Sample 25030: %GLIMMIX macro to fit the generalized linear mixed model
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%GLIMMIX macro to fit the generalized linear mixed model
| Contents: | Purpose / History / Requirements / Usage / Details / Limitations / References |
NOTE: The GLIMMIX procedure is available beginning in SAS 9.1.
- PURPOSE:
- The macro uses iteratively reweighted likelihoods to fit the generalized linear mixed model (Wolfinger, R. and O'Connell, M., 1993).
- HISTORY:
-
Initial coding 01Jun92 A few changes and additions 09Oct92 Corrections from Dale McLerran, FHCRC 16Feb94 Suggestions from David Murray, U. Minnesota 21Sep95 Suggestions from Ken Goldberg, Wyeth-Ayerst 27Oct95 Various minor updates 06Apr96 Per suggestions from Ken Goldberg, INITIAL option changed, INTERCEPT= option dropped, and FITTING, NOPREV, and NOTEST options added. 12Mar97 More Goldberg ideas: NOTES option added, PARMS specification is only used in the first iteration unless you also specify NOPREV, some clean up 19May97 7.01 conversion 01Jul97 Switched XBETA= and PRED= 14Nov97 Save spatial coordinates as suggested by Michael O'Kelly, Quintiles Dublin 01Dec97 Eliminated LSMEANS / OM check 05Dec97 Titling code from Dale McLerran, FHCRC 20Feb98 Made PRINTLAST and FITTING the default 25Mar98 Fixed problem with TYPE=SP(EXP) 30Apr98 Allowed METHOD=MIVQUE0 to persist as suggested by Svetlana Rudnaya, Ford 14Aug98 Changed output data set as suggested by Carol Gotway-Crawford, CDC 25Sep98 Improved vertical bar processing as suggested by Julie Yee, USGS, and Oliver Schabenberger, Va Tech 26Apr02 Added terms to deviance calculation for Poisson and Gamma distribution that do not sum to zero for no-intercept models and with certain repeated structures. The OLDDEVIANCE option uses the previous formulas 06Jun02 - REQUIREMENTS:
- Base SAS and SAS/STAT software. Two versions of the %GLIMMIX macro are available, one for use with Version 6.12 of the SAS System, one for use with Version 8 or later.
- USAGE:
-
Follow the instructions in the Downloads tab of this
sample to save the %GLIMMIX macro definition. Replace the text within quotes in the following statement with the location of the %GLIMMIX macro definition file on your system. In your SAS program or in the SAS editor window, specify this statement to define the %GLIMMIX macro and make it available for use:
%inc "<location of your file containing the GLIMMIX macro>";
Following this statement, you may call the %GLIMMIX macro. See the Results tab for examples.
In addition to variable names beginning with an underscore, the following are reserved variable names and should not be used in your input SAS data set:
- COL, DETA, DMU, ETA, LOWERETA, LOWERMU, MU, PRED, RESRAW,
RESCHI, STDERRETA (STDERETA in the Version 6 macro),
STDERRMU (STDERMU in the Version 6 macro), UPPERETA, UPPERMU, VAR
The following options can be specified:
data= specifies the data set you are using. It can either be a regular input data set or the _DS data set from a previous call to %GLIMMIX. The latter is used to specify starting values for %GLIMMIX and should be accompanied by the INITIAL= option described below. procopt= specifies options appropriate for a PROC MIXED statement. Refer to the PROC MIXED documentation for more information. stmts= specifies PROC MIXED statements for the analysis, separated by semicolons and listed as a single argument to the %str() macro function. Statements may include any of the following: CLASS, MODEL, RANDOM, REPEATED, PARMS, ID, CONTRAST, ESTIMATE, and LSMEANS. Syntax and options for each statement are exactly as in the PROC MIXED documentation. If you wish to use the OM option with the LSMEANS statement, you should specify OM=dataset to avoid conflicts with weights. weight= specifies a weighting variable for the analysis This allows you to construct your own weights which can modify or replace the ones constructed by %GLIMMIX. freq= specifies a frequency variable for the analysis. It replicates observations with the number of replicates being equal to the