Mixed Model Representation of Semiparametric Regression Model for Log Progesterone Concentration
Study of Log Progesterone Concentration during Menstrual Cycle

The Mixed Procedure

Model Information
Data Set WORK.PROGEST
Dependent Variable logp
Covariance Structures Banded Toeplitz, Unstructured
Subject Effect id
Estimation Method REML
Residual Variance Method Profile
Fixed Effects SE Method Model-Based
Degrees of Freedom Method Containment

Class Level Information
Class Levels Values
id 51 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 44 45 46 47 48 49 50 51

Dimensions
Covariance Parameters 5
Columns in X 5
Columns in Z Per Subject 124
Subjects 1
Max Obs Per Subject 1130

Number of Observations
Number of Observations Read 1130
Number of Observations Used 1130
Number of Observations Not Used 0

Iteration History
Iteration Evaluations -2 Res Log Like Criterion
0 1 3434.83210122  
1 2 2148.14618226 0.25510723
2 1 2134.76877669 0.16620033
3 1 2127.46081475 0.10221531
4 1 2123.49141634 0.05183805
5 1 2121.65668708 0.01843609
6 1 2121.05366158 0.00333365
7 1 2120.95388858 0.00014834
8 1 2120.94980929 0.00000035
9 1 2120.94979998 0.00000000

Convergence criteria met.

Covariance Parameter Estimates
Cov Parm Subject Estimate
Variance   0.01620
UN(1,1) id 0.6576
UN(2,1) id 0.003838
UN(2,2) id 0.001040
Residual   0.2861

Fit Statistics
-2 Res Log Likelihood 2120.9
AIC (smaller is better) 2130.9
AICC (smaller is better) 2131.0
BIC (smaller is better) 2120.9

Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
4 1313.88 <.0001

Solution for Fixed Effects
Effect Estimate Standard Error DF t Value Pr > |t|
Intercept -0.8102 0.5713 49 -1.42 0.1625
time 0.01654 0.07523 49 0.22 0.8269
group 0.1626 0.2323 1005 0.70 0.4841
time*group -0.04789 0.01193 1005 -4.02 <.0001
group*bf15 0.2962 0.02324 1005 12.74 <.0001

