Dear      I am also facing the same problem. Did you find the solution and could able to install on window 8.1 (64 bits) after adressing the problem of NLS: extension load error? Regards ... View more

Hello Jon,             Thanks for such a nice explanation. I will consider these options also. Its great to have such a helpful discussion with you, Steve and Muller. Thanks Sandhu ... View more

Dear Mulugeta,    Are you referring to "Longitudnal data analysis 2009" book by Fitzmaurice et al? i tried very hard to get this book but could not. I really feel this is very good book as per little bit information i could get from this book through internet. I will follow your's and Steve's advise for analysis. Thanks a lot for all the help. Sandhu ... View more

Thanks a lot, Steve. I will do that. Regrads Sandhu ... View more

Dear Steve and Mulugeta,          I tried both the alternatives as recommended by both of you.  By using Cholesky parameterization of the unstructured matrix, the only the quadratic term variances is zero, and not the id. But the use of random _residual_/ sub=id type=VC did not improve the model and it still resulted in zeroes for the id and quadratic term variances. A) using Steve's code with Cholesky parameterization of the unstructured matrix Covariance Parameter Estimates                                                               Standard                           Cov Parm     Subject    Estimate       Error                           CHOL(1,1)    ID           3.1811      0.4606                           CHOL(2,1)    ID          -0.1228      0.1851                           CHOL(2,2)    ID         0.000026      0.1909                           CHOL(3,1)    ID         -0.00994     0.01326                           CHOL(3,2)    ID         -2.09E-6     0.01529                           CHOL(3,3)    ID         4.38E-18           .                           SP(POW)      ID          -0.1072     0.01474                           Residual                  115.98      3.1069 Fit Statistics                               -2 Res Log Likelihood       24954.65                               AIC  (smaller is better)    24968.65                               AICC (smaller is better)    24968.68                               BIC  (smaller is better)    24994.09                               CAIC (smaller is better)    25001.09                               HQIC (smaller is better)    24978.85                               Generalized Chi-Square      388284.9                               Gener. Chi-Square / DF        115.98 it converged in 49 Iteration Log: NOTE: Convergence criterion (GCONV=1E-8) satisfied. NOTE: At least one element of the gradient is greater than 1e-3. NOTE: Estimated G matrix is not positive definite. NOTE: PROCEDURE GLIMMIX used (Total process time):       real time           25.71 seconds       cpu time            25.36 seconds B) using Mulugeta's code with diagonal covariance matrix as in "random _residual_/ sub=id type=VC and unstructured matrix UN variance for random effect Covariance Parameter Estimates                                                                 Standard                         Cov Parm         Subject    Estimate       Error                         UN(1,1)          ID         3.23E-18           .                         UN(2,1)          ID           0.1491      0.9892                         UN(2,2)          ID           1.5762      0.1915                         UN(3,1)          ID         -0.04960     0.07431                         UN(3,2)          ID         -0.07712    0.007403                         UN(3,3)          ID         0.000025           .                         Residual (VC)                 149.52      3.9873 Fit Statistics                               -2 Res Log Likelihood       25206.89                               AIC  (smaller is better)    25218.89                               AICC (smaller is better)    25218.92                               BIC  (smaller is better)    25240.70                               CAIC (smaller is better)    25246.70                               HQIC (smaller is better)    25227.64 it converged in 53 iterations LOG NOTE: Convergence criterion (GCONV=1E-8) satisfied. NOTE: At least one element of the gradient is greater than 1e-3. NOTE: Estimated G matrix is not positive definite. NOTE: PROCEDURE GLIMMIX used (Total process time):       real time           17.31 seconds       cpu time            17.05 seconds B) using Mulugeta's code with  diagonal covariance matrix as in "random _residual_/ sub=id type=VC and Cholesky parameterization of the unstructured matrix variance for random effect Covariance Parameter Estimates                                                                 Standard                         Cov Parm         Subject    Estimate       Error                         CHOL(1,1)        ID           0.6879      0.8774                         CHOL(2,1)        ID           0.1156      0.2015                         CHOL(2,2)        ID          4.1E-19           .                         