value of the FREQ variable. error= specifies the error distribution. Valid types are: binomial|b, normal|n, poisson|p, gamma|g, invgaussian|ig, and user|u When you specify error=user, you must also provide the errvar= and errdev= options. The default error distribution is binomial. errvar= specifies the user-defined variance function. It must be expressed as a function the argument "mu" (see examples). errdev= specifies the user-defined deviance function. It must be expressed as a function the arguments "_y", which is the response variable, and "mu", which is the mean. You are allowed to use "_wght" also, which corresponds to the denominator of a binomial response. Typical deviance functions are as follows: normal (_y-mu)**2 poisson 2*_y*log(_y/mu); binomial 2*_wght*(_y*log(_y/mu)+ (1-_y)*log((1-_y)/(1-mu))) gamma -2*log(_y/mu) invgaussian (((_y-mu)**2)/(_y*mu*mu)) The default deviance is binomial. link= specifies the link function. Valid types are logit, probit, cloglog, loglog, identity, power(), log, exp, reciprocal, nlin, and user. (warning: nlin has not been tested, and it currently uses an MQL-type estimation scheme.) When you specify link=nlin, you must also provide the linkn=, linknd=, and linkni= options. When you specify link=user, you must also provide the ulink=, dulink=, and iulink= options. The default link is different for each error distribution and is as follows: Distribution Default Link ------------ ------------ Binomial Logit Poisson Log Normal Identity Gamma Reciprocal Invgaussian Power(-2) linkn= specifies a nonlinear link function. It must be enclosed in %str() and assign a value to "mu" by using parameters "b1" - "bk". linknd= specifies the derivative of the nonlinear link function. linkni= specifies the initial values for the nonlinear link function. linku= specifies a user-defined link function. It must be expressed as a function with the argument "mu". linkud= specifies the derivative of the user-defined link function with respect to mu. It must be expressed as a function with argument "mu". For an approximation, use the formula (u(mu+h)-u(mu-h))/(2*h) where u() is the link and h is a small number. linkui= specifies the inverse of the user-defined link. It must be expressed as a function with argument "eta". linkuid= specifies the derivative of the inverse of the user-defined link. It must be expressed as a function with argument "eta". numder= specifies the tolerance used to numerically differentiate certain link functions (e.g. probit and power). It has a default value of 1e-5. cf= specifies the correction factor added to the data in order to avoid singularities in the initial iteration. It has a default value of 0.5. converge=sets the convergence criterion for the %GLIMMIX macro. This is not the convergence criteria used for each internal PROC MIXED call, but rather the criterion used to assess convergence of the entire macro algorithm. It has a default value of 1e-8. maxit= specifies the maximum number of iterations for the %GLIMMIX macro to converge. It has a default value of 20. offset= specifies an offset variable. By default no offset is used. zmult= (available only in %GLIMMIX for Version 8 or later) specifies a variable by which the pseudo data variable _z is multiplied during each iteration. wadd= (available only in %GLIMMIX for Version 8 or later) specifies a variable to add to the weight variable _w during each iteration. out= specifies a name for an output data set. This data set is the predicted value data set from PROC MIXED with the following additional variables: eta = linear predictor (xbeta) + offset stderreta = approximate std err of eta lowereta = lower confidence limit for eta uppereta = upper confidence limit for eta mu = inverse link transform of eta dmu = derivative of mu with respect to eta stderrmu = approx std err of mu via delta method lowermu = lower cl for mu, inv link transform of lowereta uppermu = upper cl for mu, inv link transform of uppereta var = variance resraw = raw residual, y - mu reschi = scaled residual, (y-mu)/sqrt(phi*var) deta = derivative of eta with respect to mu _w = weight used in final PROC MIXED call _z = dependent variable used in final PROC MIXED call If none is given, then a default name of _OUTFILE is used. outalpha=specifies an alpha level for the confidence limits in the out= data set. options= specifies %GLIMMIX macro options separated by spaces: FITTING (available only in %GLIMMIX for Version 6) prints the model fitting information from the final PROC MIXED run. INITIAL specifes that the input data set is actually the _DS data set from a previous call to %GLIMMIX. This allows you to restart a problem that stopped or to specify starting values. MQL computes MQL estimates (see Breslow and Clayton, 1993). The default is PQL with an extra-dispersion parameter. NOPREV prevents use of previous covariance parameter estimates as starting values for the next iteration. NOPRINT suppresses all printing. NOITPRINT suppresses printing of the iteration history. NOTES requests printing of SAS notes, date, and page numbers during macro execution. By default, the notes, date, and numbers are turned off during macro execution and turned back on after completion. OLDDEVIANCE (available only in %GLIMMIX for Version 8 or later) requests computation of deviances for poisson and gamma distribution as in earlier versions of %GLIMMIX (up to June 02). PRINTALL prints all PROC MIXED runs. PRINTDATA prints the pseudo data after each iteration. PRINTLAST (available only in %GLIMMIX for Version 6) prints the final PROC MIXED run. - COL, DETA, DMU, ETA, LOWERETA, LOWERMU, MU, PRED, RESRAW,
- DETAILS:
-
The macro uses iteratively reweighted likelihoods to fit the
model. Refer to Wolfinger, R. and O'Connell, M. (1993).
By default, %GLIMMIX uses restricted/residual psuedo likelihood (REPL) to find the parameter estimates of the generalized linear mixed model you specify. The macro calls PROC MIXED iteratively until convergence, which is decided using the relative deviation of the variance/covariance parameter estimates. An extra-dispersion scale parameter is estimated by default.
%GLIMMIX will work on any type of model with the error distributions and link functions given in the ERRLINK macro. In addition, you can specify your own error and/or link functions. In order to do this you must specify the error=user and/or link=user options in conjunction with the errvar=, errdev=, linku=, linkud=, linkui=, and linkuid= options.
- LIMITATIONS:
- This macro can produce biased results for repeated binary data with few repeats on each subject. Refer to Breslow and Clayton (1993).
- REFERENCES:
-
Breslow, N. E. and Clayton, D. G. (1993), "Approximate Inference in Generalized
Linear Mixed Models," Journal of the American Statistical Association, 88,
9-25.
McCullagh, P. and Nelder, J.A. (1989), Generalized Linear Models, Second Edition, London: Chapman and Hall.
Wolfinger, R. and O'Connell, M. (1993), "Generalized Linear Mixed Models: A Pseudo-Likelihood Approach," Journal of Statistical Computation and Simulation, 48.
These sample files and code examples are provided by SAS Institute Inc. "as is" without warranty of any kind, either express or implied, including but not limited to the implied warranties of merchantability and fitness for a particular purpose. Recipients acknowledge and agree that SAS Institute shall not be liable for any damages whatsoever arising out of their use of this material. In addition, SAS Institute will provide no support for the materials contained herein.
These sample files and code examples are provided by SAS Institute Inc. "as is" without warranty of any kind, either express or implied, including but not limited to the implied warranties of merchantability and fitness for a particular purpose. Recipients acknowledge and agree that SAS Institute shall not be liable for any damages whatsoever arising out of their use of this material. In addition, SAS Institute will provide no support for the materials contained herein.
NOTE: The following examples and results used the %GLIMMIX macro for Version 8 or later.
