Item 6  1.4032  0.0227  61.7952
## Dffclt.Item 7  1.7004  0.0301  56.5572
## Dffclt.Item 8  1.5396  0.0264  58.3250
## Dscrmn.Item 1  2.2874  0.1207  18.9563
## Dscrmn.Item 2  2.0446  0.0663  30.8468
## Dscrmn.Item 3  1.7552  0.1461  12.0163
## Dscrmn.Item 4  3.2317  0.1865  17.3307
## Dscrmn.Item 5  4.3157  0.2605  16.5653
## Dscrmn.Item 6  4.0670  0.3265  12.4575
## Dscrmn.Item 7  5.6933  0.3913  14.5495
## Dscrmn.Item 8  4.4889  0.3208  13.9927
## 
## Integration:
## method: Gauss-Hermite
## quadrature points: 21 
## 
## Optimization:
## Optimizer: optim (BFGS)
## Convergence: 0 
## max(|grad|): 0.16

#Now plot ICC and IIC for 3pl model.
plot(my3pl, type = "ICC")

plot(my3pl, type = "IIC", items=0)

Model Comparison

1PL vs 2 PL

anova(my1pl, my2pl)

## 
##  Likelihood Ratio Table
##            AIC      BIC   log.Lik    LRT df p.value
## my1pl 46850.96 46914.33 -23416.48                  
## my2pl 46315.43 46428.09 -23141.71 549.53  7  <0.001

#(the smaller the better!)

2PL vs 3 PL

anova(my2pl, my3pl)

## 
##  Likelihood Ratio Table
##            AIC      BIC   log.Lik    LRT df p.value
## my2pl 46315.43 46428.09 -23141.71                  
## my3pl 46207.26 46376.25 -23079.63 124.17  8  <0.001

3PL the smaller and better model

IRT vs CTT scoring

resp<-matrix(c(1,1,1,1,0,1,0,1), nrow=1)
factor.scores(my2pl, method="EAP", resp.patterns=resp)

## 
## Call:
## ltm(formula = Mobility ~ z1)
## 
## Scoring Method: Expected A Posteriori
## 
## Factor-Scores for specified response patterns:
##     Item 1 Item 2 Item 3 Item 4 Item 5 Item 6 Item 7 Item 8 Obs    Exp
## Exp      1      1      1      1      0      1      0      1  43 77.367
##        z1 se.z1
## Exp 1.361 0.204

#EXPLAIN: “$” addressing
#theta = dataCAT$score.dat$z1
#sem = dataCAT$score.dat$se.z1

mobIRT <- factor.scores(my3pl, resp.patterns=Mobility, method="EAP")

#Compare IRT and CTT scores

CTT_scores <- rowSums(Mobility)
IRT_scores <- mobIRT$score.dat$z1
plot(IRT_scores, CTT_scores)

#Plot the standard error and scores
IRT_errors <- mobIRT$score.dat$se.z1
plot(IRT_scores, IRT_errors, type="p")

Comparison IRT 3PL Vs CTT Score Table

IRT.score.3pl<- factor.scores(my3pl, resp.patterns=Mobility, method="EAP")
theta3.pl<- IRT.score.3pl$score.dat$z1


Mobility$score <- rowSums(Mobility[,1:8])
mydf <- data.frame(Mobility, theta = theta3.pl)
mydf1<- mydf[order(mydf$score,mydf$theta),]

options(digits = 3)
knitr::kable(subset(mydf1, subset = mydf1$score == 7), 
             caption = 'There are several different patterns all with a score of 7')