CHOL(3,1)        ID         -0.01065     0.01730                         CHOL(3,2)        ID         0.000451    0.003211                         CHOL(3,3)        ID         2.13E-16           .                         Residual (VC)                 139.60      3.6281 Fit Statistics                               -2 Res Log Likelihood       26165.98                               AIC  (smaller is better)    26175.98                               AICC (smaller is better)    26176.00                               BIC  (smaller is better)    26194.15                               CAIC (smaller is better)    26199.15                               HQIC (smaller is better)    26183.27                               Generalized Chi-Square      467391.5                               Gener. Chi-Square / DF        139.60 it converged in 41 iterations Log NOTE: Convergence criterion (GCONV=1E-8) satisfied. NOTE: At least one element of the gradient is greater than 1e-3. NOTE: Estimated G matrix is not positive definite. NOTE: PROCEDURE GLIMMIX used (Total process time):       real time           3.25 seconds       cpu time            3.19 seconds Thanks Regards Sandhu ... View more

Dear Steve Denham,                  I can not figure it out that what is causing such a large change with use of these two techniques. I think you are the best person to understand it. Therefore, i am sending code, model information, dimensions, Optimization Information, LOG etc. Interestingly, When i remove intercept, the NRRIDG technique does not work and following error is reported ERROR: "NRRIDG Optimization cannot be completed.  Optimization routine cannot improve the function value" whereas in same condition i.e. without intercept, QUANEW technique works and it converges. A) CODE (NRRIDG with random intercept) proc glimmix data=data2 ORDER=Data ; class id sex age xtime; model vas = time time*time             sex age sex*age             sex*time age*time sex*age*time             sex*time*time age*time*time sex*age*time*time / ddfm=kr s cl ; random int time time*time/ subject=id type=un v; random _residual_ / sub=id type=sp(pow)(xtime); nloptions tech= NRRIDG; run; Model Information                   Data Set                                WORK.DATA2                   Response Variable                  VAS                   Response Distribution             Gaussian                   Link Function                          Identity                   Variance Function                    Default                   Variance Matrix Blocked By     ID                   Estimation Technique               Restricted Maximum Likelihood                   Degrees of Freedom Method     Kenward-Roger                   Fixed Effects SE Adjustment    Kenward-Roger Dimensions                                G-side Cov. Parameters           6                                R-side Cov. Parameters           2                                Columns in X                          27                                Columns in Z per Subject         3                                Subjects (Blocks in V)            280                                Max Obs per Subject             12 Optimization Information                     Optimization Technique         Newton-Raphson with Ridging                     Parameters in Optimization    7                     Lower Boundaries                  4                     Upper Boundaries                  1                     Fixed Effects                         Profiled                     Residual Variance                  Profiled                     Starting From                       Data Iteration History                                                    Objective                         Max         Iteration    Restarts    Evaluations        Function          Change    Gradient                 0           0              4    30662.837656       .                     8506.067                 1           0              2    29840.553145    822.28451046    4711.142                 2           0              2    29369.643328    470.90981779    3582.741                 3           0              2    28916.249747    453.39358027    3044.089                 4           0              3    28783.541782    132.70796514    2944.675                 5           0              2     28280.91676    502.62502243    8416.694                 6           1              5    28751.288165    -470.3714047    7813.525                            Convergence criterion (XCONV=0) satisfied. Covariance Parameter Estimates                                                               Standard                            Cov Parm    Subject    Estimate       Error                            UN(1,1)     ID          52.0689           .                            UN(2,1)     ID           1.0951           .                            UN(2,2)     ID          25.7652           .                            