Package mlma. July 14, 2016

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1 Package mlma July 14, 2016 Type Package Title ultilevel ediation Analysis Version Date Author Qingzhao u, Bin Li aintainer Qingzhao u <qyu@lsuhsc.edu> Depends R (>= ), lme4, splines, car, gplots Do multilevel mediation analysis with generalized additive multilevel models. License GPL (>= 2) URL NeedsCompilation no Repository CRAN Date/Publication :28:34 R topics documented: mlma-package boot.mlma data.org mlma plot.mlma plot.mlma.boot print.mlma sim sim summary.mlma summary.mlma.boot Index 20 1

2 2 mlma-package mlma-package ultilevel ediation Analysis Details The package is used to do mediation analysis with generalized multilevel models. Package: mlma Type: Package Version: 1.0 Date: License: GPL (>= 2) "data.org" is used to transorm the variables and organize the predictor, mediators and outcome into the ormat that are ready to be used or multilevel mediation analysis. "mlma" is or multilevel mediation analysis on the original data set. "boot.mlma" is a combined unction that organized data set, do multilevel mediation analysis on original data sets and bootstrapping samples. The multilevel mediation is based on the ollowing linear multilevel additive models: K ij = u 0j(X.j,.j, Z.j )+β10t 10 (X ij X.j )+ β20kt 20k ( ijk.jk )+β30t (Zij Z.j )+rij, where u 0j(X.j,.j, Z.j ) = c 00 + β 01T 01 (X.j ) + For k = 1,..., K, k=1 K β02kt 02k (.jk ) + β03t Z.j + r0j. k=1.jk = u 0jk(X.j ) + β 10kT 10k (X ij X.j ) + r ijk, u 0jk(X.j ) = c 00k + β01k T 1 01k (X.j ) + r0jk. I or some k, k is level 2 variable,.jk = c 00k + β01k T 2 01k (X.j ) + r0jk. Note that in the models, ( ) = ( 1 ( ), 2 ( ),, l ( )) T is a set o l transormation unctions on, with the corresponding linear coeicients vector β = (β 1, β 2,, β l ) T. and l are known or model itting. l may be dierent with o dierent sub- and super-scripts. Author(s) Qingzhao u <qyu@lsuhsc.edu>, Bin Li <bli@lsu.edu> aintainer: Qingzhao u <qyu@lsuhsc.edu>

3 boot.mlma 3 boot.mlma Bootstrap ethod or Inerence on ultilevel ediation Analysis Bootstrap samples are selected rom the original data set. The bootstrap sample has the same number o groups and in each group, the same number o observations as in the original data set. Based on each bootstrap sample, a multilevel mediation analysis is done and the results saved to make inerences on the total, direct and indirect eects. Usage boot.mlma(y, biny = FALSE, x, levelx, levely, m, l1 = NULL, l2 = NULL, c1 = NULL, c1r = rep(1, length(c1)), c2 = NULL, c2r = rep(1, length(c2)), 01y = NULL, 10y = NULL, 02ky = NULL, 20ky = NULL, 01km1 = NULL, 01km2 = NULL, 10km = NULL, level=1:length(y), weight = rep(1, length(x)), random = "(1 level)", random.m1 = NULL, intercept = TRUE, w2=rep(1,length(unique(level[!is.na(level)]))), boot = 100, seed = 1, covariates=null,cy1=null,cy2=null,cm=null, joint=null,x.new=x, m.new=m, level.new=level,weight.new=weight, covariates.new=covariates) Arguments y biny x levelx levely m the vector o the outcome variable. True i the outcome is binary, otherwise False. Deault is False. the vector o the predictive variable. the level o x (1 or 2), 1 by deault. the level o y (1 or 2), 1 by deault. the matrix or vector o mediators. l1 the column numbers o level 1 continuous mediators in m. l2 the column numbers o level 2 continuous mediators in m. c1 the column numbers o level 1 categorical mediators in m. c1r the reerence groups o categorical mediators speciied by c1. c2 the column numbers o level 2 categorical mediators in m. c2r the reerence groups o categorical mediators speciied by c2. 01y 10y the transormation unction expressions on level 2 predictive variable (x.j) in explaining y (eg, c("x^2","log(x)")). the transormation unction expressions on level 1 predictive variable (xij-x.j) in explaining y.