There are several different patterns all with a score of 7

	Item.1	Item.2	Item.3	Item.4	Item.5	Item.6	Item.7	Item.8	score	theta
91	1	1	1	1	1	1	0	1	7	1.72
145	1	1	1	1	1	1	0	1	7	1.72
477	1	1	1	1	1	1	0	1	7	1.72
482	1	1	1	1	1	1	0	1	7	1.72
645	1	1	1	1	1	1	0	1	7	1.72
676	1	1	1	1	1	1	0	1	7	1.72
980	1	1	1	1	1	1	0	1	7	1.72
1346	1	1	1	1	1	1	0	1	7	1.72
2119	1	1	1	1	1	1	0	1	7	1.72
2130	1	1	1	1	1	1	0	1	7	1.72
2195	1	1	1	1	1	1	0	1	7	1.72
2246	1	1	1	1	1	1	0	1	7	1.72
2292	1	1	1	1	1	1	0	1	7	1.72
2345	1	1	1	1	1	1	0	1	7	1.72
2613	1	1	1	1	1	1	0	1	7	1.72
2618	1	1	1	1	1	1	0	1	7	1.72
2625	1	1	1	1	1	1	0	1	7	1.72
2656	1	1	1	1	1	1	0	1	7	1.72
2754	1	1	1	1	1	1	0	1	7	1.72
2916	1	1	1	1	1	1	0	1	7	1.72
2953	1	1	1	1	1	1	0	1	7	1.72
3011	1	1	1	1	1	1	0	1	7	1.72
3043	1	1	1	1	1	1	0	1	7	1.72
3211	1	1	1	1	1	1	0	1	7	1.72
3400	1	1	1	1	1	1	0	1	7	1.72
3538	1	1	1	1	1	1	0	1	7	1.72
3770	1	1	1	1	1	1	0	1	7	1.72
3935	1	1	1	1	1	1	0	1	7	1.72
5078	1	1	1	1	1	1	0	1	7	1.72
5149	1	1	1	1	1	1	0	1	7	1.72
5151	1	1	1	1	1	1	0	1	7	1.72
5173	1	1	1	1	1	1	0	1	7	1.72
5418	1	1	1	1	1	1	0	1	7	1.72
5828	1	1	1	1	1	1	0	1	7	1.72
5902	1	1	1	1	1	1	0	1	7	1.72
6302	1	1	1	1	1	1	0	1	7	1.72
6336	1	1	1	1	1	1	0	1	7	1.72
6340	1	1	1	1	1	1	0	1	7	1.72
6346	1	1	1	1	1	1	0	1	7	1.72
6456	1	1	1	1	1	1	0	1	7	1.72
6516	1	1	1	1	1	1	0	1	7	1.72
6664	1	1	1	1	1	1	0	1	7	1.72
6797	1	1	1	1	1	1	0	1	7	1.72
7051	1	1	1	1	1	1	0	1	7	1.72
7159	1	1	1	1	1	1	0	1	7	1.72
7205	1	1	1	1	1	1	0	1	7	1.72
7591	1	1	1	1	1	1	0	1	7	1.72
7602	1	1	1	1	1	1	0	1	7	1.72
7954	1	1	1	1	1	1	0	1	7	1.72
8001	1	1	1	1	1	1	0	1	7	1.72
8087	1	1	1	1	1	1	0	1	7	1.72
8330	1	1	1	1	1	1	0	1	7	1.72
448	1	1	1	1	1	1	1	0	7	1.86
2719	1	1	1	1	1	1	1	0	7	1.86
2731	1	1	1	1	1	1	1	0	7	1.86
2928	1	1	1	1	1	1	1	0	7	1.86
3544	1	1	1	1	1	1	1	0	7	1.86
4543	1	1	1	1	1	1	1	0	7	1.86
5076	1	1	1	1	1	1	1	0	7	1.86
5077	1	1	1	1	1	1	1	0	7	1.86
5596	1	1	1	1	1	1	1	0	7	1.86
6492	1	1	1	1	1	1	1	0	7	1.86
6735	1	1	1	1	1	1	1	0	7	1.86
6784	1	1	1	1	1	1	1	0	7	1.86
6827	1	1	1	1	1	1	1	0	7	1.86
7163	1	1	1	1	1	1	1	0	7	1.86
7766	1	1	1	1	1	1	1	0	7	1.86
7790	1	1	1	1	1	1	1	0	7	1.86
7927	1	1	1	1	1	1	1	0	7	1.86