UN(3,1)     ID          -2.3731           .                            UN(3,2)     ID         -10.2573           .                            UN(3,3)     ID          12.3989           .                            SP(POW) ID           0.5592     0.03979                            Residual                 280.30     32.7243 LOG NOTE: Convergence criterion (XCONV=0) satisfied. NOTE: At least one element of the gradient is greater than 1e-3. NOTE: PROCEDURE GLIMMIX used (Total process time):       real time           10.49 seconds       cpu time            10.43 seconds B) CODE (NRRIDG without random intercept) proc glimmix data=data2 ORDER=Data ; class id sex age xtime; model vas = time time*time             sex age sex*age             sex*time age*time sex*age*time             sex*time*time age*time*time sex*age*time*time / ddfm=kr s cl ; random time time*time/ subject=id type=un v; random _residual_ / sub=id type=sp(pow)(xtime); nloptions tech=  NRRIDG; run; Model information remains same Dimensions                                G-side Cov. Parameters           3                                R-side Cov. Parameters           2                                Columns in X                          27                                Columns in Z per Subject         2                                Subjects (Blocks in V)            280                                Max Obs per Subject             12 Optimization Information                     Optimization Technique          Newton-Raphson with Ridging                     Parameters in Optimization    4                     Lower Boundaries                 3                     Upper Boundaries                 1                     Fixed Effects                       Profiled                     Residual Variance                Profiled                     Starting From                      Data Iteration History                                                    Objective                         Max         Iteration    Restarts    Evaluations        Function          Change    Gradient                 0           0              4     29327.32795       .                    11583.9                 1           0              2    33917.845247    -4590.517296    11739.39                     Optimization routine cannot improve the function value. Covariance Parameter Estimates                                                               Standard                            Cov Parm    Subject    Estimate       Error                            UN(1,1)     ID          17.6726           .                            UN(2,1)     ID           1.4510           .                            UN(2,2)     ID          33.5211           .                            SP(POW) ID           0.9000           .                            Residual                1415.97           . LOG ERROR: NRRIDG Optimization cannot be completed. NOTE: Optimization routine cannot improve the function value. NOTE: PROCEDURE GLIMMIX used (Total process time):       real time           1.43 seconds       cpu time            1.37 seconds C) CODE (Dual Quasi-Newton with random intercept) proc glimmix data=data2 ORDER=Data ; class id sex age xtime; model vas = time time*time             sex age sex*age             sex*time age*time sex*age*time             sex*time*time age*time*time sex*age*time*time / ddfm=kr s cl ; random int time time*time/ subject=id type=un v; random _residual_ / sub=id type=sp(pow)(xtime); run; Model information remains same Dimensions                                G-side Cov. Parameters           6                                R-side Cov. Parameters           2                                Columns in X                          27                                Columns in Z per Subject         3                                Subjects (Blocks in V)            280                                Max Obs per Subject             12 Optimization Information                          Optimization Technique         Dual Quasi-Newton                          Parameters in Optimization    7                          Lower Boundaries                  4                          Upper Boundaries                  1                          Fixed Effects                         Profiled                          Residual Variance                 Profiled                          Starting From                        Data Iteration History                                                    Objective                         Max         Iteration    Restarts    Evaluations        Function          Change    Gradient                 0           0              4    30662.837656       .                    