- EXAMPLE 1: Salamander data
-
From McCullagh and Nelder (1989), Section 14.5.
data salaman; input day fpop$ fnum mpop$ mnum y1 y2 y3; datalines; 4 rb 1 rb 1 1 1 1 4 rb 2 rb 5 1 1 0 4 rb 3 rb 2 1 0 1 4 rb 4 rb 4 1 1 1 4 rb 5 rb 3 1 1 0 4 rb 6 ws 9 1 1 0 4 rb 7 ws 8 0 1 0 4 rb 8 ws 6 0 1 1 4 rb 9 ws 10 0 1 0 4 rb 10 ws 7 0 0 0 4 ws 1 rb 9 0 0 0 4 ws 2 rb 7 0 0 0 4 ws 3 rb 8 0 0 1 4 ws 4 rb 10 0 0 1 4 ws 5 rb 6 0 0 0 4 ws 6 ws 5 0 1 0 4 ws 7 ws 4 1 1 1 4 ws 8 ws 1 1 0 0 4 ws 9 ws 3 1 1 1 4 ws 10 ws 2 1 1 0 8 rb 1 ws 4 1 0 1 8 rb 2 ws 5 1 1 0 8 rb 3 ws 1 0 1 1 8 rb 4 ws 2 1 0 0 8 rb 5 ws 3 1 0 1 8 rb 6 rb 9 1 1 1 8 rb 7 rb 8 0 1 1 8 rb 8 rb 6 1 0 1 8 rb 9 rb 7 0 1 0 8 rb 10 rb 10 0 0 1 8 ws 1 ws 9 1 1 0 8 ws 2 ws 6 0 1 1 8 ws 3 ws 7 0 1 0 8 ws 4 ws 10 1 0 1 8 ws 5 ws 8 1 0 1 8 ws 6 rb 2 0 0 0 8 ws 7 rb 1 1 0 0 8 ws 8 rb 4 0 0 0 8 ws 9 rb 3 1 1 0 8 ws 10 rb 5 0 0 0 12 rb 1 rb 5 1 1 1 12 rb 2 rb 3 1 1 0 12 rb 3 rb 1 1 1 1 12 rb 4 rb 2 1 0 1 12 rb 5 rb 4 1 1 1 12 rb 6 ws 10 1 1 1 12 rb 7 ws 9 0 0 0 12 rb 8 ws 7 0 0 1 12 rb 9 ws 8 1 1 1 12 rb 10 ws 6 1 1 1 12 ws 1 rb 7 1 0 0 12 ws 2 rb 9 0 0 0 12 ws 3 rb 6 0 0 1 12 ws 4 rb 8 1 1 1 12 ws 5 rb 10 0 0 1 12 ws 6 ws 3 1 1 1 12 ws 7 ws 5 1 1 1 12 ws 8 ws 2 1 0 1 12 ws 9 ws 1 1 1 0 12 ws 10 ws 4 0 1 1 16 rb 1 ws 1 0 0 0 16 rb 2 ws 3 1 0 1 16 rb 3 ws 4 1 1 0 16 rb 4 ws 5 0 0 1 16 rb 5 ws 2 1 0 0 16 rb 6 rb 7 0 0 1 16 rb 7 rb 9 1 1 0 16 rb 8 rb 10 0 0 1 16 rb 9 rb 6 1 1 0 16 rb 10 rb 8 0 1 1 16 ws 1 ws 10 1 0 1 16 ws 2 ws 7 1 0 1 16 ws 3 ws 9 0 1 0 16 ws 4 ws 8 1 1 0 16 ws 5 ws 6 0 0 1 16 ws 6 rb 4 0 1 0 16 ws 7 rb 2 0 0 0 16 ws 8 rb 5 0 0 0 16 ws 9 rb 1 1 1 0 16 ws 10 rb 3 1 1 0 20 rb 1 rb 4 1 1 1 20 rb 2 rb 1 1 0 0 20 rb 3 rb 3 1 1 1 20 rb 4 rb 5 1 0 0 20 rb 5 rb 2 1 0 1 20 rb 6 ws 6 1 0 1 20 rb 7 ws 7 0 0 0 20 rb 8 ws 10 1 1 1 20 rb 9 ws 9 1 0 1 20 rb 10 ws 8 1 1 1 20 ws 1 rb 10 0 0 0 20 ws 2 rb 6 0 0 0 20 ws 3 rb 7 0 0 0 20 ws 4 rb 9 0 0 0 20 ws 5 rb 8 0 0 0 20 ws 6 ws 2 0 1 0 20 ws 7 ws 1 1 0 0 20 ws 8 ws 5 1 0 1 20 ws 9 ws 4 1 1 1 20 ws 10 ws 3 1 1 1 24 rb 1 ws 5 1 0 1 24 rb 2 ws 2 1 1 0 24 rb 3 ws 3 1 1 1 24 rb 4 ws 4 