The stochastic actor-oriented model was developed by Tom Snijders and colleagues. Its purpose is to represent network dynamics based on observed longitudinal data, and to draw conclusions about the analyzed populations based on the model. Variants of SAOM for multiplex data (co-evolution of edges) and for modeling networks collected in different groups (e.g., different classrooms) exists. The following assumptions hold for SAOM models:
The temporal exponential random graph model was developed by Steve Hanneke and colleagues and is an extension to the simple exponential random graph model (ERGM). In simple terms, ERGM is a logistic regression that calculates the probability that an edge is present or absent based on the network structure and covariates. TERGM is an extension of ERGM.
TERGM and SAOM are pretty similar. Below a description of their differences to aid when one method is more appropriate than the other: * In contrast to SAOM, TERMG does not make any assumptions about the agency of actors. While the mathematics behind the model make no claim about actor agency, the way in which the model is created has an actor-centric flavor. * TERGM does not consider the mini-steps that might occur between t and t+1. It accepts that edges which did not exist at t but exists at t+1 might have occurred sequentially or simultaneously. * SAOM purposefully models the change in networks between time periods. TERGM focuses on modeling the network. The temporal dimension is included by adding a memory term in the equation as a control variable. This memory term references the previously observed network.
While from a theoretical perspective, SAOM outperforms TERGM, testing of the two models using real data showed that TERGM more accurately predicted edges.
variants for “multiplex”, “multi-relational”, or “multi-level” ERGMs as well (Wang et al. 2013), but they have not yet been extended to the temporal case.
The relational event model was developed by Carter T Butts and colleagues. It focuses on behavioral interactions, which are defined as discrete events directed at a person or a group of people. It assumes that past interactions create the context for future interactions. This means that every action that occurs depends on the action which occurred right before it. The following assumptions apply: * At each time point t only one event can occur. * A current event t is not influenced by the realization of future events t+1 (reverse causality). * A current event t is not influenced by the non-occurrence of an event that could have appended at t-1. The consequence of these assumptions is that REM is less suited for situations in which individuals have a strategic orientation, are able to engage in forward-looking behavior, or have time for observation and reflection.
Below is a short example of the steps necessary to run a SAOM. The data represents interaction between team members in several student teams. Each team consisted of around five master students and worked on a project for a client. The network was collected at the beginning of the course (t0), 3 weeks into the course (t1), and at the end of the course in week 7, before the grades were published (t2). More information about the context is available in Unbundling Information Exchange in Ad Hoc Project Teams.
The variables we collected were information retrieval and information allocation (dependent variables), awareness of team member’s expertise (knowing, independent variable), the importance team member’s attach to each other’s expertise (valuing, independent variable), how adaptive individuals are (adaptive expertise, independent variable), their emotional attachment to their group (social identity, independent variable), and background variables (gender, age, nationality, specialization, control variable).
We analyzed the data using a hierarchical stochastic actor oriented model using Bayesian regression. We made this choice due to the small size of network. While we had two dependent variables, we did not have enough data to calculate a co-evolution model, thus we could not estimate how information retrieval and information allocation influence each other. In place of this we calculated two models, one for information allocation and one for information retrieval.
For this workshop we will be focusing on modeling information retrieval for three teams using only valuing, and adaptive expertise as dependent variables. Running the complete model, as conducted in the linked study, was computational intensive.
In general, the steps are: 1. Import the data 2. Specify independent, dependent variables 3. Select the effects and specify the model 4. Test goodness of fit
We will first load the required packages and set our working directory.
If you don’t have the packages installed, run this line. If this fails, check the error message. Did a package that is needed for RSienaTest to run, fail to install? If this fails with a non-zero exist status and you have a mac, do you have the development tools (xcode) installed?
