Automatic Short Form Creation for scales. Currently, the Ant ColonyOptimization (ACO) Algorithm and the Tabu search are implemented. Theoriginal R implementation for the ACO algorithm is from Leite, Huang, &Marcoulides (2008), while the Tabusearch function was taken from Marcoulides & Falk(2018). There does not yet seem tobe an application of Simulated Annealing (SA) within psychometrics, butDrezner & Marcoulides, 1999 (inMultiple Linear Regression Viewpoints,Volume 25(2); not available online) used SA for multiple regressionmodel selection; this package appears to be the first to implement SAfor psychometric models.
This document was created on 2024-05-22.
install.packages("ShortForm")# the CRAN-approved versionrequire("devtools")devtools::install_github("AnthonyRaborn/ShortForm",branch="devel")# the developmental versionHere are some (slightly modified) examples from the help documentationusing lavaan. Be warned, the algorithms may take some time to converge,particularly with large forms, multiple dimensions, and differentsettings. The time for these examples to converge on a laptop with anIntel Core i7 8th Gen processor is printed at the bottom. See thesessionInfo() below.
sessionInfo()## R version 4.3.3 (2024-02-29 ucrt)## Platform: x86_64-w64-mingw32/x64 (64-bit)## Running under: Windows 11 x64 (build 22621)#### Matrix products: default###### locale:## [1] LC_COLLATE=English_United States.utf8## [2] LC_CTYPE=English_United States.utf8## [3] LC_MONETARY=English_United States.utf8## [4] LC_NUMERIC=C## [5] LC_TIME=English_United States.utf8#### time zone: America/Phoenix## tzcode source: internal#### attached base packages:## [1] stats graphics grDevices utils datasets methods base#### loaded via a namespace (and not attached):## [1] compiler_4.3.3 fastmap_1.1.1 cli_3.6.2 tools_4.3.3## [5] htmltools_0.5.7 rstudioapi_0.15.0 yaml_2.3.8 rmarkdown_2.26## [9] knitr_1.45 xfun_0.42 digest_0.6.35 rlang_1.1.3## [13] evaluate_0.23
start.time.ACO<- Sys.time()library(ShortForm,quietly=T)## Package 'ShortForm' version 0.5.4# using simulated test data and the default values for lavaan.model.specsset.seed(1)# create simulation data from the `psych` package# four factors, 12 items each, 48 total items# factor loading matrix - not quite simple structurefxMatrix<-matrix(data= c(rep(x= c(.8,.8,.4,.3),times=3), rep(0.2,times=3*4*3),# first factor loadings rep(0.2,times=3*4), rep(x= c(.8,.8,.4,.3),times=3), rep(0.2,times=3*4*2),# second factor loadings rep(0.2,times=3*4*2), rep(x= c(.8,.8,.4,.3),times=3), rep(0.2,times=3*4),# third factor loadings rep(0.2,times=3*4*3), rep(x= c(.8,.8,.4,.3),times=3)# fourth factor loadings ),ncol=4)# factor correlation matrix - all factors uncorrelatedPhiMatrix<-matrix(data= c(1,0,0,0,0,1,0,0,0,0,1,0,0,0,0,1),ncol=4)antData<-psych::sim(fx=fxMatrix,Phi=PhiMatrix,n=600,mu= c(-2,-1,1,2),raw=TRUE )$observed# observed is the simulated observed datacolnames(antData)= paste0("Item",1:48)antModel<-'Trait1 =~ Item1 + Item2 + Item3 + Item4 + Item5 + Item6 + Item7 + Item8 + Item9 + Item10 + Item11 + Item12Trait2 =~ Item13 + Item14 + Item15 + Item16 + Item17 + Item18 + Item19 + Item20 + Item21 + Item22 + Item23 + Item24Trait3 =~ Item25 + Item26 + Item27 + Item28 + Item29 + Item30 + Item31 + Item32 + Item33 + Item34 + Item35 + Item36Trait4 =~ Item37 + Item38 + Item39 + Item40 + Item41 + Item42 + Item43 + Item44 + Item45 + Item46 + Item47 + Item48'# then, create the list of the items by the factorslist.items<-list( paste0("Item",1:12), paste0("Item",13:24), paste0("Item",25:36), paste0("Item",37:48) )# finally, call the function with some minor changes to the default values.abilityShortForm= antcolony.lavaan(data=antData,ants=10,evaporation=0.9,antModel=antModel,list.items=list.items,full=48,i.per.f= c(6,6,6,6),lavaan.model.specs=list(model.type="cfa",auto.var=T,estimator="default",ordered=NULL,int.ov.free=TRUE,int.lv.free=FALSE,auto.fix.first=TRUE,auto.fix.single=TRUE,std.lv=FALSE,auto.cov.lv.x=TRUE,auto.th=TRUE,auto.delta=TRUE,auto.cov.y=TRUE),factors= c("Trait1","Trait2","Trait3","Trait4"),steps=100,max.run=100,parallel=T)## Run number 1 and ant number 