7962	1	1	1	1	1	1	1	0	7	1.86
7975	1	1	1	1	1	1	1	0	7	1.86
7984	1	1	1	1	1	1	1	0	7	1.86
7992	1	1	1	1	1	1	1	0	7	1.86
8002	1	1	1	1	1	1	1	0	7	1.86
8106	1	1	1	1	1	1	1	0	7	1.86
8299	1	1	1	1	1	1	1	0	7	1.86
8362	1	1	1	1	1	1	1	0	7	1.86
8363	1	1	1	1	1	1	1	0	7	1.86
8365	1	1	1	1	1	1	1	0	7	1.86
8417	1	1	1	1	1	1	1	0	7	1.86
106	1	1	1	1	0	1	1	1	7	1.88
669	1	1	1	1	0	1	1	1	7	1.88
1018	1	1	1	1	0	1	1	1	7	1.88
1741	1	1	1	1	0	1	1	1	7	1.88
2099	1	1	1	1	0	1	1	1	7	1.88
2361	1	1	1	1	0	1	1	1	7	1.88
2878	1	1	1	1	0	1	1	1	7	1.88
3021	1	1	1	1	0	1	1	1	7	1.88
3057	1	1	1	1	0	1	1	1	7	1.88
3086	1	1	1	1	0	1	1	1	7	1.88
3118	1	1	1	1	0	1	1	1	7	1.88
3154	1	1	1	1	0	1	1	1	7	1.88
3170	1	1	1	1	0	1	1	1	7	1.88
3183	1	1	1	1	0	1	1	1	7	1.88
3206	1	1	1	1	0	1	1	1	7	1.88
3529	1	1	1	1	0	1	1	1	7	1.88
3547	1	1	1	1	0	1	1	1	7	1.88
4337	1	1	1	1	0	1	1	1	7	1.88
4408	1	1	1	1	0	1	1	1	7	1.88
4419	1	1	1	1	0	1	1	1	7	1.88
4626	1	1	1	1	0	1	1	1	7	1.88
4747	1	1	1	1	0	1	1	1	7	1.88
4935	1	1	1	1	0	1	1	1	7	1.88
5229	1	1	1	1	0	1	1	1	7	1.88
5230	1	1	1	1	0	1	1	1	7	1.88
5693	1	1	1	1	0	1	1	1	7	1.88
6770	1	1	1	1	0	1	1	1	7	1.88
6787	1	1	1	1	0	1	1	1	7	1.88
7021	1	1	1	1	0	1	1	1	7	1.88
7588	1	1	1	1	0	1	1	1	7	1.88
7624	1	1	1	1	0	1	1	1	7	1.88
7633	1	1	1	1	0	1	1	1	7	1.88
7645	1	1	1	1	0	1	1	1	7	1.88
7650	1	1	1	1	0	1	1	1	7	1.88
7666	1	1	1	1	0	1	1	1	7	1.88
7675	1	1	1	1	0	1	1	1	7	1.88
2169	1	1	1	1	1	0	1	1	7	1.90
2176	1	1	1	1	1	0	1	1	7	1.90
2527	1	1	1	1	1	0	1	1	7	1.90
3082	1	1	1	1	1	0	1	1	7	1.90
6218	1	1	1	1	1	0	1	1	7	1.90
6306	1	1	1	1	1	0	1	1	7	1.90
6319	1	1	1	1	1	0	1	1	7	1.90
6771	1	1	1	1	1	0	1	1	7	1.90
7513	1	1	1	1	1	0	1	1	7	1.90
97	1	0	1	1	1	1	1	1	7	2.05
150	1	0	1	1	1	1	1	1	7	2.05
512	1	0	1	1	1	1	1	1	7	2.05
1978	1	0	1	1	1	1	1	1	7	2.05
2341	1	0	1	1	1	1	1	1	7	2.05
3779	1	0	1	1	1	1	1	1	7	2.05
4398	1	0	1	1	1	1	1	1	7	2.05
4418	1	0	1	1	1	1	1	1	7	2.05
4704	1	0	1	1	1	1	1	1	7	2.05
4731	1	0	1	1	1	1	1	1	7	2.05
5809	1	0	1	1	1	1	1	1	7	2.05
6536	1	0	1	1	1	1	1	1	7	2.05
6629	1	0	1	1	1	1	1	1	7	2.05
6841	1	0	1	1	1	1	1	1	7	2.05
6842	1	0	1	1	1	1	1	1	7	2.05
6844	1	0	1	1	1	1	1	1	7	2.05
7167	1	0	1	1	1	1	1	1	7	2.05
8098	1	0	1	1	1	1	1	1	7	2.05