#install.packages("RUnit")
#install.packages("RSienaTest", repos="http://R-Forge.R-project.org", dependencies=T)Use setwd to set the path to your working directory. For example, setwd("~/Dropbox/longitudinal_sna_asc_workshop/data"). In windows this would look like setwd("c:/Dropbox/longitudinal_sna_asc_workshop/data"). If you are unsure about your working directory you can type getwd in the console.
library(RSienaTest)We begin with loading the data. A couple of words about the code to import the data. All the data about one variable for one team is assigned to one object (variable name <- as.matrix(...)). read.csv reads the data about one team. I have for each team one txt file. Therefore, I need to skip some rows (skip = 4) and tell the program how many rows to import (nrows = 4). I also need to add row names (row.names = 1) and column names (col.names = c(name1, name2, etc.)). I’m ok with having row names and column names that have the same names (check.names=FALSE). While not important, I’m telling R to convert string variables into dummy variables (stringsAsFactors =TRUE). That is not important as I don’t have any string variables. The only string are the header variables, and I indicated them. All data about one team is imported in one list (list(....)) to make the cleaning easier.
Network variables
adulteduc<-list(
#adulteduc t1
ae_val1<-as.matrix(read.csv("data/ae_teamdynamics_MASTER_UCINET-5.txt",na.strings=9, sep = ";", dec=",", row.names=1, col.names=c("row.nameS", "Daniel", "Liga", "Shengye", "Valentina") , skip=4, nrows=4, check.names=FALSE), stringsAsFactors=TRUE),
ae_is1<-as.matrix(read.csv("data/ae_teamdynamics_MASTER_UCINET-5.txt",na.strings=9, sep = ";", dec=",", row.names=1, col.names=c("row.nameS", "Daniel", "Liga", "Shengye", "Valentina") , skip=14, nrows=4, check.names=FALSE), stringsAsFactors=TRUE),
#aduleteduc t2
ae_val2<-as.matrix(read.csv("data/ae_teamdynamics_MASTER_UCINET-5.txt",na.strings=9, sep = ";", dec=",", row.names=1, col.names=c("row.nameS", "Daniel", "Liga", "Shengye", "Valentina") , skip=24, nrows=4, check.names=FALSE), stringsAsFactors=TRUE),
ae_is2<-as.matrix(read.csv("data/ae_teamdynamics_MASTER_UCINET-5.txt",na.strings=9, sep = ";", dec=",", row.names=1, col.names=c("row.nameS", "Daniel", "Liga", "Shengye", "Valentina") , skip=34, nrows=4, check.names=FALSE), stringsAsFactors=TRUE),
#aduleteduc t3
ae_val3<-as.matrix(read.csv("data/ae_teamdynamics_MASTER_UCINET-5.txt",na.strings=9, sep = ";", dec=",", row.names=1, col.names=c("row.nameS", "Daniel", "Liga", "Shengye", "Valentina") , skip=44, nrows=4, check.names=FALSE), stringsAsFactors=TRUE),
ae_is3<-as.matrix(read.csv("data/ae_teamdynamics_MASTER_UCINET-5.txt",na.strings=9, sep = ";", dec=",", row.names=1, col.names=c("row.nameS", "Daniel", "Liga", "Shengye", "Valentina") , skip=54, nrows=4, check.names=FALSE), stringsAsFactors=TRUE)
)
alpheus<-list(
#Alpehus t1
alp_val1<-as.matrix(read.csv("data/ae_teamdynamics_MASTER_UCINET-6.txt",na.strings=9, sep = ";", dec=",", row.names=1, col.names=c("row.nameS", "Sarah", "Harmke", "Sybil", "Sanne") , skip=4, nrows=4, check.names=FALSE), stringsAsFactors=TRUE),