1 0 0 24 rb 5 ws 1 1 0 0 24 rb 6 rb 8 1 0 1 24 rb 7 rb 6 0 1 0 24 rb 8 rb 9 1 0 0 24 rb 9 rb 10 1 1 1 24 rb 10 rb 7 0 0 1 24 ws 1 ws 8 1 1 1 24 ws 2 ws 10 0 1 1 24 ws 3 ws 6 1 1 1 24 ws 4 ws 9 1 1 0 24 ws 5 ws 7 0 0 1 24 ws 6 rb 1 0 1 0 24 ws 7 rb 5 1 0 0 24 ws 8 rb 3 0 0 0 24 ws 9 rb 4 0 1 0 24 ws 10 rb 2 0 0 0 run; /*---1st experiment---*/ data sal1; set salaman; y = y1; expt = 1; run; /* Define the GLIMMIX macro */ %inc "<location of your file containing the GLIMMIX macro>"; /*---logistic regression with random effects---*/ %glimmix(data=sal1, stmts=%str( class fpop fnum mpop mnum; model y = fpop|mpop / solution; random fpop*fnum mpop*mnum; lsmeans fpop*mpop / cl diff; ), error=binomial ) run; - RESULTS:
-
The GLIMMIX Macro Data Set : WORK.SAL1 Error Distribution : BINOMIAL Link Function : LOGIT Response Variable : Y GLIMMIX Iteration History Iteration Convergence criterion 1 1.0301877779 2 0.3698874839 3 0.1110022646 4 0.019645527 5 0.0024043459 6 0.0002225154 7 4.1481413E-6 8 1.636125E-10 Output from final Proc Mixed run: The Mixed Procedure Model Information Data Set WORK._DS Dependent Variable _z Weight Variable _w Covariance Structure Variance Components Estimation Method REML Residual Variance Method Profile Fixed Effects SE Method Model-Based Degrees of Freedom Method Containment Class Level Information Class Levels Values fpop 2 rb ws fnum 10 1 2 3 4 5 6 7 8 9 10 mpop 2 rb ws mnum 10 1 2 3 4 5 6 7 8 9 10 Dimensions Covariance Parameters 3 Columns in X 9 Columns in Z 40 Subjects 1 Max Obs Per Subject 120 Number of Observations Number of Observations Read 120 Number of Observations Used 120 Number of Observations Not Used 0 Parameter Search CovP1 CovP2 CovP3 Variance Res Log Like -2 Res Log Like 2.0201 0.6318 0.6644 0.6644 -284.4640 568.9280 Iteration History Iteration Evaluations -2 Res Log Like Criterion 1 1 568.92797414 0.00000000 Convergence criteria met. Covariance Parameter Estimates Cov Parm Estimate fpop*fnum 2.0201 mpop*mnum 0.6318 Residual 0.6644 Fit Statistics -2 Res Log Likelihood 568.9 AIC (smaller is better) 574.9 AICC (smaller is better) 