1. Run number 1 and ant number 2. Run number 1 and ant number 3. Run number 1 and ant number 4. Run number 1 and ant number 5. Run number 1 and ant number 6. Run number 1 and ant number 7. Run number 1 and ant number 8. Run number 1 and ant number 9. Run number 1 and ant number 10. Run number 2 and ant number 1. Run number 2 and ant number 2. Run number 2 and ant number 3. Run number 2 and ant number 4. Run number 2 and ant number 5. Run number 2 and ant number 6. Run number 2 and ant number 7. Run number 2 and ant number 8. Run number 2 and ant number 9. Run number 2 and ant number 10. Run number 3 and ant number 1. Run number 3 and ant number 2. Run number 3 and ant number 3. Run number 3 and ant number 4. Run number 3 and ant number 5. Run number 3 and ant number 6. Run number 3 and ant number 7. Run number 3 and ant number 8. Run number 3 and ant number 9. Run number 3 and ant number 10. Run number 4 and ant number 1. Run number 4 and ant number 2. Run number 4 and ant number 3. Run number 4 and ant number 4. Run number 4 and ant number 5. Run number 4 and ant number 6. Run number 4 and ant number 7. Run number 4 and ant number 8. Run number 4 and ant number 9. Run number 4 and ant number 10. Run number 5 and ant number 1. Run number 5 and ant number 2. Run number 5 and ant number 3. Run number 5 and ant number 4. Run number 5 and ant number 5. Run number 5 and ant number 6. Run number 5 and ant number 7. Run number 5 and ant number 8. Run number 5 and ant number 9. Run number 5 and ant number 10. Run number 6 and ant number 1. Run number 6 and ant number 2. Run number 6 and ant number 3. Run number 6 and ant number 4. Run number 6 and ant number 5. Run number 6 and ant number 6. Run number 6 and ant number 7. Run number 6 and ant number 8. Run number 6 and ant number 9. Run number 6 and ant number 10. Run number 7 and ant number 1. Run number 7 and ant number 2. Run number 7 and ant number 3. Run number 7 and ant number 4. Run number 7 and ant number 5. Run number 7 and ant number 6. Run number 7 and ant number 7. Run number 7 and ant number 8. Run number 7 and ant number 9. Run number 7 and ant number 10. Run number 8 and ant number 1. Run number 8 and ant number 2. Run number 8 and ant number 3. Run number 8 and ant number 4. Run number 8 and ant number 5. Run number 8 and ant number 6. Run number 8 and ant number 7. Run number 8 and ant number 8. Run number 8 and ant number 9. Run number 8 and ant number 10. Run number 9 and ant number 1. Run number 9 and ant number 2. Run number 9 and ant number 3. Run number 9 and ant number 4. Run number 9 and ant number 5. Run number 9 and ant number 6. Run number 9 and ant number 7. Run number 9 and ant number 8. Run number 9 and ant number 9. Run number 9 and ant number 10. Run number 10 and ant number 1. Run number 10 and ant number 2. Run number 10 and ant number 3. Run number 10 and ant number 4. Run number 10 and ant number 5. Run number 10 and ant number 6. Run number 10 and ant number 7. Run number 10 and ant number 8. Run number 10 and ant number 9. Run number 10 and ant number 10. Run number 11 and ant number 1. Run number 11 and ant number 2. Run number 11 and ant number 3. Run number 11 and ant number 4. Run number 11 and ant number 5. Run number 11 and ant number 6. Run number 11 and ant number 7. Run number 11 and ant number 8. Run number 11 and ant number 9. Run number 11 and ant number 10. Run number 12 and ant number 1. Run number 12 and ant number 2. Run number 12 and ant number 3. Run number 12 and ant number 4. Run number 12 and ant number 5. Run number 12 and ant number 6. Run number 12 and ant number 7. Run number 12 and ant number 8. Run number 12 and ant number 9. Run number 12 and ant number 10. Run number 13 and ant number 1. Run number 13 and ant number 2. Run number 13 and ant number 3. Run number 13 and ant number 4. Run number 13 and ant number 5. Run number 13 and ant number 6. Run number 13 and ant number 7. Run number 13 and ant number 8. Run number 13 and ant number 9. Run number 13 and ant number 10. Run number 14 and ant number 1. Run number 14 and ant number 2. Run number 14 