4 4 boot.mlma 02ky 20ky 01km1 01km2 10km level weight random random.m1 intercept w2 boot the transormation-unction-expression list on level 2 mediators (m.jk) in explaining y (eg, list(2:3,c("log(x)","sqrt(x)"), "2*x")). The irst item lists column numbers o the level 2 mediators in m, which needs to be transormed. By that order, each o the rest items o 01ky list the transormation unctional expressions or each mediator. The mediators not speciied in the list will not be transormed in any way. the transormation-unction-expression list on level 1 mediators (mijk-m.jk) in explaining y.the irst item lists column numbers o the level 1 mediators in m, which needs to be transormed. By that order, each o the rest items o 02ky list the transormation unctional expressions or each mediator. The mediators not speciied in the list will not be transormed in any way. the transormation-unction-expression list on level 2 predictor (x.j) in explaining the level 1 mediators. The irst item lists column numbers o the level 1 mediators in m, which should be explained by the transormed predictor(s). By that order, each o the rest items o 01km1 lists the transormation unctional expressions or the (aggregated) level 2 predictor in explaining each mediator. The mediators not speciied in the list will be explained by the original ormat o the level 2 predictor only. the transormation-unction-expression list on level 2 predictor (x.j) in explaining the level 2 mediators. The irst item lists column numbers o the level 2 mediators in m, which should be explained by the transormed level 2 predictor(s). By that order, each o the rest items o 01km2 lists the transormation unctional expressions or the predictor in explaining each mediator. The mediators not speciied in the list will be explained by the original ormat o the (aggregated) level 2 predictor only. the transormation-unction-expression list on level 1 predictor (xij-x.j) in explaining the level 1 mediators. The irst item lists column numbers o the level 1 mediators in m, which should be explained by the transormed level 1 predictor(s). By that order, each o the rest items o 10km lists the transormation unctional expressions or the level 1 predictor in explaining each mediator. The mediators not speciied in the list will be explained by the original ormat o the level 1 predictor only. a vector that record the group number or each observation. the weight o cases in groups. the random eect part or the ull model. random = "(1 level)" by deault. the random eect part or model explaining the mediators. All other random eects are random = "(1 level)" i not speciied here. True i it an intercept to models, by deault. the weight or observations at level 2, which should be the same order as unique(level[!is.na(level)]). the number o bootstrapping samples. seed set seed, deault is 1. covariates the covariates matrix to explain the outcome, y, and/or the mediators, m. cy1 the column numbers o covariates that are level 1 and used to explain y. cy2 the column numbers o covariates that are level 2 and used to explain y.

5 boot.mlma 5 cm Details the column numbers o covariates that are used to explain m. cm[[1]] gives the mediators (in l1, cl, l2, or c2) that can be partially explained by covariates. Each o the rest items o the cm list shows the column number(s) in covariates that should be used to explain each mediator listed in cm[[1]] and by that order.for example, joint=list(1,c("m.2","m.4")) means ind the joint eects o level 1 mediators m.2 and m.4. joint the list o group(s) o mediators whose joint mediation eect is o interests. joint[[1]] list the levels o mediators in each group and by the order o the list. Note that i any mediator in the group is o level 2, the level o the group should be 2. x.new, covariates.new, m.new, level.new, weight.new the settings that we want to make inerences on the mediation eects. I m.new=null, generate new mediators rom x.new. The multilevel mediation is based on the ollowing linear multilevel additive models: K ij = u 0j(X.j,.j, Z.j )+β10t 10 (X ij X.j )+ β20kt 20k ( ijk.jk )+β30t (Zij Z.j )+rij, where u 0j(X.j,.j, Z.j ) = c 00 + β 01T 01 (X.j ) + For k = 1,..., K, I or some k, k is level 2 variable, k=1 K β02kt 02k (.jk ) + β03t Z.j + r0j. k=1.jk = u 0jk(X.j ) + β 10kT 10k (X ij X.j ) + r ijk, u 0jk(X.j ) = c 00k + β01k T 1 01k (X.j ) + r0jk..jk = c 00k + β01k T 2 01k (X.j ) + r0jk. Note that in the models, ( ) = ( 1 ( ), 2 ( ),, l ( )) T is a set o l transormation unctions on, with the corresponding linear coeicients vector β = (β 1, β 2,, β l ) T. and l are known or model itting. l may be dierent with o dierent sub- and super-scripts. Value Return a "mlma.boot" mode list, which include the ollowing items: de1 de2 an n by boot matrix, where each column is the level 1 direct eects rom one bootstrap sampling. n is the number o observations in the original data. an g by boot matrix, where each column is the level 2 direct eects rom one bootstrap sampling. g is the number o groups in the original data.