alp_is1<-as.matrix(read.csv("data/ae_teamdynamics_MASTER_UCINET-6.txt",na.strings=9, sep = ";", dec=",", row.names=1, col.names=c("row.nameS", "Sarah", "Harmke", "Sybil", "Sanne") , skip=14, nrows=4, check.names=FALSE), stringsAsFactors=TRUE),
#Alpehus t2
alp_val2<-as.matrix(read.csv("data/ae_teamdynamics_MASTER_UCINET-6.txt",na.strings=9, sep = ";", dec=",", row.names=1, col.names=c("row.nameS", "Sarah", "Harmke", "Sybil", "Sanne") , skip=24, nrows=4, check.names=FALSE), stringsAsFactors=TRUE),
alp_is2<-as.matrix(read.csv("data/ae_teamdynamics_MASTER_UCINET-6.txt",na.strings=9, sep = ";", dec=",", row.names=1, col.names=c("row.nameS", "Sarah", "Harmke", "Sybil", "Sanne") , skip=34, nrows=4, check.names=FALSE), stringsAsFactors=TRUE),
#Alpehus t3
alp_val3<-as.matrix(read.csv("data/ae_teamdynamics_MASTER_UCINET-6.txt",na.strings=9, sep = ";", dec=",", row.names=1, col.names=c("row.nameS", "Sarah", "Harmke", "Sybil", "Sanne") , skip=44, nrows=4, check.names=FALSE), stringsAsFactors=TRUE),
alp_is3<-as.matrix(read.csv("data/ae_teamdynamics_MASTER_UCINET-6.txt",na.strings=9, sep = ";", dec=",", row.names=1, col.names=c("row.nameS", "Sarah", "Harmke", "Sybil", "Sanne") , skip=54, nrows=4, check.names=FALSE), stringsAsFactors=TRUE)
)
hht<-list(
#hht T1
hht_val1<-as.matrix(read.csv("data/ae_teamdynamics_MASTER_UCINET-7.txt",na.strings=9, sep = ";", dec=",", row.names=1, col.names=c("row.nameS", "Anja","Johanna","Erika","Esmina","Saulius") , skip=5, nrows=5, check.names=FALSE), stringsAsFactors=TRUE),
hht_is1<-as.matrix(read.csv("data/ae_teamdynamics_MASTER_UCINET-7.txt",na.strings=9, sep = ";", dec=",", row.names=1, col.names=c("row.nameS", "Anja","Johanna","Erika","Esmina","Saulius") , skip=17, nrows=5, check.names=FALSE), stringsAsFactors=TRUE),
#hht T2
hht_val2<-as.matrix(read.csv("data/ae_teamdynamics_MASTER_UCINET-7.txt",na.strings=9, sep = ";", dec=",", row.names=1, col.names=c("row.nameS", "Anja","Johanna","Erika","Esmina","Saulius") , skip=29, nrows=5, check.names=FALSE), stringsAsFactors=TRUE),
hht_is2<-as.matrix(read.csv("data/ae_teamdynamics_MASTER_UCINET-7.txt",na.strings=9, sep = ";", dec=",", row.names=1, col.names=c("row.nameS", "Anja","Johanna","Erika","Esmina","Saulius") , skip=41, nrows=5, check.names=FALSE), stringsAsFactors=TRUE),
#hht T3
hht_val3<-as.matrix(read.csv("data/ae_teamdynamics_MASTER_UCINET-7.txt",na.strings=9, sep = ";", dec=",", row.names=1, col.names=c("row.nameS", "Anja","Johanna","Erika","Esmina","Saulius") , skip=53, nrows=5, check.names=FALSE), stringsAsFactors=TRUE),
hht_is3<-as.matrix(read.csv("data/ae_teamdynamics_MASTER_UCINET-7.txt",na.strings=9, sep = ";", dec=",", row.names=1, col.names=c("row.nameS", "Anja","Johanna","Erika","Esmina","Saulius") , skip=65, nrows=5, check.names=FALSE), stringsAsFactors=TRUE)
)Actor attributes
attributes<-read.csv("data/attributes_article.csv", header=TRUE, row.names=1)
ae_att<-subset(attributes, team =="adult education")
alp_att<-subset(attributes, team =="alpheus")
hht_att<-subset(attributes, team =="hht")Now that we have the data we need to prepare it. The network variables are valued ranging from 2 (rarely for information retrieval and strongly disagree for valuing) to 6 (very frequent for information retrieval and strongly agree for valuing). While it is possible to do SAOM with valued data I did the simpler route and dichotomized my networks.