and ant number 3. Run number 14 and ant number 4. Run number 14 and ant number 5. Run number 14 and ant number 6. Run number 14 and ant number 7. Run number 14 and ant number 8. Run number 14 and ant number 9. Run number 14 and ant number 10. Run number 15 and ant number 1. Run number 15 and ant number 2. Run number 15 and ant number 3. Run number 15 and ant number 4. Run number 15 and ant number 5. Run number 15 and ant number 6. Run number 15 and ant number 7. Run number 15 and ant number 8. Run number 15 and ant number 9. Run number 15 and ant number 10. Run number 16 and ant number 1. Run number 16 and ant number 2. Run number 16 and ant number 3. Run number 16 and ant number 4. Run number 16 and ant number 5. Run number 16 and ant number 6. Run number 16 and ant number 7. Run number 16 and ant number 8. Run number 16 and ant number 9. Run number 16 and ant number 10. Run number 17 and ant number 1. Run number 17 and ant number 2. Run number 17 and ant number 3. Run number 17 and ant number 4. Run number 17 and ant number 5. Run number 17 and ant number 6. Run number 17 and ant number 7. Run number 17 and ant number 8. Run number 17 and ant number 9. Run number 17 and ant number 10. Run number 18 and ant number 1. Run number 18 and ant number 2. Run number 18 and ant number 3. Run number 18 and ant number 4. Run number 18 and ant number 5. Run number 18 and ant number 6. Run number 18 and ant number 7. Run number 18 and ant number 8. Run number 18 and ant number 9. Run number 18 and ant number 10. Run number 19 and ant number 1. Run number 19 and ant number 2. Run number 19 and ant number 3. Run number 19 and ant number 4. Run number 19 and ant number 5. Run number 19 and ant number 6. Run number 19 and ant number 7. Run number 19 and ant number 8. Run number 19 and ant number 9. Run number 19 and ant number 10. Run number 20 and ant number 1. Run number 20 and ant number 2. Run number 20 and ant number 3. Run number 20 and ant number 4. Run number 20 and ant number 5. Run number 20 and ant number 6. Run number 20 and ant number 7. Run number 20 and ant number 8. Run number 20 and ant number 9. Run number 20 and ant number 10. Run number 21 and ant number 1. Run number 21 and ant number 2. Run number 21 and ant number 3. Run number 21 and ant number 4. Run number 21 and ant number 5. Run number 21 and ant number 6. Run number 21 and ant number 7. Run number 21 and ant number 8. Run number 21 and ant number 9. Run number 21 and ant number 10. Run number 22 and ant number 1. Run number 22 and ant number 2. Run number 22 and ant number 3. Run number 22 and ant number 4. Run number 22 and ant number 5. Run number 22 and ant number 6. Run number 22 and ant number 7. Run number 22 and ant number 8. Run number 22 and ant number 9. Run number 22 and ant number 10. Run number 23 and ant number 1. Run number 23 and ant number 2. Run number 23 and ant number 3. Run number 23 and ant number 4. Run number 23 and ant number 5. Run number 23 and ant number 6. Run number 23 and ant number 7. Run number 23 and ant number 8. Run number 23 and ant number 9. Run number 23 and ant number 10. Run number 24 and ant number 1. Run number 24 and ant number 2. Run number 24 and ant number 3. Run number 24 and ant number 4. Run number 24 and ant number 5. Run number 24 and ant number 6. Run number 24 and ant number 7. Run number 24 and ant number 8. Run number 24 and ant number 9. Run number 24 and ant number 10. Run number 25 and ant number 1. Run number 25 and ant number 2. Run number 25 and ant number 3. Run number 25 and ant number 4. Run number 25 and ant number 5. Run number 25 and ant number 6. Run number 25 and ant number 7. Run number 25 and ant number 8. Run number 25 and ant number 9. Run number 25 and ant number 10. Run number 26 and ant number 1. Run number 26 and ant number 2. Run number 26 and ant number 3. Run number 26 and ant number 4. Run number 26 and ant number 5. Run number 26 and ant number 6. Run number 26 and ant number 7. Run number 26 and ant number 8. Run number 26 and ant number 9. Run number 26 and ant number 10. Run number 27 and ant number 1. Run