6 6 data.org ie1 ie1 ie12 sum.boot1 sum.boot2 ull xboot xjboot levelx level an v1 by n*boot matrix, where each column is the level 1 indirect eects rom the boot bootstrap samples or one level 1 mediator. v1 is the number o level 1 mediators. an v2 by g*boot matrix, where each column is the level 2 indirect eects rom the boot bootstrap samples or one level 2 mediator. v2 is the number o level 2 mediators. an v1 by g*boot matrix, where each column is the aggregated level 2 indirect eects rom the boot bootstrap samples or one level 1 mediator. v1 is the number o level 1 mediators. summary results o level 1 mediation eects rom bootstrap sample. summary results o level 2 mediation eects rom bootstrap sample. an "mlma" results using the original data set. a n*boot vector o the level 1 predictors in all boot bootstrap samples. a g*boot vector o the (aggregated) level 2 predictors in all boot bootstrap samples. inherited rom the same argument. inherited rom the same argument. Author(s) Qingzhao u (qyu@lsuhsc.edu), Bin Li (bli@lsu.edu). Examples data(sim.111) temp111<-boot.mlma(y=sim.111$y, biny=false, sim.111$x, levelx=1, m=sim.111$m, l1=1:2, c1=3,c1r=1, 01y=c("x","log(x^2)"), 10y=c("x^2","sqrt(x+6)"), 20ky=list(2,c("x","x^3")), 01km1=list(2,"sqrt(x)+3"), 10km=list(2,"log(x+2)"), level=sim.111$level, boot=2) data(sim.211) temp211<-boot.mlma(y=sim.211$y, biny=false, x=sim.211$x, levelx=2, m=sim.211$m, l1=2,l2=1, c1=3,c1r=1, 01y=c("x","log(x^2)"), 02ky=list(1,c("x","x^2")), 20ky=list(2,c("x","x^3")), 01km1=list(2,"sqrt(x)+3"), 01km2=list(1,c("x^1.2","x^2.3")), level=sim.211$level, boot=2) data.org Transorm and Organize Data or ediation Analysis To transorm variables and generate data sets or mediation analysis.

7 data.org 7 Usage data.org(x, levelx=1, levely=1, m, l1 = NULL, l2 = NULL, c1 = NULL, c1r = rep(1, length(c1)), c2 = NULL, c2r = rep(1, length(c2)), 01y = NULL, 10y = NULL, 02ky = NULL, 20ky = NULL, 01km1 = NULL, 01km2 = NULL, 10km = NULL, level=1:length(x), weight = rep(1, length(x))) Arguments x levelx levely m l1 l2 c1 the vector o the predictive variable. the level o x (1 or 2), 1 by deault. the level o y (1 or 2), 1 by deault. the matrix or vector o mediators. the column numbers o level 1 continuous mediators in m or the list o names o the level 1 continuous mediators. the column numbers o level 2 continuous mediators in m or the list o names o the level 2 continuous mediators. the column numbers o level 1 categorical mediators in m or the list o names o the level 1 categorical mediators. c1r the reerence groups o categorical mediators speciied by c1. c2 the column numbers o level 2 categorical mediators in m or the list o names o the level 2 categorical mediators. c2r the reerence groups o categorical mediators speciied by c2. 01y 10y 02ky 20ky 01km1 the transormation unction expressions on level 2 predictive variable (x.j) in explaining y (eg, c("x^2","log(x)")). the transormation unction expressions on level 1 predictive variable (xij-x.j) in explaining y. the transormation-unction-expression list on level 2 mediators (m.jk) in explaining y (eg, list(2:3,c("log(x)","sqrt(x)"), "2*x")). The irst item lists column numbers/variable names o the level 2 mediators in m, which needs to be transormed. By that order, each o the rest items o 01ky list the transormation unctional expressions or each mediator. The mediators not speciied in the list will not be transormed in any way. the transormation-unction-expression list on level 1 mediators (mijk-m.jk) in explaining y.the irst item lists column numbers/variable names o the level 1 mediators in m, which needs to be transormed. By that order, each o the rest items o 02ky list the transormation unctional expressions or each mediator. The mediators not speciied in the list will not be transormed in any way. the transormation-unction-expression list on level 2 predictor (x.j) in explaining the level 1 mediators. The irst item lists column numbers/variable names o the level 1 mediators in m, which should be explained by the transormed predictor(s). By that order, each o the rest items o 01km1 lists the transormation unctional expressions or the (aggregated) level 2 predictor in explaining each mediator. The mediators not speciied in the list will be explained by the original ormat o the level 2 predictor only.