Comparison IRT 1PL Vs CTT Score Table

data<-Mobility[,1:8]
IRT.score.1pl<- factor.scores(my1pl, resp.patterns=data, method="EAP")
theta1.pl<- IRT.score.1pl$score.dat$z1


Mobility$score <- rowSums(Mobility[,1:8])
mydf <- data.frame(Mobility, theta = theta1.pl)
mydf2<- mydf[order(mydf$score,mydf$theta),]

options(digits = 3)
knitr::kable(subset(mydf2, subset = mydf2$score == 7), 
             caption = 'There are several different patterns all with a score of 7')

There are several different patterns all with a score of 7

	Item.1	Item.2	Item.3	Item.4	Item.5	Item.6	Item.7	Item.8	score	theta
91	1	1	1	1	1	1	0	1	7	1.94
145	1	1	1	1	1	1	0	1	7	1.94
477	1	1	1	1	1	1	0	1	7	1.94
482	1	1	1	1	1	1	0	1	7	1.94
645	1	1	1	1	1	1	0	1	7	1.94
676	1	1	1	1	1	1	0	1	7	1.94
980	1	1	1	1	1	1	0	1	7	1.94
1346	1	1	1	1	1	1	0	1	7	1.94
2119	1	1	1	1	1	1	0	1	7	1.94
2130	1	1	1	1	1	1	0	1	7	1.94
2195	1	1	1	1	1	1	0	1	7	1.94
2246	1	1	1	1	1	1	0	1	7	1.94
2292	1	1	1	1	1	1	0	1	7	1.94
2345	1	1	1	1	1	1	0	1	7	1.94
2613	1	1	1	1	1	1	0	1	7	1.94
2618	1	1	1	1	1	1	0	1	7	1.94
2625	1	1	1	1	1	1	0	1	7	1.94
2656	1	1	1	1	1	1	0	1	7	1.94
2754	1	1	1	1	1	1	0	1	7	1.94
2916	1	1	1	1	1	1	0	1	7	1.94
2953	1	1	1	1	1	1	0	1	7	1.94
3011	1	1	1	1	1	1	0	1	7	1.94
3043	1	1	1	1	1	1	0	1	7	1.94
3211	1	1	1	1	1	1	0	1	7	1.94
3400	1	1	1	1	1	1	0	1	7	1.94
3538	1	1	1	1	1	1	0	1	7	1.94
3770	1	1	1	1	1	1	0	1	7	1.94
3935	1	1	1	1	1	1	0	1	7	1.94
5078	1	1	1	1	1	1	0	1	7	1.94
5149	1	1	1	1	1	1	0	1	7	1.94
5151	1	1	1	1	1	1	0	1	7	1.94
5173	1	1	1	1	1	1	0	1	7	1.94
5418	1	1	1	1	1	1	0	1	7	1.94
5828	1	1	1	1	1	1	0	1	7	1.94
5902	1	1	1	1	1	1	0	1	7	1.94
6302	1	1	1	1	1	1	0	1	7	1.94
6336	1	1	1	1	1	1	0	1	7	1.94
6340	1	1	1	1	1	1	0	1	7	1.94
6346	1	1	1	1	1	1	0	1	7	1.94
6456	1	1	1	1	1	1	0	1	7	1.94
6516	1	1	1	1	1	1	0	1	7	1.94
6664	1	1	1	1	1	1	0	1	7	1.94
6797	1	1	1	1	1	1	0	1	7	1.94
7051	1	1	1	1	1	1	0	1	7	1.94
7159	1	1	1	1	1	1	0	1	7	1.94
7205	1	1	1	1	1	1	0	1	7	1.94
7591	1	1	1	1	1	1	0	1	7	1.94
7602	1	1	1	1	1	1	0	1	7	1.94
7954	1	1	1	1	1	1	0	1	7	1.94
8001	1	1	1	1	1	1	0	1	7	1.94
8087	1	1	1	1	1	1	0	1	7	1.94
8330	1	1	1	1	1	1	0	1	7	1.94
448	1	1	1	1	1	1	1	0	7	1.94
2719	1	1	1	1	1	1	1	0	7	1.94
2731	1	1	1	1	1	1	1	0	7	1.94
2928	1	1	1	1	1	1	1	0	7	1.94
3544	1	1	1	1	1	1	1	0	7	1.94
4543	1	1	1	1	1	1	1	0	7	1.94
5076	1	1	1	1	1	1	1	0	7	1.94
5077	1	1	1	1	1	1	1	0	7	1.94
5596	1	1	1	1	1	1	1	0	7	1.94