number 27 and ant number 2. Run number 27 and ant number 3. Run number 27 and ant number 4. Run number 27 and ant number 5. Run number 27 and ant number 6. Run number 27 and ant number 7. Run number 27 and ant number 8. Run number 27 and ant number 9. Run number 27 and ant number 10. Run number 28 and ant number 1. Run number 28 and ant number 2. Run number 28 and ant number 3. Run number 28 and ant number 4. Run number 28 and ant number 5. Run number 28 and ant number 6. Run number 28 and ant number 7. Run number 28 and ant number 8. Run number 28 and ant number 9. Run number 28 and ant number 10. Run number 29 and ant number 1. Run number 29 and ant number 2. Run number 29 and ant number 3. Run number 29 and ant number 4. Run number 29 and ant number 5. Run number 29 and ant number 6. Run number 29 and ant number 7. Run number 29 and ant number 8. Run number 29 and ant number 9. Run number 29 and ant number 10. Run number 30 and ant number 1. Run number 30 and ant number 2. Run number 30 and ant number 3. Run number 30 and ant number 4. Run number 30 and ant number 5. Run number 30 and ant number 6. Run number 30 and ant number 7. Run number 30 and ant number 8. Run number 30 and ant number 9. Run number 30 and ant number 10. Run number 31 and ant number 1. Run number 31 and ant number 2. Run number 31 and ant number 3. Run number 31 and ant number 4. Run number 31 and ant number 5. Run number 31 and ant number 6. Run number 31 and ant number 7. Run number 31 and ant number 8. Run number 31 and ant number 9. Run number 31 and ant number 10. Run number 32 and ant number 1. Run number 32 and ant number 2. Run number 32 and ant number 3. Run number 32 and ant number 4. Run number 32 and ant number 5. Run number 32 and ant number 6. Run number 32 and ant number 7. Run number 32 and ant number 8. Run number 32 and ant number 9. Run number 32 and ant number 10. Run number 33 and ant number 1. Run number 33 and ant number 2. Run number 33 and ant number 3. Run number 33 and ant number 4. Run number 33 and ant number 5. Run number 33 and ant number 6. Run number 33 and ant number 7. Run number 33 and ant number 8. Run number 33 and ant number 9. Run number 33 and ant number 10. Run number 34 and ant number 1. Run number 34 and ant number 2. Run number 34 and ant number 3. Run number 34 and ant number 4. Run number 34 and ant number 5. Run number 34 and ant number 6. Run number 34 and ant number 7. Run number 34 and ant number 8. Run number 34 and ant number 9. Run number 34 and ant number 10. Run number 35 and ant number 1. Run number 35 and ant number 2. Run number 35 and ant number 3. Run number 35 and ant number 4. Run number 35 and ant number 5. Run number 35 and ant number 6. Run number 35 and ant number 7. Run number 35 and ant number 8. Run number 35 and ant number 9. Run number 35 and ant number 10. Run number 36 and ant number 1. Run number 36 and ant number 2. Run number 36 and ant number 3. Run number 36 and ant number 4. Run number 36 and ant number 5. Run number 36 and ant number 6. Run number 36 and ant number 7. Run number 36 and ant number 8. Run number 36 and ant number 9. Run number 36 and ant number 10. Run number 37 and ant number 1. Run number 37 and ant number 2. Run number 37 and ant number 3. Run number 37 and ant number 4. Run number 37 and ant number 5. Run number 37 and ant number 6. Run number 37 and ant number 7. Run number 37 and ant number 8. Run number 37 and ant number 9. Run number 37 and ant number 10. Run number 38 and ant number 1. Run number 38 and ant number 2. Run number 38 and ant number 3. Run number 38 and ant number 4. Run number 38 and ant number 5. Run number 38 and ant number 6. Run number 38 and ant number 7. Run number 38 and ant number 8. Run number 38 and ant number 9. Run number 38 and ant number 10. Run number 39 and ant number 1. Run number 39 and ant number 2. Run number 39 and ant number 3. Run number 39 and ant number 4. Run number 39 and ant number 5. Run number 39 and ant number 6. Run number 39 and ant number 7. Run number 39 and ant number 8. Run number 39 and ant number 9. Run number 39 and ant number 