Results: recursion.sas

Binary repeated measures on Ana's recursion data

The Print Procedure

Data Set WORK.BINARY

Obs Participant AgeinMonths Agegroup Condition Item AllTargets
1 1 48.5 4yos A a1a 1
2 1 48.5 4yos A a1b 0
3 1 48.5 4yos A a2 0
4 1 48.5 4yos A a3 0
5 1 48.5 4yos A a4 0
6 1 48.5 4yos A a6 0
7 1 48.5 4yos B b1 1
8 1 48.5 4yos B b2 0
9 1 48.5 4yos B b3 1
10 1 48.5 4yos B b4 0

Binary repeated measures on Ana's recursion data

The FREQ Procedure

The Freq Procedure

Table Condition * Agegroup

Cross-Tabular Freq Table

Frequency
Table of Condition by Agegroup
Condition Agegroup
4yos 5yos 6yos Total
A
172
173
147
492
B
150
150
126
426
C
150
150
126
426
E
124
125
105
354
Total
596
598
504
1698

Table Condition * Item

Cross-Tabular Freq Table

Frequency
Table of Condition by Item
Condition Item
a1a a1b a2 a3 a4 a5 a6 b1 b2 b3 b4 b5 b6 c1 c2 c3 c4 c5 c6 e1 e2 e3 e4 e5 Total
A
71
71
71
70
71
69
69
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
492
B
0
0
0
0
0
0
0
71
71
71
71
71
71
0
0
0
0
0
0
0
0
0
0
0
426
C
0
0
0
0
0
0
0
0
0
0
0
0
0
71
71
71
71
71
71
0
0
0
0
0
426
E
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
71
71
70
71
71
354
Total
71
71
71
70
71
69
69
71
71
71
71
71
71
71
71
71
71
71
71
71
71
70
71
71
1698

Binary repeated measures on Ana's recursion data

Age in months

The UNIVARIATE Procedure

Variable: AgeinMonths

The Univariate Procedure

AgeinMonths

Moments

Moments
N 1698 Sum Weights 1698
Mean 64.6602473 Sum Observations 109793.1
Std Deviation 9.64985907 Variance 93.11978
Skewness 0.2886039 Kurtosis -1.1674136
Uncorrected SS 7257273.27 Corrected SS 158024.267
Coeff Variation 14.9239439 Std Error Mean 0.23418125

Basic Measures of Location and Variability

Basic Statistical Measures
Location Variability
Mean 64.66025 Std Deviation 9.64986
Median 63.00000 Variance 93.11978
Mode 75.00000 Range 34.50000
    Interquartile Range 19.00000

Tests For Location

Tests for Location: Mu0=0
Test Statistic p Value
Student's t t 276.112 Pr > |t| <.0001
Sign M 849 Pr >= |M| <.0001
Signed Rank S 721225.5 Pr >= |S| <.0001

Quantiles

Quantiles (Definition 5)
Level Quantile
100% Max 83.0
99% 83.0
95% 82.0
90% 78.0
75% Q3 75.0
50% Median 63.0
25% Q1 56.0
10% 53.0
5% 51.6
1% 48.5
0% Min 48.5

Extreme Observations

Extreme Observations
Lowest Highest
Value Obs Value Obs
48.5 22 83 1526
48.5 21 83 1527
48.5 20 83 1528
48.5 19 83 1529
48.5 18 83 1530

Plots for AgeinMonths

Plots for AgeinMonths

Binary repeated measures on Ana's recursion data

Check relationships with AllTargets (no tests)

The FREQ Procedure

The Freq Procedure

Table Condition * AllTargets

Cross-Tabular Freq Table

Frequency
Row Pct
Table of Condition by AllTargets
Condition AllTargets
0 1 Total
A
362
73.58
130
26.42
492
 
B
299
70.19
127
29.81
426
 
C
376
88.26
50
11.74
426
 
E
325
91.81
29
8.19
354
 
Total
1362
336
1698

Table Agegroup * AllTargets

Cross-Tabular Freq Table

Frequency
Row Pct
Table of Agegroup by AllTargets
Agegroup AllTargets
0 1 Total
4yos
523
87.75
73
12.25
596
 
5yos
511
85.45
87
14.55
598
 
6yos
328
65.08
176
34.92
504
 
Total
1362
336
1698

Binary repeated measures on Ana's recursion data

Logistic regression to get starting values for simple regression

The LOGISTIC Procedure

The Logistic Procedure

Model Information

Model Information
Data Set WORK.BINARY
Response Variable AllTargets
Number of Response Levels 2
Model binary logit
Optimization Technique Fisher's scoring

Observations Summary

Number of Observations Read 1698
Number of Observations Used 1698

Response Profile

Response Profile
Ordered
Value		 AllTargets Total
Frequency
1 0 1362
2 1 336

Probability modeled is AllTargets=1.