8 8 data.org 01km2 10km level weight the transormation-unction-expression list on level 2 predictor (x.j) in explaining the level 2 mediators. The irst item lists column numbers/variable names o the level 2 mediators in m, which should be explained by the transormed level 2 predictor(s). By that order, each o the rest items o 01km2 lists the transormation unctional expressions or the predictor in explaining each mediator. The mediators not speciied in the list will be explained by the original ormat o the (aggregated) level 2 predictor only. the transormation-unction-expression list on level 1 predictor (xij-x.j) in explaining the level 1 mediators. The irst item lists column numbers/variable names o the level 1 mediators in m, which should be explained by the transormed level 1 predictor(s). By that order, each o the rest items o 10km lists the transormation unctional expressions or the level 1 predictor in explaining each mediator. The mediators not speciied in the list will be explained by the original ormat o the level 1 predictor only. a vector that record the group number or each observation. the weight o cases in groups. Details The arguments starting with "" are used to speciy the transormation unctions o the predictor or mediators in explaining y, or the transormation unctions o the predictor in explaining the mediators. I the name o the argument includes a "k", the transormation is on the mediators. I the names o the arguments end with "y", the transormation is to explain the outcome. Otherwise, the transormation is on x to predict mediators (the argument ends with "m1" or "m" (or level 1 mediator), or "m2" (or level 2 mediator)). The unctions corresponds to the unctions in the ollowing multilevel additive models, reading as +subscript+superscript. For example, 01y speciies 01. K ij = u 0j(X.j,.j, Z.j )+β10t 10 (X ij X.j )+ β20kt 20k ( ijk.jk )+β30t (Zij Z.j )+rij, where u 0j(X.j,.j, Z.j ) = c 00 + β 01T 01 (X.j ) + For k = 1,..., K, I or some k, k is level 2 variable, k=1 K β02kt 02k (.jk ) + β03t Z.j + r0j. k=1.jk = u 0jk(X.j ) + β 10kT 10k (X ij X.j ) + r ijk, u 0jk(X.j ) = c 00k + β01k T 1 01k (X.j ) + r0jk..jk = c 00k + β01k T 2 01k (X.j ) + r0jk. The transormation unction can be any unction that is dierentiable by the unction deriv(), or the ielse unction with those unctions. The transormation unction can also be the ns() and bs() unctions or natural and b spline basis.

9 data.org 9 Value The unction returns a list with transormed and organized data with the ollowing items: x1 the level 1 and 2 transormed predictor variable matrix in explaining y (eg, 01y(x.j) & 10y(xij-x.j)). l1x the column numbers o level 1 predictors in x1. l2x the column numbers o level 2 predictors in x1. m1y m1 m2y m2 m12 xm1 m11 the level 1 mediator matrix in explaining y (eg, 20ky(mijk-m.jk) & mijk or binarized mijk or categorical mediators). a list where the irst item identiy column numbers o level 1 mediators in m (eg l1 and c1). For every mediator identiied by m1[[1]] and by that order, each o the rest item identiy the column number(s) in m1y the (transormed) value(s) o the mediator in explaining y. the level 2 mediator (original or aggregated) matrix in explaining y (eg, 02ky(m.jk) & m.jk). a list where the irst item identiy column numbers o level 2 mediators in m (eg l2 and c2). For every mediator identiied by m2[[1]] and by that order, each o the rest item identiy the column number(s) in m2y the (transormed) value(s) o the mediator in explaining y. a list where the irst item identiy column numbers o aggregated level 2 mediators in m (eg, aggregated 20ky). For every mediator identiied by m12[[1]] and by that order, each o the rest item identiy the column number(s) in m2y the aggregated value(s) o the mediator in explaining y. the (transormed) level 1 and level 2 predictor(s) in explaining level 1 mediators. a list where the irst item identiy column numbers o level 1 mediators in m. For every mediator identiied by m11[[1]] and by that order, each o the rest item identiy the column number(s) in xm1 the (transormed) level 1 predictor(s) in explaining the mediator. m12 a list where the irst item identiy column numbers o level 1 mediators in m. For every mediator identiied by m12[[1]] and by that order, each o the rest item identiy the column number(s) in xm1 the (transormed/aggregated) level 2 predictor(s) in explaining the mediator. m.2 a matrix o level 2 mediators (one row or each group). xm2 m22 the (transormed/aggregated) level 2 predictor(s) in explaining level 2 mediators (one row or each group). a list where the irst item identiy column numbers o level 2 mediators in m. For every mediator identiied by m22[[1]] and by that order, each o the rest item identiy the column number(s) in xm2 the (transormed) level 2 predictor(s) in explaining the mediator. x1.der, m2y.der, m1y.der, xm2.der, xm1.der the derivative o x1, m2y, m1y, xm2, and xm1 respectively. parameter The list o arguments used.