575.1 BIC (smaller is better) 577.9 PARMS Model Likelihood Ratio Test DF Chi-Square Pr > ChiSq 2 0.00 1.0000 Solution for Fixed Effects Standard Effect fpop mpop Estimate Error DF t Value Pr > |t| Intercept 1.1755 0.6513 17 1.80 0.0888 fpop rb -0.3200 0.8363 18 -0.38 0.7065 fpop ws 0 . . . . mpop rb -2.8383 0.7177 17 -3.95 0.0010 mpop ws 0 . . . . fpop*mpop rb rb 3.3477 0.8325 81 4.02 0.0001 fpop*mpop rb ws 0 . . . . fpop*mpop ws rb 0 . . . . fpop*mpop ws ws 0 . . . . Type 3 Tests of Fixed Effects Num Den Effect DF DF F Value Pr > F fpop 1 18 3.24 0.0887 mpop 1 17 4.60 0.0468 fpop*mpop 1 81 16.17 0.0001 Least Squares Means Standard Effect fpop mpop Estimate Error DF t Value Pr > |t| Alpha fpop*mpop rb rb 1.3649 0.6623 81 2.06 0.0425 0.05 fpop*mpop rb ws 0.8556 0.6341 81 1.35 0.1810 0.05 fpop*mpop ws rb -1.6628 0.6765 81 -2.46 0.0161 0.05 fpop*mpop ws ws 1.1755 0.6513 81 1.80 0.0748 0.05 Least Squares Means Effect fpop mpop Lower Upper fpop*mpop rb rb 0.04711 2.6828 fpop*mpop rb ws -0.4061 2.1172 fpop*mpop ws rb -3.0089 -0.3167 fpop*mpop ws ws -0.1203 2.4714 Differences of Least Squares Means Standard Effect fpop mpop _fpop _mpop Estimate Error DF t Value Pr > |t| fpop*mpop rb rb rb ws 0.5094 0.6494 81 0.78 0.4351 fpop*mpop rb rb ws rb 3.0278 0.8827 81 3.43 0.0010 fpop*mpop rb rb ws ws 0.1894 0.9289 81 0.20 0.8389 fpop*mpop rb ws ws rb 2.5184 0.9270 81 2.72 0.0081 fpop*mpop rb ws ws ws -0.3200 0.8363 81 -0.38 0.7030 fpop*mpop ws rb ws ws -2.8383 0.7177 81 -3.95 0.0002 Differences of Least Squares Means Effect fpop mpop _fpop _mpop Alpha Lower Upper fpop*mpop rb rb rb ws 0.05 -0.7827 1.8015 fpop*mpop rb rb ws rb 0.05 1.2715 4.7840 fpop*mpop rb rb ws ws 0.05 -1.6587 2.0376 fpop*mpop rb ws ws rb 0.05 0.6740 4.3627 fpop*mpop rb ws ws ws 0.05 -1.9839 1.3439 fpop*mpop ws rb ws ws 0.05 -4.2663 -1.4104 GLIMMIX Model Statistics Description Value Deviance 85.2361 Scaled Deviance 128.2962 Pearson Chi-Square 63.5935 Scaled Pearson Chi-Square 95.7201 Extra-Dispersion Scale 0.6644 - EXAMPLE 2: Simulated overdispersed binomial data
-
As in Breslow and Clayton (1993), p. 14.