Below we define a simple function dicoGT4 that takes a matrix and changes all values above 4 to 1 and the other values to 0. We apply this function to our networks. As we have stored them in a list, this is done in 1 line, instead of 18 lines (3 (for each team) x 3 (for each wave of data) X 2 (for each network variable))
dichoGT4<-function(m){(m>4)+ 0}
alpheusgt4<-lapply(alpheus, dichoGT4)
adulteducgt4<-lapply(adulteduc, dichoGT4)
hhtgt4<-lapply(hht, dichoGT4)Now we have our variables and we are ready to create siena variables. These are necessary to tell the program RSiena which variables are dependent (sienanet) and which are independent. Independent variables can be dyadic covariates (varDyadCovar) or individual covariates (coCovar). The covariates can be changing or static. In my case they were static, meaning that they did not change between data collection periods. Once this is done, the last step is to put it all together and tell the program which variables belong to which team.
Remember that we loaded our variables for each team as a list. When you have a list, you need to include two square brackets [[ ]] to get to the content of the list. Imagine a list like an excel file with each list item as an excel sheet. The dim variable indicates how many actors are in the network (5) and how many time periods (3).
ae_is <- sienaNet(array(c(adulteducgt4[[2]],adulteducgt4[[4]],adulteducgt4[[6]]), dim=c(4,4,3)), allowOnly=FALSE)
alp_is <-sienaNet(array(c(alpheusgt4[[2]],alpheusgt4[[4]],alpheusgt4[[6]]), dim=c(4,4,3)), allowOnly=FALSE)
hht_is <-sienaNet(array(c(hhtgt4[[2]],hhtgt4[[4]],hhtgt4[[6]]), dim=c(5,5,3)), allowOnly=FALSE)
ae_val <- varDyadCovar(array(c(adulteduc[[1]], adulteduc[[3]]), dim=c(4,4,2)))
alp_val <-varDyadCovar(array(c(alpheus[[1]], alpheus[[3]]), dim=c(4,4,2)))
hht_val <-varDyadCovar(array(c(hht[[1]], hht[[3]]), dim=c(5,5,2)))
ae_ae<-coCovar(ae_att$aev2)
alp_ae<-coCovar(alp_att$aev2)
hht_ae<-coCovar(hht_att$aev2)Let’s create the groups!
group.1<- sienaDataCreate(IS = ae_is,
val=ae_val,
ae = ae_ae
)
group.2<- sienaDataCreate(IS = alp_is,
val=alp_val,
ae = alp_ae
)
group.3<- sienaDataCreate(IS = hht_is,
val = hht_val,
ae = hht_ae)We will now begin with running a basic model. This will be our null model and only contains the most basic effects you can think off. To have good convergence, use theory and exploration of your data to consider what network structures could explain your network. Similar to running an ERGM this is a bit of try and error (or an art as I heard other people say). You should have a look at the extensive documentation of network effects. Of course, you can also create your own network effects, interactions between variables.
sienaGroupCreate creates the groups. It just puts them together. The model we are using will have a random intercept for each group, but a fixed slope. getEffects creates an object with the theoretical network structures for our groups. coevalgo The file coeveffect.html provides an overview of all the effects and their naming. It contains more effects that are available to you right now, as it is based on the complete data set.
ir <- sienaGroupCreate(list(group.1, group.2, group.3))
ir_effect <- getEffects(ir)
ir_algo<-sienaAlgorithmCreate(projname = "InfoRetrieval", maxlike=TRUE, mult=6)
#get initial description
print01Report(ir, modelname = 'InfoRetrieval')The last line in the code above prints a report about your data. It contains some basic statistics (e.g., mean).