10 10 mlma Author(s) Qingzhao u (qyu@lsuhsc.edu), Bin Li (bli@lsu.edu). Examples data(sim.211) example1<-data.org(x=sim.211$x, levelx=2, m=sim.211$m, l1=2,l2=1, c1=3, c1r=1, 01y=c("x","log(x^2)"), 02ky=list(1,c("x","x^2")), 20ky=list(2,c("x","x^3")), 01km1=list(2,"sqrt(x)+3"), 01km2=list(1,c("x^1.2","x^2.3")), level=sim.211$level) data(sim.111) example2<-data.org(sim.111$x, levelx=1, m=sim.111$m, l1=1:2, c1=3, c1r=1, 01y=c("x","log(x^2)"), 10y=c("x^2","sqrt(x+6)"), 20ky=list(2,c("x","x^3")), 01km1=list(2,"sqrt(x)+3"), 10km=list(2,"log(x+2)"), level=sim.111$level) mlma ultilevel ediation Analysis Usage The unction transorms the data set and does multilevel mediation analysis. The total, direct, and indirect eects will be returned as the results. mlma(y, biny=false, data1=null, x, levelx=1, levely=1, m, l1=null, l2=null,c1=null,c1r=rep(1,length(c1)), c2=null, c2r=rep(1,length(c2)), level=1:length(y),weight=rep(1,length(x)), random="(1 level)", random.m1=null,intercept=true,covariates=null,cy1=null,cy2=null,cm=null, joint=null,org.data=false,01y=null,10y=null,02ky=null,20ky=null, 01km1=NULL,01km2=NULL,10km=NULL) Arguments y biny data1 x levelx levely m the vector o the outcome variable. True i the outcome is binary, otherwise False. Deault is False. The transormed and organized data set rom data.org. I the data set has not been organized, leave data1=null (by deault), and set org.data=t with the transormation unctions ( arguments). Otherwise, set data1 as the output rom the data.org unction and do not include the arguments: org.data and s. the vector o the predictive variable. the level o x (1 or 2), 1 by deault. the level o y (1 or 2), 1 by deault. the matrix or vector o mediators.

11 mlma 11 l1 l2 c1 the column numbers o level 1 continuous mediators in m or the list o names o the level 1 continuous mediators. the column numbers o level 2 continuous mediators in m or the list o names o the level 2 continuous mediators. the column numbers o level 1 categorical mediators in m or the list o names o the level 1 categorical mediators. c1r the reerence groups o categorical mediators speciied by c1. c2 the column numbers o level 2 categorical mediators in m or the list o names o the level 2 categorical mediators. c2r the reerence groups o categorical mediators speciied by c2. level weight random random.m1 intercept a vector that record the group number or each observation. the weight o cases in groups. the random eect part or the ull model. random = "(1 level)" by deault. the random eect part or model explaining the mediators. All other random eects are random = "(1 level)" i not speciied here. True i it an intercept to models, by deault. covariates the covariates matrix to explain the outcome, y, and/or the mediators, m. cy1 the column numbers o covariates that are level 1 and used to explain y. cy2 the column numbers o covariates that are level 2 and used to explain y. cm Details joint the column numbers o covariates that are used to explain m. cm[[1]] gives the mediators (in l1, cl, l2, or c2) that can be partially explained by covariates. Each o the rest items o the cm list shows the column number(s) in covariates that should be used to explain each mediator listed in cm[[1]] and by that order. the list o group(s) o mediators whose joint mediation eect is o interests. joint[[1]] list the levels o mediators in each group and by the order o the list. Note that i any mediator in the group is o level 2, the level o the group should be 2. org.data i is TRUE, irst organize the data set and do transormations using the unction "data.org". In such case, need to speciy the transormation unction arguments. 01y, 10y, 02ky, 20ky, 01km1, 01km2, 10km the transormation unctions as describe in the unction "data.org". Need these arguments only when org.data=t. The multilevel mediation is based on the ollowing linear multilevel additive models: K ij = u 0j(X.j,.j, Z.j )+β10t 10 (X ij X.j )+ β20kt 20k ( ijk.jk )+β30t (Zij Z.j )+rij, where u 0j(X.j,.j, Z.j ) = c 00 + β 01T 01 (X.j ) + k=1 K β02kt 02k (.jk ) + β03t Z.j + r0j. k=1