data bin; seed = 78080347; n = 1; do k = 1 to 100; bb = rannor(seed); do l = 1 to 7; eta = -2.1972246 + bb; p = exp(eta)/(1 + exp(eta)); y = ranbin(seed,n,p); output; end; end; drop seed l; run; /* Define the GLIMMIX macro */ %inc "<location of your file containing the GLIMMIX macro>"; /*---PQL analysis---*/ %glimmix(data=bin, procopt=noprofile, stmts=%str( class k; model y/n = / cl; random int / sub=k; parms (0.2) (1) / eqcons=2; ) ) run; - RESULTS:
-
The GLIMMIX Macro Data Set : WORK.BIN Error Distribution : BINOMIAL Link Function : LOGIT Response Variable : Y/N GLIMMIX Iteration History Iteration Convergence criterion 1 2 2 0.4629372605 3 0.0357933422 4 0.006966794 5 0.0004458137 6 8.536141E-10 Output from final Proc Mixed run: The Mixed Procedure Model Information Data Set WORK._DS Dependent Variable _z Weight Variable _w Covariance Structure Variance Components Subject Effect k Estimation Method REML Residual Variance Method Parameter Fixed Effects SE Method Model-Based Degrees of Freedom Method Containment Class Level Information Class Levels Values k 100 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 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 Dimensions Covariance Parameters 2 Columns in X 1 Columns in Z Per Subject 1 Subjects 100 Max Obs Per Subject 7 Number of Observations Number of Observations Read 700 Number of Observations Used 700 Number of Observations Not Used 0 Parameter Search CovP1 CovP2 Res Log Like -2 Res Log Like 0.2118 1.0000 -1724.5749 3449.1498 Iteration History Iteration Evaluations -2 Res Log Like Criterion 1 1 3449.14983271 0.00000000 Convergence criteria met. Covariance Parameter Estimates Cov Parm Subject Estimate Intercept k 0.2118 Residual 1.0000 Fit Statistics -2 Res Log Likelihood 3449.1 AIC (smaller is better) 3451.1 AICC (smaller is better) 3451.2 BIC (smaller is better) 3453.8 PARMS Model Likelihood Ratio Test DF Chi-Square Pr > ChiSq 1 0.00 1.0000 Solution for Fixed Effects Standard Effect Estimate Error DF t Value Pr > |t| Alpha Intercept -1.8873 0.1208 99 -15.62 <.0001 0.05 Solution for Fixed Effects Effect Lower Upper Intercept -2.1270 -1.6476 GLIMMIX Model Statistics Description Value Deviance 517.1315 Scaled Deviance 517.1315 Pearson Chi-Square 609.0697 Scaled Pearson Chi-Square 609.0697 Extra-Dispersion Scale 1.0000 - EXAMPLE 3: Ship data
-
From McCullagh and Nelder (1989), Section 6.3.
data ship; length type $1. year $7. period $8.; input type year period service y; datalines; B 1965-69 1975-79 9.9218 53 C 1965-69 1975-79 6.5162 1 D 1965-69 1975-79 5.2575 0 E 1965-69 1975-79 6.0799 7 A 1965-69 1975-79 6.9985 4 A 1965-69 1960-74 6.9985 3 B 1965-69 1960-74 10.2615 58 C 1965-69 1960-74 6.6606 0 D 1965-69 1960-74 5.6630 0 E 1965-69 1960-74 6.6708 7 A 1970-64 1960-74 7.3212 6 B 1970-64 1960-74 8.8628 12 C 1970-64 1960-74 6.6631 6 D 1970-64 1960-74 5.8551 2 E 1970-64 1960-74 7.0536 5 A 1970-64 1975-79 8.1176 18 B 1970-64 1975-79 9.4803 44 C 1970-64 1975-79 7.5746 2 D 1970-64 1975-79 7.0967 11 E 1970-64 1975-79 7.6783 12 A 1975-69 1975-79 7.7160 11 B 1975-69 1975-79 8.8702 18 C 1975-69 1975-79 5.6131 1 D 1975-69 1975-79 7.6261 4 E 1975-69 1975-79 6.2953 1 A 1960-64 1960-74 4.8442 0 B 1960-64 1960-74 10.7118 39 C 1960-64 1960-74 7.0724 1 D 1960-64 1960-74 5.5255 0 E 1960-64 1960-74 3.8067 0 A 1960-64 1975-79 4.1431 0 B 1960-64 1975-79 9.7513 29 C 1960-64 