6492	1	1	1	1	1	1	1	0	7	1.94
6735	1	1	1	1	1	1	1	0	7	1.94
6784	1	1	1	1	1	1	1	0	7	1.94
6827	1	1	1	1	1	1	1	0	7	1.94
7163	1	1	1	1	1	1	1	0	7	1.94
7766	1	1	1	1	1	1	1	0	7	1.94
7790	1	1	1	1	1	1	1	0	7	1.94
7927	1	1	1	1	1	1	1	0	7	1.94
7962	1	1	1	1	1	1	1	0	7	1.94
7975	1	1	1	1	1	1	1	0	7	1.94
7984	1	1	1	1	1	1	1	0	7	1.94
7992	1	1	1	1	1	1	1	0	7	1.94
8002	1	1	1	1	1	1	1	0	7	1.94
8106	1	1	1	1	1	1	1	0	7	1.94
8299	1	1	1	1	1	1	1	0	7	1.94
8362	1	1	1	1	1	1	1	0	7	1.94
8363	1	1	1	1	1	1	1	0	7	1.94
8365	1	1	1	1	1	1	1	0	7	1.94
8417	1	1	1	1	1	1	1	0	7	1.94
106	1	1	1	1	0	1	1	1	7	1.94
669	1	1	1	1	0	1	1	1	7	1.94
1018	1	1	1	1	0	1	1	1	7	1.94
1741	1	1	1	1	0	1	1	1	7	1.94
2099	1	1	1	1	0	1	1	1	7	1.94
2169	1	1	1	1	1	0	1	1	7	1.94
2176	1	1	1	1	1	0	1	1	7	1.94
2361	1	1	1	1	0	1	1	1	7	1.94
2527	1	1	1	1	1	0	1	1	7	1.94
2878	1	1	1	1	0	1	1	1	7	1.94
3021	1	1	1	1	0	1	1	1	7	1.94
3057	1	1	1	1	0	1	1	1	7	1.94
3082	1	1	1	1	1	0	1	1	7	1.94
3086	1	1	1	1	0	1	1	1	7	1.94
3118	1	1	1	1	0	1	1	1	7	1.94
3154	1	1	1	1	0	1	1	1	7	1.94
3170	1	1	1	1	0	1	1	1	7	1.94
3183	1	1	1	1	0	1	1	1	7	1.94
3206	1	1	1	1	0	1	1	1	7	1.94
3529	1	1	1	1	0	1	1	1	7	1.94
3547	1	1	1	1	0	1	1	1	7	1.94
4337	1	1	1	1	0	1	1	1	7	1.94
4408	1	1	1	1	0	1	1	1	7	1.94
4419	1	1	1	1	0	1	1	1	7	1.94
4626	1	1	1	1	0	1	1	1	7	1.94
4747	1	1	1	1	0	1	1	1	7	1.94
4935	1	1	1	1	0	1	1	1	7	1.94
5229	1	1	1	1	0	1	1	1	7	1.94
5230	1	1	1	1	0	1	1	1	7	1.94
5693	1	1	1	1	0	1	1	1	7	1.94
6218	1	1	1	1	1	0	1	1	7	1.94
6306	1	1	1	1	1	0	1	1	7	1.94
6319	1	1	1	1	1	0	1	1	7	1.94
6770	1	1	1	1	0	1	1	1	7	1.94
6771	1	1	1	1	1	0	1	1	7	1.94
6787	1	1	1	1	0	1	1	1	7	1.94
7021	1	1	1	1	0	1	1	1	7	1.94
7513	1	1	1	1	1	0	1	1	7	1.94
7588	1	1	1	1	0	1	1	1	7	1.94
7624	1	1	1	1	0	1	1	1	7	1.94
7633	1	1	1	1	0	1	1	1	7	1.94
7645	1	1	1	1	0	1	1	1	7	1.94
7650	1	1	1	1	0	1	1	1	7	1.94
7666	1	1	1	1	0	1	1	1	7	1.94
7675	1	1	1	1	0	1	1	1	7	1.94
97	1	0	1	1	1	1	1	1	7	1.94
150	1	0	1	1	1	1	1	1	7	1.94
512	1	0	1	1	1	1	1	1	7	1.94
1978	1	0	1	1	1	1	1	1	7	1.94
2341	1	0	1	1	1	1	1	1	7	1.94
3779	1	0	1	1	1	1	1	1	7	1.94
4398	1	0	1	1	1	1	1	1	7	1.94
4418	1	0	1	1	1	1	1	1	7	1.94
4704	1	0	1	1	1	1	1	1	7	1.94
4731	1	0	1	1	1	1	1	1	7	1.94
5809	1	0	1	1	1	1	1	1	7	1.94
6536	1	0	1	1	1	1	1	1	7	1.94
6629	1	0	1	1	1	1	1	1	7	1.94
6841	1	0	1	1	1	1	1	1	7	1.94
6842	1	0	1	1	1	1	1	1	7	1.94
6844	1	0	1	1	1	1	1	1	7	1.94
7167	1	0	1	1	1	1	1	1	7	1.94
8098	1	0	1	1	1	1	1	1	7	1.94