Solution for Random Effects
Effect id Estimate Std Err Pred DF t Value Pr > |t|
bf1   -0.01880 0.09859 1005 -0.19 0.8488
bf2   -0.04152 0.08888 1005 -0.47 0.6405
bf3   0.01522 0.08840 1005 0.17 0.8634
bf4   0.02093 0.08837 1005 0.24 0.8128
bf5   0.1021 0.08857 1005 1.15 0.2491
bf6   0.01119 0.08857 1005 0.13 0.8995
bf7   0.07304 0.08817 1005 0.83 0.4077
bf8   0.1205 0.08858 1005 1.36 0.1742
bf9   0.1345 0.08901 1005 1.51 0.1310
bf10   0.08574 0.08835 1005 0.97 0.3320
bf11   -0.1223 0.08835 1005 -1.38 0.1667
bf12   -0.05969 0.08835 1005 -0.68 0.4994
bf13   -0.1861 0.08837 1005 -2.11 0.0355
bf14   -0.1399 0.08886 1005 -1.57 0.1157
bf15   -0.1365 0.08920 1005 -1.53 0.1264
bf16   -0.07127 0.08910 1005 -0.80 0.4239
bf17   0.08151 0.08889 1005 0.92 0.3593
bf18   0.04012 0.08850 1005 0.45 0.6504
bf19   -0.04219 0.08930 1005 -0.47 0.6368
bf20   -0.01596 0.08959 1005 -0.18 0.8587
bf21   -0.05959 0.09211 1005 -0.65 0.5178
bf22   -0.09459 0.1048 1005 -0.90 0.3668
Intercept 1 1.0426 0.1903 1005 5.48 <.0001
time 1 0.04801 0.01518 1005 3.16 0.0016
Intercept 2 0.06322 0.1907 1005 0.33 0.7404
time 2 0.003916 0.01648 1005 0.24 0.8122
Intercept 3 0.4822 0.1912 1005 2.52 0.0118
time 3 -0.00208 0.01725 1005 -0.12 0.9041
Intercept 4 0.05331 0.1996 1005 0.27 0.7895
time 4 0.02519 0.01563 1005 1.61 0.1074
Intercept 5 0.3447 0.1950 1005 1.77 0.0774
time 5 0.007210 0.01820 1005 0.40 0.6920
Intercept 6 -0.1756 0.1930 1005 -0.91 0.3633
time 6 -0.00113 0.01666 1005 -0.07 0.9462
Intercept 7 -0.7735 0.1912 1005 -4.05 <.0001
time 7 -0.01725 0.01725 1005 -1.00 0.3175
Intercept 8 -1.5469 0.1940 1005 -7.97 <.0001
time 8 0.01814 0.01646 1005 1.10 0.2708
Intercept 9 0.3440 0.1907 1005 1.80 0.0715
time 9 -0.00340 0.01648 1005 -0.21 0.8367
Intercept 10 -0.5586 0.1905 1005 -2.93 0.0034
time 10 -0.05183 0.01579 1005 -3.28 0.0011
Intercept 11 0.7918 0.2001 1005 3.96 <.0001
time 11 0.02941 0.01912 1005 1.54 0.1243
Intercept 12 -0.09611 0.1907 1005 -0.50 0.6144
time 12 -0.00611 0.01648 1005 -0.37 0.7108
Intercept 13 1.5906 0.1917 1005 8.30 <.0001
time 13 0.02762 0.01661 1005 1.66 0.0967
Intercept 14 1.2569 0.1937 1005 6.49 <.0001
time 14 0.04628 0.01633 1005 2.83 0.0047
Intercept 15 -0.8487 0.2548 1005 -3.33 0.0009
time 15 -0.04028 0.02930 1005 -1.37 0.1695
Intercept 16 0.4618 0.1903 1005 2.43 0.0154
time 16 -0.02515 0.01518 1005 -1.66 0.0978
Intercept 17 1.2655 0.1940 1005 6.52 <.0001
time 17 -0.02060 0.01646 1005 -1.25 0.2111
Intercept 18 -0.06118 0.1912 1005 -0.32 0.7490
time 18 0.02727 0.01725 1005 1.58 0.1142
Intercept 19 -0.4898 0.1905 1005 -2.57 0.0103
time 19 0.006810 0.01579 1005 0.43 0.6663
Intercept 20 0.2481 0.2175 1005 1.14 0.2544
time 20 -0.01699 0.02257 1005 -0.75 0.4518
Intercept 21 -1.6594 0.1907 1005 -8.70 <.0001
time 21 -0.00819 0.01648 1005 -0.50 0.6195
Intercept 22 -0.4382 0.1912 1005 -2.29 0.0221
time 22 0.01231 0.01725 1005 0.71 0.4757
Intercept 23 -1.4046 0.1905 1005 -7.38 <.0001
time 23 -0.04301 0.01579 1005 -2.72 0.0066
Intercept 24 0.9933 0.1903 1005 5.22 <.0001
time 24 -0.01164 0.01518 1005 -0.77 0.4433
Intercept 25 0.2525 0.1903 1005 1.33 0.1849
time 25 -0.00165 0.01518 1005 -0.11 0.9133
Intercept 26 -0.8681 0.1903 1005 -4.56 <.0001
time 26 -0.02498 0.01518 1005 -1.65 0.1001
Intercept 27 -0.3389 0.1905 1005 -1.78 0.0755
time 27 0.01889 0.01579 1005 1.20 0.2319
Intercept 28 -0.3572 0.1903 1005 -1.88 0.0608
time 28 0.01619 0.01518 1005 1.07 0.2863
Intercept 29 0.4262 0.1907 1005 2.23 0.0256
time 29 -0.01295 0.01648 1005 -0.79 0.4321
Intercept 30 -0.01194 0.2079 1005 -0.06 0.9542
time 30 0.01989 0.01537 1005 1.29 0.1962
Intercept 31 0.3263 0.2079 1005 1.57 0.1168
time 31 0.004971 0.01537 1005 0.32 0.7465
Intercept 32 0.2952 0.2079 1005 1.42 0.1559
time 32 0.000521 0.01537 1005 0.03 0.9730
Intercept 33 -0.07868 0.2079 1005 -0.38 0.7051
time 33 0.01573 0.01537 1005 1.02 0.3065
Intercept 34 -0.01412 0.2098 1005 -0.07 0.9464
time 34 0.01584 0.01550 1005 1.02 0.3070
Intercept 35 0.5448 0.2082 1005 2.62 0.0090
time 35 0.02149 0.01563 1005 1.37 0.1695
Intercept 36 0.2349 0.2079 1005 1.13 0.2587
time 36 -0.02599 0.01537 1005 -1.69 0.0913
Intercept 37 -1.1068 0.2079 1005 -5.32 <.0001
time 37 -0.01657 0.01537 1005 -1.08 0.2813
Intercept 38 1.1127 0.2079 1005 5.35 <.0001
time 38 0.01125 0.01537 1005 0.73 0.4647
Intercept 39 0.3801 0.2079 1005 1.83 0.0678
time 39 -0.04085 0.01537 1005 -2.66 0.0080
Intercept 40 0.1574 0.2133 1005 0.74 0.4609
time 40 0.005152 0.01969 1005 0.26 0.7937
Intercept 41 0.08268 0.2079 1005 0.40 0.6909
time 41 0.02139 0.01537 1005 1.39 0.1644
Intercept 42 -1.4218 0.2103 1005 -6.76 <.0001
time 42 0.06301 0.01558 1005 4.05 <.0001
Intercept 43 -0.7307 0.2079 1005 -3.52 0.0005
time 43 -0.01484 0.01537 1005 -0.97 0.3347
Intercept 44 -0.4392 0.2079 1005 -2.11 0.0349
time 44 0.005619 0.01537 1005 0.37 0.7148
Intercept 45 -0.9719 0.2079 1005 -4.68 <.0001
time 45 0.004091 0.01537 1005 0.27 0.7902
Intercept 46 2.0673 0.2093 1005 9.88 <.0001
time 46 -0.01695 0.01540 1005 -1.10 0.2712
Intercept 47 -0.06664 0.2079 1005 -0.32 0.7486
time 47 0.01247 0.01537 1005 0.81 0.4174
Intercept 48 -0.6482 0.2079 1005 -3.12 0.0019
time 48 -0.1070 0.01537 1005 -6.96 <.0001
Intercept 49 0.4693 0.2079 1005 2.26 0.0242
time 49 0.003035 0.01537 1005 0.20 0.8435
Intercept 50 0.01968 0.2080 1005 0.09 0.9246
time 50 0.02695 0.01601 1005 1.68 0.0926
Intercept 51 -0.2002 0.2079 1005 -0.96 0.3359
time 51 -0.00924 0.01537 1005 -0.60 0.5479

Type 3 Tests of Fixed Effects
Effect Num DF Den DF F Value Pr > F
time 1 49 0.05 0.8269
group 1 1005 0.49 0.4841
time*group 1 1005 16.13 <.0001
group*bf15 1 1005 162.33 <.0001