8506.067                 1           0              5    28668.856677    1993.9809793    2199.816                 2           0             58    26208.493502    2460.3631744    263595.8                 3           0              5    26208.485885      0.00761685    270900.4                 4           0              3    26188.347277     20.13860824    308956.5                 5           0              4    26158.678073     29.66920398      616998                 6           0              5    26140.803057     17.87501606    654371.3                 7           0              5    26124.120621     16.68243649      688251                 8           0              5    26107.310639     16.80998203    722089.4                 9           0              5    26090.520122     16.79051661    755560.3                10           0              5    26073.888382     16.63173957    788085.5                11           0              5    26057.541672     16.34671061    818876.5                12           0              5    26041.594314     15.94735789    846943.3                13           0              5    26026.150001     15.44431333    871095.6                14           0              5    26011.302731     14.84726934    889940.6                15           0              2    25964.073338     47.22939308    11515841                16           1             20    25867.099209     96.97412875    635971.6                17           1              3    25828.607906     38.49130370    51872.11                18           1             11    25635.995456    192.61245002     6136433                19           1              7    25632.646006      3.34945002    13163228                20           1              6     25628.79396      3.85204595    13931469                21           1              3     25605.60941     23.18454998    10127958                22           1              3    25568.842337     36.76707290     4627900                .                .                .                .                80           2              5    23953.312146      0.00000207    63380.05                81           2              4    23953.311488      0.00065810    59514.87                82           2              3    23953.311486      0.00000236    53165.53                          Convergence criterion (GCONV=1E-8) satisfied.                           Estimated G matrix is not positive definite. Covariance Parameter Estimates                                                               Standard                            Cov Parm    Subject    Estimate       Error                            UN(1,1)     ID         9.86E-22           .                            UN(2,1)     ID          -3.9026      0.8652                            UN(2,2)     ID           2.4122      0.2092                            UN(3,1)     ID           0.2268     0.06188                            UN(3,2)     ID          -0.1050    0.008000                            UN(3,3)     ID         7.877E-8           .                            SP(POW) ID          0.09958     0.01372                            Residual                 140.27      4.8014 LOG NOTE: Convergence criterion (GCONV=1E-8) satisfied. NOTE: At least one element of the gradient is greater than 1e-3. NOTE: Estimated G matrix is not positive definite. NOTE: PROCEDURE GLIMMIX used (Total process time):       real time           25.57 seconds       cpu time            25.30 seconds D) CODE (Dual Quasi-Newton without random intercept) proc glimmix data=data2 ORDER=Data ; class id sex age xtime; model vas = time time*time             sex age sex*age             sex*time age*time sex*age*time             sex*time*time age*time*time sex*age*time*time / ddfm=kr s cl ; random time time*time/ subject=id type=un v; random _residual_ / sub=id type=sp(pow)(xtime); run; Model information remains same Dimensions                                G-side Cov. Parameters           3                                R-side Cov. Parameters           2                                Columns in X                          27                                Columns in Z per Subject         2                                Subjects (Blocks in V)            280                                Max Obs per Subject             12 Optimization Information                          Optimization Technique          Dual Quasi-Newton                          Parameters in Optimization    4                          Lower Boundaries                  3                          Upper Boundaries                  1                          Fixed Effects                         Profiled                          Residual Variance                  Profiled                          Starting From                        Data Iteration History                                                    Objective                         Max         Iteration    Restarts    Evaluations        Function          Change    Gradient                 0           0              4     29327.32795       .                       