Convergence Status

Model Convergence Status
Convergence criterion (GCONV=1E-8) satisfied.

Fit Statistics

Model Fit Statistics
Criterion Intercept Only Intercept and Covariates
AIC 1691.337 1589.481
SC 1696.775 1600.356
-2 Log L 1689.337 1585.481

Global Tests

Testing Global Null Hypothesis: BETA=0
Test Chi-Square DF Pr > ChiSq
Likelihood Ratio 103.8562 1 <.0001
Score 104.1363 1 <.0001
Wald 97.4342 1 <.0001

Parameter Estimates

Analysis of Maximum Likelihood Estimates
Parameter DF Estimate Standard
Error		 Wald
Chi-Square		 Pr > ChiSq
Intercept 1 -5.7369 0.4551 158.8857 <.0001
AgeinMonths 1 0.0653 0.00661 97.4342 <.0001

Odds Ratios

Odds Ratio Estimates
Effect Point Estimate 95% Wald
Confidence Limits
AgeinMonths 1.067 1.054 1.081

Association Statistics

Association of Predicted Probabilities and Observed Responses
Percent Concordant 65.3 Somers' D 0.331
Percent Discordant 32.2 Gamma 0.339
Percent Tied 2.5 Tau-a 0.105
Pairs 457632 c 0.665

Binary repeated measures on Ana's recursion data

Simple regression

Compare R's beta0hat = -6.21336, beta1hat = 0.06973, sigmasqhat = 0.6957

The NLMIXED Procedure

The Nlmixed Procedure

Specifications

Specifications
Data Set WORK.BINARY
Dependent Variable AllTargets
Distribution for Dependent Variable Binomial
Random Effects delta
Distribution for Random Effects Normal
Subject Variable Participant
Optimization Technique Dual Quasi-Newton
Integration Method Adaptive Gaussian Quadrature

Dimensions

Dimensions
Observations Used 1698
Observations Not Used 0
Total Observations 1698
Subjects 71
Max Obs per Subject 24
Parameters 3
Quadrature Points 1

Initial Parameters

Initial Parameters
beta0 beta1 sigmasq Negative
Log
Likelihood
-5.7369 0.0653 0.1 778.066049

Iteration History

Iteration History
Iteration Calls Negative
Log
Likelihood		 Difference Maximum
Gradient		 Slope
1 7 777.9431 0.122936 96.9077 -2250.89
2 11 766.0488 11.8943 18.1128 -114.686
3 15 764.0484 2.000408 86.1433 -1.09400
4 19 763.8047 0.243714 57.7910 -0.23138
5 23 763.7870 0.017684 7.27956 -0.01159
6 25 763.7597 0.027273 81.3356 -0.00887
7 27 763.7190 0.040772 107.516 -0.02089
8 29 763.6676 0.051353 18.2072 -0.04599
9 32 763.6649 0.00267 0.91919 -0.00500
10 35 763.6649 0.000027 0.011884 -0.00005
11 38 763.6649 4.722E-9 0.000826 -9.28E-9

Convergence Status

NOTE: GCONV convergence criterion satisfied.

Fit Statistics

Fit Statistics
-2 Log Likelihood 1527.3
AIC (smaller is better) 1533.3
AICC (smaller is better) 1533.3
BIC (smaller is better) 1540.1

Parameter Estimates

Parameter Estimates
Parameter Estimate Standard
Error		 DF t Value Pr > |t| 95% Confidence Limits Gradient
beta0 -6.2224 0.8470 70 -7.35 <.0001 -7.9117 -4.5330 9.116E-6
beta1 0.06984 0.01264 70 5.52 <.0001 0.04463 0.09506 0.000826
sigmasq 0.6979 0.2064 70 3.38 0.0012 0.2861 1.1096 3.435E-6

Binary repeated measures on Ana's recursion data

Logistic regression to get starting values for AgeGroup by Condition

The LOGISTIC Procedure

The Logistic Procedure

Model Information

Model Information
Data Set WORK.BINARY
Response Variable AllTargets
Number of Response Levels 2
Model binary logit
Optimization Technique Fisher's scoring

Observations Summary

Number of Observations Read 1698
Number of Observations Used 1698

Response Profile

Response Profile
Ordered
Value		 AllTargets Total
Frequency
1 0 1362
2 1 336

Probability modeled is AllTargets=1.

