A STATA CODE FOR MULTILEVEL MODEL

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1 Appendix A STATA CODE FOR MULTILEVEL MODEL ********************************************************************** ********************** ********** Two-level Multilevel random-intercepts and random slopes model ******* ********** Rajeev Kumar: Department Biostatistics and Medical Informatics ******** ************************************************************************************ *************************** STATA 11.0 stware was applied to fit the multilevel models, complex multilevel model and bootstrapping and other diagnostics was performed using MlwiN stware. The STATA codes to fit the various multilevel models, graphs, comparison nested models, testing assumptions multilevel models are as follows: Brief explanation STATA command : The syntax for estimating multilevel models in STATA starts from.xtmixed followed by response and a list covariates/independent s followed by double vertical line after that cluster (journal in our case) and random effect s are specified ( random slope). For random intercept model only cluster followed by colon. By default STATA stware RMLE method, to change this method; option command was and specifies mle for maximum likelihood estimation. User can also specify the other options. The syntax empty model in our study is:.xtmixed quality_score Journal:, mle var Use c:\ internationaldata.dta, clear *Command to draw the journal wise box-whisker plot quality score.graph box quality_score, over(journalname).graph save Graph path name\filename.gph *To run the multilevel command without any covariate(null model).xtmixed quality_score Journal:, mle var *Command to store the estimates the null model as nullmodel.estimates store nullmodel *Command to predict the random intercept residuals.predict u0, reffects *reffects calculate the shrunken residuals/best linear unbiased prediction random intercepts. predict u0se, reses *reses calculate the standard errors shrunken residuals.egen pickone==tag(journal).sort u0.gen u0rank=sum(pickone) *to draw the caterpillar graph with 95% confidence band intercept residuals.serrbar u0, u0se u0rank if pickone=1, scale(1.96) yline(0) Rajeev Kumar Multilevel Modeling Page 196

2 *Command generates the five-block years. gen block_year=0 if (year=2000 year=2001).replace block_year=1 if (year=2002 year=2003).replace block_year=2 if (year=2004 year=2005).replace block_year=3 if (year=2006 year=2007).replace block_year=4 if(year=2008 year=2009) *Command forlog(natural) transformation sample size and calculation grand mean and centering.gen logsample_size=ln(sample_size).egen mean_logsample=mean(logsample_size).egen mean_author=mean(author).gen center_logsample=logsample_size mean_logsample.gen center_author=author mean_author ** Command for graphically testing the non-linearity sample size and authors with quality score across the journals.lowess quality_score center_logsample, addplot((lfit quality score center_logsample)(qfit quality_score center_logsample)) by(journal).lowess quality_score center_logsample, addplot((lfit quality score center_author)(qfit quality_score center_author)) by(journal) ****Multilevel commands to run the random intercept model for each level-1 covariates.xtmixed quality_score StatisticianorEpidemiolgist Journal:, mle var.estimates store statistician.xtmixed quality_score center_logsample Journal:, mle var.estimates store logsample_center *Command to create the dummy s for stware.gen sas_st=1 if stware_code==2.gen stata_st=1 if stware_code==3.gen spss_st=1 if stware _code==1.gen other_st=1 if stware_code=9.xtmixed quality_score sas_st stat_st spss_st other_st Journal:, mle var.estimates store stware.xtmixed quality_score center_author Journal:, mle var.estimates store author *Block-year is five year block code as 0,1,2,3,4 and considered as continuous.xtmixed quality_score Block_year Journal:, mle var.estimates store blockyear.xtmixed quality_score firstcountrystatus Journal:, mle var.estimates store firstauthor Rajeev Kumar Multilevel Modeling Page 197

3 *Likelihood ratio test to compare null model with random intercept models.lrtest nullmodel statistician.lrtest nullmodel logsample_center.lrtest nullmodel stware.lrtest nullmodel author.lrtest nullmodel blockyear ***Command for random intercepts model considering covariates with p<0.25 into model (STEP-2) center_author Block_year firstcountrystatus Journal:, mle var.estimates store finalrandomintercept *Command for checking the random slopes model for each the article level covariates one-byone center_author Block_year firstcountrystatus Journal: StatisticianorEpidemiolgist,.estimates store randslopstatistician center_author Block_year firstcountrystatus Journal:center_logsample, covariance(unstructured) mle var.estimates store randslopssize center_author Block_year firstcountrystatus Journal: center_author, covariance(unstructured) mle var.estimates store randslopauthor center_author Block_year firstcountrystatus Journal:Block_year,.estimates store randslopblockyear center_author Block_year firstcountrystatus Journal:firstcountrystatus, covariance(unstructured) mle var.estimates store randslopfirstcountrystatus **LR test to compare the final model step-2 with above models.lrtest finalrandomintercept randslopstatistician.lrtest finalrandomintercept randslopssize.lrtest finalrandomintercept randslopauthor.lrtest finalrandomintercept randslopblockyear.lrtest finalrandomintercept randslopfirstcountrystatus *final random intercepts and random slopes model (Step-3) Rajeev Kumar Multilevel Modeling Page 198