12 12 mlma Value For k = 1,..., K, I or some k, k is level 2 variable,.jk = u 0jk(X.j ) + β 10kT 10k (X ij X.j ) + r ijk, u 0jk(X.j ) = c 00k + β01k T 1 01k (X.j ) + r0jk..jk = c 00k + β01k T 2 01k (X.j ) + r0jk. Note that in the models, ( ) = ( 1 ( ), 2 ( ),, l ( )) T is a set o l transormation unctions on, with the corresponding linear coeicients vector β = (β 1, β 2,, β l ) T. and l are known or model itting. l may be dierent with o dierent sub- and super-scripts. A "mlma" mode list will be returned with the ollowing items: de1 de2 ie1 ie12 ie2 1 m1 m2 ie1_list ie2_list level 1 direct eect rom predictor. level 2 direct eect rom predictor. level 1 indirect eect rom level 1 mediator. level 2 indirect eect rom level 1 mediator. level 2 indirect eect rom level 2 mediator. the overall multilevel model. a list, where the irst item identiies the level 1 mediators, and in that order, the ollowing items give the prediction unctions o the mediators. a list, where the irst item identiies the level 2 mediators, and in that order, the ollowing items give the prediction unctions o the mediators. a list, where the irst item identiies the level 1 mediators, and in that order, the ollowing items give the column(s) o the indirect eects o the mediator in ie1. a list, where the irst item identiies the level 2 mediators, and in that order, the ollowing items give the column(s) o the indirect eects o the mediator in ie2. iej2_list a list, where the irst item identiies the level 2 joint mediators, and in that order, the ollowing items give the column(s) o the indirect eects o the mediator in cbind(ie12,ie2). ie12_1,ie12_2, ie1_1, ie1_2, ie2_1, ie2_2 the irst and second part o the corresponding indirect eects. x x.j the vector o the predictive variable. the vector o the aggregated variable at the higher level by the order o unique(level[!is.na(level)]). data1 The results rom data.org. Author(s) Qingzhao u (qyu@lsuhsc.edu), Bin Li (bli@lsu.edu).

13 plot.mlma 13 Examples data(sim.111) data1<-data.org(x=sim.111$x, levelx=1, m=sim.111$m, l1=1:2, c1=3, c1r=1, 01y=c("x","log(x^2)"), 10y=c("x^2","sqrt(x+6)"), 20ky=list(2,c("x","x^3")), 01km1=list(2,"sqrt(x)+3"), 10km=list(2,"log(x+2)"), level=sim.111$level) temp<-mlma(y=sim.111$y, biny=false, data1=data1, x=sim.111$x, levelx=1, m=sim.111$m, l1=1:2,c1=3, c1r=1,level=sim.111$level) #can also do the above analysis using the ollowing code temp<-mlma(y=sim.111$y, biny=false, data1=data1, x=sim.111$x, levelx=1, m=sim.111$m, l1=1:2,c1=3, c1r=1,level=sim.111$level,org.data=true, 01y=c("x","log(x^2)"), 10y=c("x^2","sqrt(x+6)"), 20ky=list(2,c("x","x^3")), 01km1=list(2,"sqrt(x)+3"), 10km=list(2,"log(x+2)")) data(sim.211) data1<-data.org(x=sim.211$x, levelx=2, m=sim.211$m, l1=2,l2=1, c1=3, c1r=1, 01y=c("x","log(x^2)"), 02ky=list(1,c("x","x^2")), 20ky=list(2,c("x","x^3")), 01km1=list(2,"sqrt(x)+3"), 01km2=list(1,c("x^1.2","x^2.3")), level=sim.211$level) temp<-mlma(y=sim.211$y, biny=false, data1, x=sim.211$x, levelx=2, m=sim.211$m, l1=2, l2=1, c1=3, c1r=1,level=sim.211$level) plot.mlma Plot "mlma" Object Plot the overall mediation eect or decomposed indirect eect rom the selected mediator. Usage ## S3 method or class 'mlma' plot(x,..., var = NULL, cate = FALSE, w2 = rep(1, length(object$de2))) Arguments x an "mlma" object.... arguments to be passed to methods. var cate w2 the name o the mediator that is to be plotted. I var is NULL, plot the relative mediation eects o all mediators. TRUE when the mediator is a categorical variable. By deault is FALSE. the weight or observations at level 2, which should be the same order as unique(level[!is.na(level)]). The deault is rep(1,length(object$de2)).