Class Level Information

Class Level Information
Class Value Design Variables
Agegroup 4yos 1 0  
  5yos 0 1  
  6yos -1 -1  
Condition A 1 0 0
  B 0 1 0
  C 0 0 1
  E -1 -1 -1

Convergence Status

Model Convergence Status
Convergence criterion (GCONV=1E-8) satisfied.

Fit Statistics

Model Fit Statistics
Criterion Intercept Only Intercept and Covariates
AIC 1691.337 1512.211
SC 1696.775 1577.458
-2 Log L 1689.337 1488.211

Global Tests

Testing Global Null Hypothesis: BETA=0
Test Chi-Square DF Pr > ChiSq
Likelihood Ratio 201.1262 11 <.0001
Score 198.5416 11 <.0001
Wald 155.9628 11 <.0001

Joint Tests

Joint Tests
Effect DF Wald
Chi-Square		 Pr > ChiSq
Agegroup 2 89.3264 <.0001
Condition 3 76.8413 <.0001
Agegroup*Condition 6 3.7657 0.7084

Note:Under full-rank parameterizations, Type 3 effect tests are replaced by joint tests. The joint test for an effect is a test that all the parameters associated with that effect are zero. Such joint tests might not be equivalent to Type 3 effect tests under GLM parameterization.

Parameter Estimates

Analysis of Maximum Likelihood Estimates
Parameter     DF Estimate Standard
Error		 Wald
Chi-Square		 Pr > ChiSq
Intercept     1 -1.6958 0.0850 398.0943 <.0001
Agegroup 4yos   1 -0.5607 0.1287 18.9739 <.0001
Agegroup 5yos   1 -0.4127 0.1270 10.5544 0.0012
Condition A   1 0.6441 0.1139 31.9708 <.0001
Condition B   1 0.8237 0.1157 50.6883 <.0001
Condition C   1 -0.4319 0.1453 8.8324 0.0030
Agegroup*Condition 4yos A 1 0.0977 0.1699 0.3303 0.5655
Agegroup*Condition 4yos B 1 -0.0390 0.1734 0.0507 0.8218
Agegroup*Condition 4yos C 1 0.0493 0.2198 0.0503 0.8225
Agegroup*Condition 5yos A 1 0.0564 0.1673 0.1135 0.7362
Agegroup*Condition 5yos B 1 0.2039 0.1679 1.4757 0.2245
Agegroup*Condition 5yos C 1 0.00385 0.2154 0.0003 0.9857

Association Statistics

Association of Predicted Probabilities and Observed Responses
Percent Concordant 69.2 Somers' D 0.460
Percent Discordant 23.2 Gamma 0.498
Percent Tied 7.5 Tau-a 0.146
Pairs 457632 c 0.730

Binary repeated measures on Ana's recursion data

AgeGroup by Condition with proc nlmixed

The NLMIXED Procedure

The Nlmixed Procedure

Specifications

Specifications
Data Set WORK.BINARY
Dependent Variable AllTargets
Distribution for Dependent Variable Binomial
Random Effects delta
Distribution for Random Effects Normal
Subject Variable Participant
Optimization Technique Dual Quasi-Newton
Integration Method Adaptive Gaussian Quadrature

Dimensions

Dimensions
Observations Used 1698
Observations Not Used 0
Total Observations 1698
Subjects 71
Max Obs per Subject 24
Parameters 13
Quadrature Points 1

Initial Parameters

Initial Parameters
beta0 beta1 beta2 beta3 beta4 beta5 beta6 beta7 beta8 beta9 beta10 beta11 sigmasq Negative
Log
Likelihood
-1.6958 -0.5607 -0.4127 0.6441 0.8237 -0.4319 0.0977 -0.039 0.0493 0.0564 0.2039 0.00385 0.1 726.792596

Iteration History

Iteration History
Iteration Calls Negative
Log
Likelihood		 Difference Maximum
Gradient		 Slope
1 4 708.8397 17.95287 10.2061 -574.125
2 8 707.4989 1.340844 3.90691 -0.96790
3 10 707.0504 0.44845 4.41335 -1.28158
4 12 706.7853 0.265167 1.08760 -0.57720
5 14 706.7559 0.029321 0.56195 -0.04260
6 17 706.7465 0.009471 0.16520 -0.01552
7 20 706.7453 0.0012 0.050364 -0.00133
8 23 706.7452 0.000078 0.016639 -0.00010
9 26 706.7452 0.000013 0.007900 -0.00001
10 29 706.7452 3.736E-6 0.005499 -3.31E-6

Convergence Status

NOTE: GCONV convergence criterion satisfied.