4 center_author Block_year firstcountrystatus Journal:center_logsample, covariance(unstructured) mle var.estimates store finalrandinterceptslop **command to include the journals level covariates in the model obtained from step-3 (step-4) center_author Block_year firstcountrystatus speciality_code Journal:center_logsample, ** Cross-level interaction.gen samplesizexspeciality=center_logsample*speciality_code **command to include the cross level interaction in the step-4 final model center_author Block_year firstcountrystatus speciality_codesamplesizexspeciality Journal:center_logsample, *Final model for international journals study center_author Block_year firstcountrystatus speciality_code Journal:center_logsample,.estimates store finalstudymodel.predict f1 f0, reffects.predict f1 f0, reses.graph box f1 f0 if pickone==1 *Command to find the article level standard residuals. predict residual_level_1 rstandard *Command to draw the scater plot level-1 residuals against center_logsample.scatter residuals_level_1 center_logsample, yline(0) xline(0) Qnorm residual_level_1, yline(o) xline(0) *Command to test the normality intercepts and slopes residuals using Shapiro-Francia and skewness and kurtosis test.sfrancia f1 f0 if pickone==1.sktest f1 f0 if pickone==1 *Command to apply Leven s test for testing homogeneity variance articles level residuals across the journals.robvar residual_level_1, by(journal) **Command to calculate the article level residuals for involvement statistician or non-involvement.xtmixed std_score StatisticanorEpidemilogist Code_indian sas_st stat_st center_author block_code center_logsample speciality_code Journal: center_logsample, covariance(unstructured) residuals(independent, by ( StatisticanorEpidemilogist)) mle var Rajeev Kumar Multilevel Modeling Page 199

5 Excel format to record raw data Appendix B Article per journal Article per block Random article per block Journal Title the article Authors name Journal name Year and volume Block-year Number MLR articles Journal publishing country name Two digit 1 to 50 Twodigit 1 to 10 Threedigit Twodigit 1 to 30 This information recorded after evaluated the MLR articles Specialit y journal Number issue per year Impac t factor as on 2009 No. author' s Data is matche d paired Type logistic (conditional or unconditional) Stware Sampl e size the study year Name the countr y first author Status first author income country Name stwar e C=conditional UC=unconditiona l Total sampl e size Low+middle= 0 and high =1 income group Rajeev Kumar Multilevel Modeling Page 200

6 Type model IF Predicte d model than intercept is given or not Involvemen t Statistician or Epidemiolo gist as coauthor Suffici ent events Sample size minimum event Number s conside red for model Confor mity gradien t tested to test the conformi ty gradient Checking Interactio n Colline arity tested Valida tion done Metho d valida tion P- value ORS, CI P=predi cation, NP=Oth ers t fulfilled 1=Fulfill ed 2=NA Name method if Name valida tion if Goodn ess fit done for goodnes s fit Selection independen t for selecting the Coding independ ent Model procedur e name procedur e sample size descriptio n given or not to convert continuous into categorical Missing treatment to treat missing value Name method for testing goodness for selecting the s Name model procedure 0 =No treatment 1=yes 2= NA Imputatio n method or name treatment applied if Rajeev Kumar Multilevel Modeling Page 201

7 Appendix C: Table showing the journal-wise and criterion wise proportion manuscripts that met the recommended criteria Jour nal Num ber Journal Name Suffici ent case (10:1) Conformit y linear gradient Interaction s or modifier effect Testing collineari ty validati on P-value OR and 95% CI Goodnes s--fit or classifica tion summary Selection plausible s Coding variabl e Model Proced ure 1 Academic Emergency Medicine American Journal t l Anesthesia & Analgesia Annals Surgery Annals Thoracic surgery Archives Internal Medicine British Journal cancer British Journal Ophthalmology Cerebrovascular Diseases Chest Clinical Infectious Diseases CMAJ Diabetes Care Environ Health Perspective Epidemiology Infection European Journal Public H Fertility lth and sterility Heart Hypertension Intensive Care Medicine Lancet NEJM Neurology Obstetric Gynecology Pediatrics Sexually Transmitted Disease Spine Stroke The American Journal P Transplantation hi t Total Rajeev Kumar Multilevel Modeling Page 202