1975-79 6.3135 1 D 1960-64 1975-79 4.6540 0 run; /* Define the GLIMMIX macro */ %inc "<location of your file containing the GLIMMIX macro>"; /*---poisson regression (log-linear model) with random effects, parameterization for TYPE matches McCullagh and Nelder's---*/ %glimmix(data=ship, procopt=order=data, stmts=%str( class type year period; model y = type / solution; random year|period; estimate 'E vs. Others' type -1 -1 -1 4 -1 / divisor=4 cl; ), error=poisson, link=log, offset=service ) run; - RESULTS:
-
The GLIMMIX Macro Data Set : WORK.SHIP Error Distribution : POISSON Link Function : LOG Response Variable : Y GLIMMIX Iteration History Iteration Convergence criterion 1 2 2 0.2090120075 3 0.0377717984 4 0.0012833596 5 1.5332658E-6 6 1.0416946E-9 Output from final Proc Mixed run: The Mixed Procedure Model Information Data Set WORK._DS Dependent Variable _z Weight Variable _w Covariance Structure Variance Components Estimation Method REML Residual Variance Method Profile Fixed Effects SE Method Model-Based Degrees of Freedom Method Containment Class Level Information Class Levels Values type 5 B C D E A year 4 1965-69 1970-64 1975-69 1960-64 period 2 1975-79 1960-74 Dimensions Covariance Parameters 4 Columns in X 6 Columns in Z 13 Subjects 1 Max Obs Per Subject 34 Number of Observations Number of Observations Read 34 Number of Observations Used 34 Number of Observations Not Used 0 Parameter Search CovP1 CovP2 CovP3 CovP4 Variance Res Log Like 0.1174 0.07066 0 1.6702 1.6702 -41.1538 Parameter Search -2 Res Log Like 82.3076 Iteration History Iteration Evaluations -2 Res Log Like Criterion 1 1 82.30761547 0.00000000 Convergence criteria met. Covariance Parameter Estimates Cov Parm Estimate year 0.1174 period 0.07066 year*period 0 Residual 1.6702 Fit Statistics -2 Res Log Likelihood 82.3 AIC (smaller is better) 88.3 AICC (smaller is better) 89.3 BIC (smaller is better) 86.5 PARMS Model Likelihood Ratio Test DF Chi-Square Pr > ChiSq 2 0.00 1.0000 Solution for Fixed Effects Standard Effect type Estimate Error DF t Value Pr > |t| Intercept -5.6799 0.3286 1 -17.28 0.0368 type B -0.5798 0.2277 23 -2.55 0.0180 type C -0.6984 0.4248 23 -1.64 0.1138 type D -0.08703 0.3746 23 -0.23 0.8183 type E 0.3301 0.3046 23 1.08 0.2897 type A 0 . . . . Type 3 Tests of Fixed Effects Num Den Effect DF DF F Value Pr > F type 4 23 4.38 0.0089 Estimates Standard Label Estimate Error DF t Value Pr > |t| Alpha E VS. OTHERS 0.6714 0.2675 23 2.51 0.0196 0.05 Estimates Label Lower Upper E VS. OTHERS 0.1180 1.2249 GLIMMIX Model Statistics Description Value Deviance 39.5309 Scaled Deviance 23.6678 Pearson Chi-Square 42.9235 Scaled Pearson Chi-Square 25.6990 Extra-Dispersion Scale 1.6702
Right-click on the appropriate link below and select Save to save
the %GLIMMIX macro definition
to a file. It is recommended that you name the file
glimmix.sas.
Download and save %GLIMMIX for Version 8 or later.
Download and save %GLIMMIX for Version 6.12.
The %GLIMMIX macro uses iteratively reweighted likelihoods to fit the generalized linear mixed model.
| Type: | Sample |
| Topic: | SAS Reference ==> Procedures ==> MIXED |
| Date Modified: | 2007-08-14 03:03:10 |
| Date Created: | 2005-01-17 08:28:25 |
Operating System and Release Information
| Product Family | Product | Host | SAS Release | |
| Starting | Ending | |||
| SAS System | SAS/STAT | All | 6.12 | n/a |