10. Run number 40 and ant number 1. Run number 40 and ant number 2. Run number 40 and ant number 3. Run number 40 and ant number 4. Run number 40 and ant number 5. Run number 40 and ant number 6. Run number 40 and ant number 7. Run number 40 and ant number 8. Run number 40 and ant number 9. Run number 40 and ant number 10. Run number 41 and ant number 1. Run number 41 and ant number 2. Run number 41 and ant number 3. Run number 41 and ant number 4. Run number 41 and ant number 5. Run number 41 and ant number 6. Run number 41 and ant number 7. Run number 41 and ant number 8. Run number 41 and ant number 9. Run number 41 and ant number 10. Run number 42 and ant number 1. Run number 42 and ant number 2. Run number 42 and ant number 3. Run number 42 and ant number 4. Run number 42 and ant number 5. Run number 42 and ant number 6. Run number 42 and ant number 7. Run number 42 and ant number 8. Run number 42 and ant number 9. Run number 42 and ant number 10. Run number 43 and ant number 1. Run number 43 and ant number 2. Run number 43 and ant number 3. Run number 43 and ant number 4. Run number 43 and ant number 5. Run number 43 and ant number 6. Run number 43 and ant number 7. Run number 43 and ant number 8. Run number 43 and ant number 9. Run number 43 and ant number 10. Run number 44 and ant number 1. Run number 44 and ant number 2. Run number 44 and ant number 3. Run number 44 and ant number 4. Run number 44 and ant number 5. Run number 44 and ant number 6. Run number 44 and ant number 7. Run number 44 and ant number 8. Run number 44 and ant number 9. Run number 44 and ant number 10. Run number 45 and ant number 1. Run number 45 and ant number 2. Run number 45 and ant number 3. Run number 45 and ant number 4. Run number 45 and ant number 5. Run number 45 and ant number 6. Run number 45 and ant number 7. Run number 45 and ant number 8. Run number 45 and ant number 9. Run number 45 and ant number 10. Run number 46 and ant number 1. Run number 46 and ant number 2. Run number 46 and ant number 3. Run number 46 and ant number 4. Run number 46 and ant number 5. Run number 46 and ant number 6. Run number 46 and ant number 7. Run number 46 and ant number 8. Run number 46 and ant number 9. Run number 46 and ant number 10. Run number 47 and ant number 1. Run number 47 and ant number 2. Run number 47 and ant number 3. Run number 47 and ant number 4. Run number 47 and ant number 5. Run number 47 and ant number 6. Run number 47 and ant number 7. Run number 47 and ant number 8. Run number 47 and ant number 9. Run number 47 and ant number 10. Run number 48 and ant number 1. Run number 48 and ant number 2. Run number 48 and ant number 3. Run number 48 and ant number 4. Run number 48 and ant number 5. Run number 48 and ant number 6. Run number 48 and ant number 7. Run number 48 and ant number 8. Run number 48 and ant number 9. Run number 48 and ant number 10. [1] "Compiling results."abilityShortForm# print the results of the final short form## Algorithm: Ant Colony Optimization## Total Run Time: 1.015 mins#### Function call:## antcolony.lavaan(data = antData, ants = 10, evaporation = 0.9, antModel =## antModel, list.items = list.items, full = 48, i.per.f = c(6, 6, 6, 6), factors## = c("Trait1", "Trait2", "Trait3", "Trait4"), steps = 100, lavaan.model.specs## = list(model.type = "cfa", auto.var = T, estimator = "default", ordered## = NULL, int.ov.free = TRUE, int.lv.free = FALSE, auto.fix.first = TRUE,## auto.fix.single = TRUE, std.lv = FALSE, auto.cov.lv.x = TRUE, auto.th = TRUE,## auto.delta = TRUE, auto.cov.y = TRUE), max.run = 100, parallel = T)#### Final Model Syntax:#### Trait1 =~ Item9 + Item2 + Item10 + Item5 + Item11 + Item6## Trait2 =~ Item21 + Item14 + Item13 + Item22 + Item18 + Item17## Trait3 =~ Item29 + Item34 + Item25 + Item30 + Item33 + Item26## Trait4 =~ Item45 + Item46 + Item41 + Item38 + Item37 + Item42plot(abilityShortForm,type='pheromone')# the pheromone plot for class "antcolony"
A similar example can be found in theantcolony.mplus function, butrequires you to have a valid Mplus installation on the computer. It tooka total of 1.06 mins to run this example.