Fit Statistics

Fit Statistics
-2 Log Likelihood 1413.5
AIC (smaller is better) 1439.5
AICC (smaller is better) 1439.7
BIC (smaller is better) 1468.9

Parameter Estimates

Parameter Estimates
Parameter Estimate Standard
Error		 DF t Value Pr > |t| 95% Confidence Limits Gradient
beta0 -1.9487 0.1520 70 -12.82 <.0001 -2.2519 -1.6456 -0.00042
beta1 -0.6511 0.2120 70 -3.07 0.0030 -1.0739 -0.2282 -0.00063
beta2 -0.4793 0.2098 70 -2.28 0.0254 -0.8977 -0.06090 -0.00550
beta3 0.7087 0.1201 70 5.90 <.0001 0.4691 0.9483 -0.00275
beta4 0.9084 0.1228 70 7.40 <.0001 0.6636 1.1532 0.003877
beta5 -0.4906 0.1507 70 -3.25 0.0018 -0.7912 -0.1900 0.004747
beta6 0.09970 0.1784 70 0.56 0.5780 -0.2561 0.4555 0.002672
beta7 -0.05771 0.1825 70 -0.32 0.7527 -0.4216 0.3062 -0.00372
beta8 0.06014 0.2271 70 0.26 0.7919 -0.3929 0.5132 -0.00048
beta9 0.05321 0.1755 70 0.30 0.7627 -0.2968 0.4032 0.003896
beta10 0.2157 0.1771 70 1.22 0.2273 -0.1375 0.5690 -0.00225
beta11 0.002760 0.2224 70 0.01 0.9901 -0.4409 0.4464 0.003456
sigmasq 0.8810 0.2485 70 3.55 0.0007 0.3854 1.3765 0.001684

Contrasts

Contrasts
Label Num DF Den DF F Value Pr > F
Age group 2 70 15.92 <.0001
Condition 3 70 28.22 <.0001
AgeGroup by Condition 6 70 0.60 0.7322

Binary repeated measures on Ana's recursion data

Logistic regression to get starting values for AgeinMonths, Condition

The LOGISTIC Procedure

The Logistic Procedure

Model Information

Model Information
Data Set WORK.BINARY
Response Variable AllTargets
Number of Response Levels 2
Model binary logit
Optimization Technique Fisher's scoring

Observations Summary

Number of Observations Read 1698
Number of Observations Used 1698

Response Profile

Response Profile
Ordered
Value		 AllTargets Total
Frequency
1 0 1362
2 1 336

Probability modeled is AllTargets=1.

Convergence Status

Model Convergence Status
Convergence criterion (GCONV=1E-8) satisfied.

Fit Statistics

Model Fit Statistics
Criterion Without Covariates With Covariates
AIC 2353.928 1496.155
SC 2353.928 1523.341
-2 Log L 2353.928 1486.155

Global Tests

Testing Global Null Hypothesis: BETA=0
Test Chi-Square DF Pr > ChiSq
Likelihood Ratio 867.7728 5 <.0001
Score 741.8310 5 <.0001
Wald 499.3629 5 <.0001

Parameter Estimates

Analysis of Maximum Likelihood Estimates
Parameter DF Estimate Standard
Error		 Wald
Chi-Square		 Pr > ChiSq
condA 1 -5.6202 0.4768 138.9288 <.0001
condB 1 -5.4298 0.4741 131.1965 <.0001
condC 1 -6.6776 0.5024 176.6865 <.0001
condE 1 -7.0959 0.5205 185.8658 <.0001
AgeinMonths 1 0.0695 0.00688 101.8612 <.0001