11583.9                 1           0              5    29281.411327     45.91662314    12868.42                 2           0              5    29240.295101     41.11622587    14297.88                 3           0             70    26042.998139    3197.2969629    5.6897E9                 4           0              4    25979.595376     63.40276297     9.877E8                 5           0              3     25957.25277     22.34260529    1.139E10                 6           0              3    25939.317553     17.93521689     1.29E10                 7           0             18    25841.391645     97.92590789    7.1394E8                 8           0             11    25819.989261     21.40238439    9.1343E8                 9           0             10    25767.475697     52.51356388    1.5118E9                10           0              6     25765.64274      1.83295751    2.6814E9                11           0              4    25735.316611     30.32612824    3.7442E9                12           0              2    25707.023322     28.29328991    7.3018E9                13           0              2    25665.354323     41.66899876    1.3357E9                14           0              5    25649.042009     16.31231406     5.624E9                15           0              4     25599.39337     49.64863832    1.5771E9                16           0              3    25591.215318      8.17805200    4.4921E9                17           0              4     25575.47631     15.73900814    1.106E10                18           0              2    25550.179798     25.29651182     3.693E9                19           0              5    25522.241508     27.93829080    6.2534E9                20           0              3    25496.791043     25.45046438    6.5937E9                21           0              2    25471.721861     25.06918217    2.1984E9                22           0              9    25439.671707     32.05015405    2.8937E9                .                .                .               130           0              2    24125.065516     22.98137596    1.1381E8               131           0              3    24112.207432     12.85808339    1.2729E8               132           0              5    24107.301953      4.90547927    55729947               133           0              3    24106.054818      1.24713534    50910488               134           0              3    24105.477952      0.57686577     9767172               135           0              3    24105.407721      0.07023051    993324.6               136           0              3     24105.40601      0.00171169    106808.8               137           0              3    24105.405963      0.00004618    89331.43                          Convergence criterion (GCONV=1E-8) satisfied.                           Estimated G matrix is not positive definite. LOG NOTE: Convergence criterion (GCONV=1E-8) satisfied. NOTE: At least one element of the gradient is greater than 1e-3. NOTE: Estimated G matrix is not positive definite. NOTE: PROCEDURE GLIMMIX used (Total process time):       real time           29.81 seconds       cpu time            29.12 seconds I hope my presentation of above facts is clear. Please let me know if i can provide any additional information. Thanks. Regards, Sandhu ... View more

Dear Steve Denham,      There are couple of things which i feel are responsible for these problems. When i was running the original quadratic code, i was getting G matrix not positive warning as follow: proc glimmix data=data ORDER=Data ;    class id sex age ; model vas = time time*time             sex age sex*age             sex*time age*time sex*age*time             sex*time*time age*time*time sex*age*time*time / ddfm=kr s cl ; random int time time*time/ subject=id type=un v; run; NOTE: Convergence criterion (GCONV=1E-8) satisfied. NOTE: At least one element of the gradient is greater than 1e-3. NOTE: Estimated G matrix is not positive definite. NOTE: PROCEDURE GLIMMIX used (Total process time):       real time           22.37 seconds       cpu time            22.12 seconds Therefore, i used nobound option in the procedure as recommended (by Little 2006) for PROC MIXED procedure: proc glimmix data=data ORDER=Data nobound ; class id sex age ; model vas = time time*time             sex age sex*age             sex*time age*time sex*age*time             sex*time*time age*time*time sex*age*time*time / ddfm=kr s cl ; random int time time*time/ subject=id type=un v; run; It worked fine for quadrartic code even after adding nobound. Now when i added random _residual_ statement in this above code along with nobound option, the problem of "Optimization stopped because of infinite objective function." as i mentioned in the previous post. This problem persisted even with ddfm=kr(firstorder),   ddfm=satterthwaite and ddfm=bw . But when i removed nobound, it worked even with ddfm=kr. proc glimmix data=data2 ORDER=Data ; class id sex age xtime; model vas = time time*time             sex age sex*age             sex*time age*time sex*age*time             sex*time*time age*time*time sex*age*time*time / ddfm=kr s cl ; random int time time*time/ subject=id type=un v; random _residual_ / sub=id type=sp(pow)(xtime); run; Log is: NOTE: Convergence criterion (GCONV=1E-8) satisfied. NOTE: At least one element of the gradient is greater than 1e-3. NOTE: Estimated G matrix is not positive definite. NOTE: PROCEDURE GLIMMIX used (Total process time):       real time           23.30 seconds       cpu time            23.10 seconds Now here is my dilemma : should i use nobound option and no random _residual_ statement OR should i use random _residual_ statement and no nobound option. IF i am not using nobound option, then how to justify the effect of Estimated G matrix is not positive definite. These above codes were with default Optimization Technique i.e.  