14 14 plot.mlma.boot Details Plot the relative eects o direct eects and indirect eects o mediators at level 1 (i levelx=1) and level 2 respectively i var=null. Otherwise, plot the indirect eect o var, the estimated dierential eect o the predictor on var, and the predicted relationship between y and var at individual level and/or (aggregated) group level. Author(s) Qingzhao u (qyu@lsuhsc.edu), Bin Li (bli@lsu.edu). Examples data(sim.111) data1<-data.org(x=sim.111$x, levelx=1, m=sim.111$m, l1=1:2, c1=3, c1r=1, 01y=c("x","log(x^2)"), 10y=c("x^2","sqrt(x+6)"), 20ky=list(2,c("x","x^3")), 01km1=list(2,"sqrt(x)+3"), 10km=list(2,"log(x+2)"), level=sim.111$level) temp111<-mlma(y=sim.111$y, biny=false, data1=data1, x=sim.111$x, levelx=1, m=sim.111$m, l1=1:2,c1=3, c1r=1,level=sim.111$level) plot(temp111) plot(temp111,var="m.2") plot(temp111,var="m.3") plot(temp111,var="m.4", cate=true) data(sim.211) data1<-data.org(x=sim.211$x, levelx=2, m=sim.211$m, l1=2,l2=1, c1=3, c1r=1, 01y=c("x","log(x^2)"), 02ky=list(1,c("x","x^2")), 20ky=list(2,c("x","x^3")), 01km1=list(2,"sqrt(x)+3"), 01km2=list(1,c("x^1.2","x^2.3")), level=sim.211$level) temp211<-mlma(y=sim.211$y, biny=false, data1, x=sim.211$x, levelx=2, m=sim.211$m, l1=2, l2=1, c1=3, c1r=1,level=sim.211$level) plot(temp211) plot(temp211,var="m.1") plot(temp211,var="m.4", cate=true) plot(temp211,var="m.3") plot.mlma.boot Plot the "mlma.boot" Object Usage For the mediator identiied by var, the unction draws the level 1 and/or (aggregated) level 2 indirect eects versus the predictor and the conidence bands at alpha signiicance level. I var is NULL, draw the relative mediation eects with conidence intervals. ## S3 method or class 'mlma.boot' plot(x,..., var = NULL, alpha = 0.05, quant=false)

15 print.mlma 15 Arguments x an "mlma" object.... arguments to be passed to methods. var alpha quant Author(s) the name o the mediator that is to be plotted. the signiicance level at which to draw the conidence bands. i true, conidence interval is calculated using quantil when plot the relative eects. By deault, the CIs are calculated using normal approximation. This argument does nothing or the CIs calculated when var is not null. Qingzhao u (qyu@lsuhsc.edu), Bin Li (bli@lsu.edu). Examples #1-1-1 model data(sim.111) temp111<-boot.mlma(y=sim.111$y, biny=false, sim.111$x, levelx=1, m=sim.111$m, l1=1:2, c1=3,c1r=1, 01y=c("x","log(x^2)"), 10y=c("x^2","sqrt(x+6)"), 20ky=list(2,c("x","x^3")), 01km1=list(2,"sqrt(x)+3"), 10km=list(2,"log(x+2)"), level=sim.111$level, boot=2) plot(temp111) plot(temp111,var="m.2") plot(temp111,var="m.3") plot(temp111,var="m.4") #2-1-1 model data(sim.211) temp211<-boot.mlma(y=sim.211$y, biny=false, x=sim.211$x, levelx=2, m=sim.211$m, l1=2,l2=1, c1=3,c1r=1, 01y=c("x","log(x^2)"), 02ky=list(1,c("x","x^2")), 20ky=list(2,c("x","x^3")), 01km1=list(2,"sqrt(x)+3"), 01km2=list(1,c("x^1.2","x^2.3")), level=sim.211$level, boot=2) plot(temp211) plot(temp211,var="m.1") plot(temp211,var="m.4") plot(temp211,var="m.3") print.mlma Print "mlma" Object print the level 1 and level 2 mediation eecs rom the object.

16 16 sim.111 Usage ## S3 method or class 'mlma' print(x,..., w2 = rep(1, length(object$de2))) Arguments x an "mlma" object.... arguments to be passed to methods. w2 the weight or observations at level 2, which should be the same order as unique(level[!is.na(level)]). The deault is rep(1,length(object$de2)). Author(s) Qingzhao u (qyu@lsuhsc.edu), Bin Li (bli@lsu.edu). Examples data(sim.111) data1<-data.org(x=sim.111$x, levelx=1, m=sim.111$m, l1=1:2, c1=3, c1r=1, 01y=c("x","log(x^2)"), 10y=c("x^2","sqrt(x+6)"), 20ky=list(2,c("x","x^3")), 01km1=list(2,"sqrt(x)+3"), 10km=list(2,"log(x+2)"), level=sim.111$level) temp111<-mlma(y=sim.111$y, biny=false, data1=data1, x=sim.111$x, levelx=1, m=sim.111$m, l1=1:2,c1=3, c1r=1,level=sim.111$level) print(temp111) data(sim.211) data1<-data.org(x=sim.211$x, levelx=2, m=sim.211$m, l1=2,l2=1, c1=3, c1r=1, 01y=c("x","log(x^2)"), 02ky=list(1,c("x","x^2")), 20ky=list(2,c("x","x^3")), 01km1=list(2,"sqrt(x)+3"), 01km2=list(1,c("x^1.2","x^2.3")), level=sim.211$level) temp211<-mlma(y=sim.211$y, biny=false, data1, x=sim.211$x, levelx=2, m=sim.211$m, l1=2, l2=1, c1=3, c1r=1,level=sim.211$level) print(temp211) sim.111 Simulated Data set A simulated data set, where both predictor and outcome are level 1 variables. Usage data("sim.111")