This example demonstrates how to use the Tabu search for modelspecification searches when the original model may be misspecified insome way.
start.time.Tabu<- Sys.time()library(ShortForm,quietly=T)set.seed(2)# create simulation data from the `psych` package# two factors, 12 items total# factor loading matrix - not quite simple structurefxMatrix<-matrix(data= c(# first factor loadings rep(x= c(.8,.8,.6,.6),times=3),# second factor loadings rep(x= c(.2),times=12) ),ncol=2)# factor correlation matrix - all factors uncorrelatedPhiMatrix<-matrix(data= c(1,0,0,1 ),ncol=2)tabuData<-psych::sim(fx=fxMatrix,Phi=PhiMatrix,n=600,raw=TRUE )$observed# observed is the simulated observed datacolnames(tabuData)= paste0("Item",1:12)tabuModel<-'Trait1 =~ Item1 + Item2 + Item3 + Item4 + Item5 + Item6 + 0*Item7 + 0*Item8 + 0*Item9 + 0*Item10 + 0*Item11 + 0*Item12Trait2 =~ 0*Item1 + 0*Item2 + 0*Item3 + 0*Item4 + 0*Item5 + 0*Item6 + Item7 + Item8 + Item9 + Item10 + Item11 + Item12'# fit the initial misspecified model for Tabuinit.model<-lavaan::lavaan(model=tabuModel,data=tabuData,auto.var=TRUE,auto.fix.first=FALSE,std.lv=TRUE,auto.cov.lv.x=FALSE)# use search.prep to prepare for the Tabu searchptab<- search.prep(fitted.model=init.model,loadings=TRUE,fcov=FALSE,errors=FALSE)Tabu_example<- suppressWarnings( tabu.sem(init.model=init.model,ptab=ptab,obj=AIC,niter=20,tabu.size=10) )# the suppressWarning wrapping hides the lavaan WARNING output from improper models## Running iteration 1 of 20. Running iteration 2 of 20. Running iteration 3 of 20. Running iteration 4 of 20. Running iteration 5 of 20. Running iteration 6 of 20. Running iteration 7 of 20. Running iteration 8 of 20. Running iteration 9 of 20. Running iteration 10 of 20. Running iteration 11 of 20. Running iteration 12 of 20. Running iteration 13 of 20. Running iteration 14 of 20. Running iteration 15 of 20. Running iteration 16 of 20. Running iteration 17 of 20. Running iteration 18 of 20. Running iteration 19 of 20. Running iteration 20 of 20.# check the final modelsummary(Tabu_example)## Algorithm: Tabu Search## Total Run Time: 1.908 mins#### lavaan 0.6.17 ended normally after 32 iterations#### Estimator ML## Optimization method NLMINB## Number of model parameters 29#### Number of observations 600#### Model Test User Model:#### Test statistic 42.131## Degrees of freedom 49## P-value (Chi-square) 0.746###### Final Model Syntax:## Trait1 =~ Item1 + Item2 + Item3 + Item4 + Item5 + Item6 + Item7 + Item8 + Item9## + Item10 + Item11 + Item12## Trait2 =~ Item1 + Item3 + Item5 + Item10 + Item11# plot the change in the objective/criterion function over each runplot(Tabu_example)
It took a total of 1.92 mins to run this example.