Dual Quasi-Newton. Now part two of the problem is changing  Optimization Technique from  Dual Quasi-Newton to Newton-Raphson with Ridging with nloptions tech= nrridge. when i run same quadratic code (without random _residual_ statement) along with nobound option as : proc glimmix data=data2 ORDER=Data  nobound; class id sex age xtime; model vas = time time*time             sex age sex*age             sex*time age*time sex*age*time             sex*time*time age*time*time sex*age*time*time / ddfm=kr s cl ; random int time time*time/ subject=id type=un v; nloptions tech= nrridge;                *Newton-Raphson with Ridging technique*; run; there is no difference in results for from previous Optimization Technique i.e  Dual Quasi-Newton. The Fit criteria, Type III test of fixed effect are exactly same, so as the : NOTE: Convergence criterion (GCONV=1E-8) satisfied. NOTE: Estimated G matrix is not positive definite. NOTE: PROCEDURE GLIMMIX used (Total process time):       real time           3.75 seconds       cpu time            3.71 seconds This Newton-Raphson with Ridging technique also did not work with nobound option as it happened with  Dual Quasi-Newton after i added random _residual_ statement. BUT The problem occurs when i use nloptions tech= nrridge (i.e Newton-Raphson with Ridging technique) along with random _ residual_ statement but without nobound option. proc glimmix data=data ORDER=Data ; class id sex age xtime; model vas = time time*time             sex age sex*age             sex*time age*time sex*age*time             sex*time*time age*time*time sex*age*time*time / ddfm=kr s cl ; random int time time*time/ subject=id type=un v; random _residual_ / sub=id type=sp(pow)(xtime); nloptions tech= nrridge; run; now log is: NOTE: Convergence criterion (XCONV=0) satisfied. NOTE: At least one element of the gradient is greater than 1e-3. NOTE: PROCEDURE GLIMMIX used (Total process time):       real time           10.43 seconds       cpu time            10.34 seconds IN CONTRAST to log from same statement but with Dual Quasi-Newton technique, the above log (with Newton-Raphson with Ridging technique) shows No NOTE  of Estimated G matrix is not positive definite and  Convergence criterion changes from (GCONV=1E-8) to  (XCONV=0). Another important differences are in Fit Statistics and Type III tests of fixed effects Fit Statistics (from Dual Quasi-Newton technique)                               -2 Res Log Likelihood       24037.76                               AIC  (smaller is better)    24053.76                               AICC (smaller is better)    24053.80                               BIC  (smaller is better)    24082.84                               CAIC (smaller is better)    24090.84                               HQIC (smaller is better)    24065.42                               Generalized Chi-Square      424340.5                               Gener. Chi-Square / DF        126.74 Fit Statistics ( Newton-Raphson with Ridging technique)                               -2 Res Log Likelihood       28283.79                               AIC  (smaller is better)    28299.79                               AICC (smaller is better)    28299.83                               BIC  (smaller is better)    28328.87                               CAIC (smaller is better)    28336.87                               HQIC (smaller is better)    28311.45                               Generalized Chi-Square      939474.5                               Gener. Chi-Square / DF        280.61 Type III Tests of Fixed Effects (from Dual Quasi-Newton technique)                                            Num      Den                      Effect                 DF       DF    F Value    Pr > F                      TIME                           1     1048      90.45    <.0001                      TIME*TIME                  1     2540       0.84    0.3598                      SEX                            1    131.9       4.35    0.0389                      AGE                           1    131.9       1.97    0.1626                      SEX*AGE                    1    131.9       5.22    0.0240                      TIME*SEX                    1     1048       0.03    0.8587                      TIME*AGE                   1     1048       0.00    0.9442                      