17 sim Format The data set contains 10 groups, each group has 30 observations. The ormat is list, where there are our elements: x: the level 1 continuous predictor. y: the level 1 continuous outcome. m: the matrix o mediators, where there are three level 1 mediators, where m.2 and m.3 are continuous, and m.4 is categorical with 3 levels. level: the group level or each observation. Examples data(sim.111) sim.211 Simulated Data A simulated data set, where the predictor is a level 2 and the outcome is a level 1 variable. Usage data("sim.211") Format The data set contains 10 groups, each group has 30 observations. The ormat is list, where there are our elements: x: the level 1 continuous predictor. y: the level 1 continuous outcome. m: the matrix o mediators, where there are one level 2 mediator, m.1, and two level 1 mediators, m.3 and m.4. m.4 is categorical with 3 levels. level: the group level or each observation. Examples data(sim.211)

18 18 summary.mlma.boot summary.mlma Summary o "mlma" Object This unction provides ANOVA tests on the predictors and mediators in the ull model and on the predictors or models in explaining each mediators. Usage ## S3 method or class 'mlma' summary(object,...,type="iii") ## S3 method or class 'summary.mlma' print(x,...) Arguments object an "mlma" object. x a summary.mlma.boot object created initially call to summary.mlma.boot.... arguments to be passed to methods. type type o test, "II", "III", 2, or 3. Author(s) Qingzhao u (qyu@lsuhsc.edu), Bin Li (bli@lsu.edu). Examples data(sim.111) temp<-mlma(y=sim.111$y, biny=false, data1=data1, x=sim.111$x, levelx=1, m=sim.111$m, l1=1:2,c1=3, c1r=1,level=sim.111$level,org.data=true, 01y=c("x","log(x^2)"), 10y=c("x^2","sqrt(x+6)"), 20ky=list(2,c("x","x^3")), 01km1=list(2,"sqrt(x)+3"), 10km=list(2,"log(x+2)")) summary(temp) summary.mlma.boot Summary o "mlma.boot" Object This unction provide summary statistics or all mediation eects.

19 summary.mlma.boot 19 Usage ## S3 method or class 'mlma.boot' summary(object,..., alpha = 0.05,RE=FALSE) ## S3 method or class 'summary.mlma.boot' print(x,...) Arguments object x an "mlma" object. a summary.mlma.boot object created initially call to summary.mlma.boot.... arguments to be passed to methods. alpha RE Author(s) the signiicance level at which to draw the conidence bands. i true, print the relative eects, otherwise show the mediation eects. Qingzhao u (qyu@lsuhsc.edu), Bin Li (bli@lsu.edu). Examples #1-1-1 model data(sim.111) temp111<-boot.mlma(y=sim.111$y, biny=false, sim.111$x, levelx=1, m=sim.111$m, l1=1:2, c1=3,c1r=1, 01y=c("x","log(x^2)"), 10y=c("x^2","sqrt(x+6)"), 20ky=list(2,c("x","x^3")), 01km1=list(2,"sqrt(x)+3"), 10km=list(2,"log(x+2)"), level=sim.111$level, boot=2) summary(temp111) #2-1-1 model data(sim.211) temp211<-boot.mlma(y=sim.211$y, biny=false, x=sim.211$x, levelx=2, m=sim.211$m, l1=2,l2=1, c1=3,c1r=1, 01y=c("x","log(x^2)"), 02ky=list(1,c("x","x^2")), 20ky=list(2,c("x","x^3")), 01km1=list(2,"sqrt(x)+3"), 01km2=list(1,c("x^1.2","x^2.3")), level=sim.211$level, boot=2) summary(temp211)

20 Index Topic Data Transormation data.org, 6 Topic ultilevel ediation Analysis mlma, 10 Topic \textasciitildeinerences on LA boot.mlma, 3 Topic \textasciitildeultilevel ediation Analysis boot.mlma, 3 Topic \textasciitildekwd2 data.org, 6 Topic datasets sim.111, 16 sim.211, 17 Topic plot plot.mlma, 13 plot.mlma.boot, 14 Topic print print.mlma, 15 Topic summary statistics summary.mlma, 18 summary.mlma.boot, 18 summary.mlma.boot, 18 boot.mlma, 2, 3 data.org, 2, 6, 11 mlma, 2, 10 mlma-package, 2 plot.mlma, 13 plot.mlma.boot, 14 print.mlma, 15 print.summary.mlma (summary.mlma), 18 print.summary.mlma.boot (summary.mlma.boot), 18 sim.111, 16 sim.211, 17 summary.mlma, 18 20