The next Tabu example demonstrates how to use it to find a short form ofa prespecified length with different data.
start.time.Tabu<- Sys.time()library(ShortForm,quietly=T)# set the seed to reproduce this exampleset.seed(3)# create simulation data from the `psych` package# four factors, 12 items each, 48 total items# factor loading matrix - not quite simple structurefxMatrix<-matrix(data= c(rep(x= c(.8,.8,.4,.3),times=3), rep(0.2,times=3*4*3),# first factor loadings rep(0.2,times=3*4), rep(x= c(.8,.8,.4,.3),times=3), rep(0.2,times=3*4*2),# second factor loadings rep(0.2,times=3*4*2), rep(x= c(.8,.8,.4,.3),times=3), rep(0.2,times=3*4),# third factor loadings rep(0.2,times=3*4*3), rep(x= c(.8,.8,.4,.3),times=3)# fourth factor loadings ),ncol=4)# factor correlation matrix - all factors uncorrelatedPhiMatrix<-matrix(data= c(1,0,0,0,0,1,0,0,0,0,1,0,0,0,0,1),ncol=4)tabuData<-psych::sim(fx=fxMatrix,Phi=PhiMatrix,n=600,mu= c(-2,-1,1,2),raw=TRUE )$observed# observed is the simulated observed datacolnames(tabuData)= paste0("Item",1:48)tabuModel<-'Trait1 =~ Item1 + Item2 + Item3 + Item4 + Item5 + Item6 + Item7 + Item8 + Item9 + Item10 + Item11 + Item12Trait2 =~ Item13 + Item14 + Item15 + Item16 + Item17 + Item18 + Item19 + Item20 + Item21 + Item22 + Item23 + Item24Trait3 =~ Item25 + Item26 + Item27 + Item28 + Item29 + Item30 + Item31 + Item32 + Item33 + Item34 + Item35 + Item36Trait4 =~ Item37 + Item38 + Item39 + Item40 + Item41 + Item42 + Item43 + Item44 + Item45 + Item46 + Item47 + Item48'# specify the criterion function that the Tabu Search minimizes# wrap this in a tryCatch in case a model does not converge!# specify an appropriate error value: since we're minimizing, error value must be largetabuCriterion=function(x) { tryCatch(lavaan::fitmeasures(object=x,fit.measures='chisq'),error=function(e)Inf)}# use the tabuShortForm function# reduce form to the best 12 items, 3 per factortabuShort<- tabuShortForm(initialModel=tabuModel,originalData=tabuData,numItems= c(5,5,5,5),criterion=tabuCriterion,niter=20,tabu.size=10,verbose=FALSE )## Running iteration 1 of 20. Running iteration 2 of 20. Running iteration 3 of 20. Running iteration 4 of 20. Running iteration 5 of 20. Running iteration 6 of 20. Running iteration 7 of 20. Running iteration 8 of 20. Running iteration 9 of 20. Running iteration 10 of 20. Running iteration 11 of 20. Running iteration 12 of 20. Running iteration 13 of 20. Running iteration 14 of 20. Running iteration 15 of 20. Running iteration 16 of 20. Running iteration 17 of 20. Running iteration 18 of 20. Running iteration 19 of 20. Running iteration 20 of 20.# check the chosen modelsummary(tabuShort)## Algorithm: Tabu Search## Total Run Time: 2.137 mins#### lavaan 0.6.17 ended normally after 32 iterations#### Estimator ML## Optimization method NLMINB## Number of model parameters 46#### Number of observations 600#### Model Test User Model:#### Test statistic 129.734## Degrees of freedom 164## P-value (Chi-square) 0.978###### Final Model Syntax:## Trait1 =~ Item1 + Item2 + Item5 + Item6 + Item9## Trait2 =~ Item13 + Item14 + Item17 + Item18 + Item22## Trait3 =~ Item26 + Item29 + Item30 + Item33 + Item34## Trait4 =~ Item39 + Item43 + Item44 + Item47 + Item40# plot the changes in the objective function over each iterationplot(tabuShort)
It took a total of 2.14 mins to run this example.