TIME*SEX*AGE            1     1048       0.09    0.7703                      TIME*TIME*SEX           1     2540       0.10    0.7469                      TIME*TIME*AGE           1     2540       0.01    0.9334                      TIME*TIME*SEX*AGE       1     2540       0.00    0.9970 Type III Tests of Fixed Effects  ( Newton-Raphson with Ridging technique)                                            Num      Den                      Effect                 DF       DF    F Value    Pr > F                      TIME                          1      537      13.28    0.0003                      TIME*TIME                  1     3348       0.76    0.3819                      SEX                             1    135.9       0.10    0.7577                      AGE                             1    135.9       0.05    0.8315                      SEX*AGE                      1    135.9       0.12    0.7270                      TIME*SEX                      1      537       0.14    0.7074                      TIME*AGE                      1      537       0.03    0.8522                      TIME*SEX*AGE               1      537       0.03    0.8736                      TIME*TIME*SEX               1     3348       0.00    0.9580                      TIME*TIME*AGE              1     3348       0.00    0.9760                      TIME*TIME*SEX*AGE       1     3348       0.00    0.9762 WHY is such as dramatic difference between these two technique when incorporate covariance structure (i.e. random _residual_ statement) with spatial power structure. (I am not sure same effect will be observed if we use ar(1) or any other covariance strucute, BUT definitely it happened with sp(pow)(xtime) covariance structure) AND what is this criterion difference from  (GCONV=1E-8) to  (XCONV=0). According to LITTLE 2006,  Newton-Raphson with Ridging technique makes PROC GLIMMIX almost identical to PROC MIXED. I really feel that i am asking very exhausting questions. Thanks for your patience and all the help. Regards Sandhu  ... View more

Dear Steve Denham,           I tried this code with random _residual_ statement for my data which comprised of 280 subject and each subject had 12 repeated measurements. your prediction was correct. It did not work. The log was : NOTE: Convergence criterion (ABSGCONV=0.00001) satisfied. WARNING: Optimization stopped because of infinite objective function. NOTE: PROCEDURE GLIMMIX used (Total process time):       real time           1.01 seconds       cpu time            0.96 seconds It converged but "Optimization stopped because of infinite objective function." this happened with both Dual Quasi-Newton and  Newton-Raphson with Ridging optimization techniques. If i am correct, the  Newton-Raphson with Ridging technique makes PROC GLIMMIX almost similar to PROC MIXED. So this mean random _residual_  in PROC GLIMMIX or Repeated statement Repeated xtime/ subject=id type=sp (pow)(xtime) in PROC MIXED will not work? if so, then how to model covariance structure. Regards Sandhu ... View more

Dear Steve Denham, Thanks a lot for replying. I am using SAS 9.2 and do not have access to SAS/STAT 12.1. Following is the code that i can think of fitting a second order (quadratic) polynomial trend by using GLIMMIX proc glimmix data=data ORDER=Data nobound; class id sex age; model vas = time time*time                   sex age sex*age                   sex*time age*time sex*age*time                   sex*time*time age*time*time sex*age*time*time             / ddfm=kr s cl ; random int time time*time / subject=id type=un v; lsmeans sex / pdiff adjust=simulate(acc=.0005 seed=121211 report) adjdfe=row cl; lsmeans age / pdiff adjust=simulate(acc=.0005 seed=121211 report) adjdfe=row cl; lsmeans sex*age / pdiff adjust=simulate(acc=.0005 seed=121211 report) adjdfe=row cl; run; is this code appropriate for analysis of quadratic trend? should i use random _residual_ statement also to model covariance structure e.g. random _residual / sub=id type=sp(pow)(xtime). i am thinking of spatial power because my time points are not equally spaced. i can use xtime as class variable and time as continuous variable.  So code will be like this:  proc glimmix data=data ORDER=Data nobound; class id sex age xtime; model vas = time time*time                   sex age sex*age                   sex*time age*time sex*age*time                   sex*time*time age*time*time sex*age*time*time             / ddfm=kr s cl ; random int time time*time / subject=id type=un v; random _residual / sub=id type=sp(pow)(xtime); lsmeans sex / pdiff adjust=simulate(acc=.0005 seed=121211 report) adjdfe=row cl; lsmeans age / pdiff adjust=simulate(acc=.0005 seed=121211 report) adjdfe=row cl; lsmeans sex*age / pdiff adjust=simulate(acc=.0005 seed=121211 report) adjdfe=row cl; run; is this code for analysis and multiple comparison by using lsmeans statement appropriate? or should i use ESTIMATE statement for doing multiple comparisons.  Thanks a lot for the help Regards Sandhu ... View more