Odds Ratios

Odds Ratio Estimates
Effect Point Estimate 95% Wald
Confidence Limits
condA 0.004 0.001 0.009
condB 0.004 0.002 0.011
condC 0.001 <0.001 0.003
condE <0.001 <0.001 0.002
AgeinMonths 1.072 1.058 1.086

Association Statistics

Association of Predicted Probabilities and Observed Responses
Percent Concordant 73.3 Somers' D 0.471
Percent Discordant 26.2 Gamma 0.474
Percent Tied 0.6 Tau-a 0.150
Pairs 457632 c 0.735

Binary repeated measures on Ana's recursion data

Age in months and experimental Condition

The NLMIXED Procedure

The Nlmixed Procedure

Specifications

Specifications
Data Set WORK.BINARY
Dependent Variable AllTargets
Distribution for Dependent Variable Binomial
Random Effects delta
Distribution for Random Effects Normal
Subject Variable Participant
Optimization Technique Dual Quasi-Newton
Integration Method Adaptive Gaussian Quadrature

Dimensions

Dimensions
Observations Used 1698
Observations Not Used 0
Total Observations 1698
Subjects 71
Max Obs per Subject 24
Parameters 6
Quadrature Points 1

Initial Parameters

Initial Parameters
beta1 beta2 beta3 beta4 beta5 sigmasq Negative
Log
Likelihood
-5.6202 -5.4298 -6.6776 -7.0959 0.0695 0.1 727.227089

Iteration History

Iteration History
Iteration Calls Negative
Log
Likelihood		 Difference Maximum
Gradient		 Slope
1 7 727.1238 0.103303 108.136 -2013.76
2 9 716.3328 10.79098 41.6351 -169.878
3 13 710.1730 6.159804 86.7583 -4.37865
4 17 708.9531 1.219905 74.5786 -0.82824
5 21 708.8631 0.090018 33.1336 -0.09599
6 24 708.8525 0.010537 9.28567 -0.01088
7 26 708.8480 0.004562 41.9457 -0.00473
8 30 708.8383 0.00972 6.66443 -0.01190
9 34 708.7887 0.04957 90.8756 -0.00808
10 38 708.6419 0.146771 53.7906 -0.06617
11 41 708.6181 0.02381 19.3141 -0.02546
12 44 708.6165 0.001572 4.90603 -0.00145
13 47 708.6164 0.000186 0.44720 -0.00029
14 50 708.6163 2.453E-6 0.024056 -4.14E-6

Convergence Status

NOTE: GCONV convergence criterion satisfied.

Fit Statistics

Fit Statistics
-2 Log Likelihood 1417.2
AIC (smaller is better) 1429.2
AICC (smaller is better) 1429.3
BIC (smaller is better) 1442.8

Parameter Estimates

Parameter Estimates
Parameter Estimate Standard
Error		 DF t Value Pr > |t| 95% Confidence Limits Gradient
beta1 -6.2077 0.9232 70 -6.72 <.0001 -8.0490 -4.3664 0.000065
beta2 -5.9986 0.9212 70 -6.51 <.0001 -7.8357 -4.1614 0.000525
beta3 -7.3942 0.9412 70 -7.86 <.0001 -9.2714 -5.5170 -0.00016
beta4 -7.8483 0.9531 70 -8.23 <.0001 -9.7491 -5.9474 -0.00010
beta5 0.07587 0.01378 70 5.51 <.0001 0.04839 0.1034 0.024056
sigmasq 0.8552 0.2444 70 3.50 0.0008 0.3676 1.3427 -0.00004

Contrasts

Contrasts
Label Num DF Den DF F Value Pr > F
A vs B 1 70 1.62 0.2078
A vs C 1 70 35.36 <.0001
A vs E 1 70 47.80 <.0001
B vs C 1 70 47.26 <.0001
B vs E 1 70 59.20 <.0001
C vs E 1 70 3.03 0.0862

Additional Estimates

Additional Estimates
Label Estimate Standard
Error		 DF t Value Pr > |t| Alpha Lower Upper
P(Y=1|A,x=xbar) 0.2139 0.02780 70 7.69 <.0001 0.05 0.1584 0.2693
P(Y=1|B,x=xbar) 0.2511 0.03149 70 7.98 <.0001 0.05 0.1883 0.3139
P(Y=1|C,x=xbar) 0.07668 0.01471 70 5.21 <.0001 0.05 0.04735 0.1060
P(Y=1|E,x=xbar) 0.05010 0.01167 70 4.29 <.0001 0.05 0.02683 0.07337