This example demonstrates the use of simulated annealing for creatingshort forms.
start.time.SA<- Sys.time()library(ShortForm,quietly=T)# create simulation data from the `psych` package# four factors, 12 items each, 48 total items# factor loading matrix - not quite simple structureset.seed(4)fxMatrix<-matrix(data= c(rep(x= c(.8,.8,.4,.3),times=3), rep(0.2,times=3*4*3),# first factor loadings rep(0.2,times=3*4), rep(x= c(.8,.8,.4,.3),times=3), rep(0.2,times=3*4*2),# second factor loadings rep(0.2,times=3*4*2), rep(x= c(.8,.8,.4,.3),times=3), rep(0.2,times=3*4),# third factor loadings rep(0.2,times=3*4*3), rep(x= c(.8,.8,.4,.3),times=3)# fourth factor loadings ),ncol=4)# factor correlation matrix - all factors uncorrelatedPhiMatrix<-matrix(data= c(1,0,0,0,0,1,0,0,0,0,1,0,0,0,0,1),ncol=4)annealData<-psych::sim(fx=fxMatrix,Phi=PhiMatrix,n=600,mu= c(-2,-1,1,2),raw=TRUE )$observed# observed is the simulated observed datacolnames(annealData)= paste0("Item",1:48)annealModel<-'Trait1 =~ Item1 + Item2 + Item3 + Item4 + Item5 + Item6 + Item7 + Item8 + Item9 + Item10 + Item11 + Item12Trait2 =~ Item13 + Item14 + Item15 + Item16 + Item17 + Item18 + Item19 + Item20 + Item21 + Item22 + Item23 + Item24Trait3 =~ Item25 + Item26 + Item27 + Item28 + Item29 + Item30 + Item31 + Item32 + Item33 + Item34 + Item35 + Item36Trait4 =~ Item37 + Item38 + Item39 + Item40 + Item41 + Item42 + Item43 + Item44 + Item45 + Item46 + Item47 + Item48'lavaan.model.specs<-list(model.type="cfa",auto.var=TRUE,estimator="default",ordered=NULL,int.ov.free=TRUE,int.lv.free=FALSE,std.lv=TRUE,auto.fix.first=FALSE,auto.fix.single=TRUE,auto.cov.lv.x=TRUE,auto.th=TRUE,auto.delta=TRUE,auto.cov.y=TRUE)# perform the SA algorithmset.seed(1)SA_example<- simulatedAnnealing(initialModel=annealModel,originalData=annealData,maxSteps=200,fitStatistic='cfi',maximize=TRUE,temperature="logistic",items= paste0("Item",1:48),lavaan.model.specs=lavaan.model.specs,maxChanges=3,maxItems= c(6,6,6,6),setChains=4)## Initializing short form creation.## The initial short form is:## Trait1 =~ Item9 + Item4 + Item7 + Item1 + Item2 + Item5## Trait2 =~ Item19 + Item23 + Item14 + Item15 + Item13 + Item17## Trait3 =~ Item29 + Item34 + Item30 + Item31 + Item25 + Item33## Trait4 =~ Item41 + Item48 + Item45 + Item46 + Item42 + Item47## Using the short form randomNeighbor function.## Finished initializing short form options.## Current Progress:## Chain number 1 complete.## Chain number 2 complete.## Chain number 3 complete.## Chain number 4 complete.summary(SA_example)## Algorithm: Simulated Annealing## Total Run Time: 41.456 secs#### lavaan 0.6.17 ended normally after 33 iterations#### Estimator ML## Optimization method NLMINB## Number of model parameters 54#### Number of observations 600#### Model Test User Model:#### Test statistic 367.147## Degrees of freedom 246## P-value (Chi-square) 0.000###### Final Model Syntax:## Trait1 =~ Item11 + Item2 + Item3 + Item6 + Item4 + Item9## Trait2 =~ Item17 + Item21 + Item13 + Item24 + Item16 + Item23## Trait3 =~ Item26 + Item35 + Item33 + Item34 + Item30 + Item25## Trait4 =~ Item43 + Item37 + Item42 + Item40 + Item38 + Item46plot(SA_example)# plot showing how the fit value changes at each step
It took a total of 42.09 secs to run the SA example, and a total of 5.82mins to run all four together.