We will begin by adding some variables to our model. This is done by adding effects to our effect object ir_effect. We begin by changing reciprocity (recip) from a fixed effect to a random effect.
ir_effect <- setEffect(ir_effect, recip, random=T)## effectName include fix test initialValue parm
## 1 reciprocity TRUE FALSE FALSE 0 0The model is based on Bayesian analysis. This is beyond the scope of this workshop. Focusing on but-what-do-I-do-with you can leave the values for fix, test, initialValue, and parm untouched (for now). You can type ?setEffect to get information about the different options.
Then we add the variable valuing by stating its name (interaction1 = “val”) and that we want to know how it impacts the creation, maintenance, or dissolution of ties (type = “eval”). You can also only test the impact of a variable on the evaluation (XXX) and/or endowment (XX) of ties. X indicates the network for which the effects are included. We do the same for the variable adaptive expertise. Here, we say that this variable impacts the position of the ego, and hence add egoX and not X. Finally, we are checking if all is ok b asking R to print the effects.
ir_effect <- includeEffects(ir_effect, X, interaction1= "val", type="eval")## effectName include fix test initialValue parm
## 1 val TRUE FALSE FALSE 0 0ir_effect <- includeEffects(ir_effect,egoX, interaction1= "ae", type="eval")## effectName include fix test initialValue parm
## 1 ae ego TRUE FALSE FALSE 0 0print(ir_effect, includeRandoms=T)## effectName include fix test initialValue parm
## 1 constant IS rate (period 1) TRUE FALSE FALSE 4.36923 0
## 2 constant IS rate (period 2) TRUE FALSE FALSE 0.67692 0
## 3 constant IS rate (period 4) TRUE FALSE FALSE 2.48000 0
## 4 constant IS rate (period 5) TRUE FALSE FALSE 1.90769 0
## 5 constant IS rate (period 7) TRUE FALSE FALSE 3.85714 0
## 6 constant IS rate (period 8) TRUE FALSE FALSE 1.63158 0
## 7 outdegree (density) TRUE FALSE FALSE -0.39226 0
## 8 reciprocity TRUE FALSE FALSE 0.00000 0
## 9 val TRUE FALSE FALSE 0.00000 0
## 10 ae ego TRUE FALSE FALSE 0.00000 0
## randomEffects
## 1 FALSE
## 2 FALSE
## 3 FALSE
## 4 FALSE
## 5 FALSE
## 6 FALSE
## 7 TRUE
## 8 TRUE
## 9 FALSE
## 10 FALSE
## Dimensions of priorMu and priorSigma for sienaBayes should be 2 + 2 = 4 .The output shows the variables we are including. We assume that density and reciprocity vary between groups. The effect of valuing and adaptive expertise is the same across teams.
Now that the model is specified we can run it. This is done by using sienaBayes. You can change a lot of the parameters for running the algorithms. Higher numbers for nwarm, nmain, nrunMHBatches will give you more accurate results, but will also increase the computation times. So, be careful how you change them. nbrNodes indicates the number of processes to use on your CPU.
The first line fit1 <- sienaBayes(...) contains all the information to run the model. In the following line we are asking R to return the model and then we save it all in a text file called results_of_model.txt. This is done with an opening statement sink(filename) and a closing statement (sink()). We are appending the current results to the file. If you are running several models and want to keep track of the results this might be helpful. Without append =T you will overwrite the file.
The parameters used in this sienaBayes call are not the ones I used in my analysis. All the values are lowered for the workshop. The original values I used were sienaBayes(coevalgo, data=coev, effects=coeveffect, nwarm=100, nmain=50000, nrunMHBatches=20, initgainGroupwise=0, initgainGlobal=0, silentstart=TRUE, nbrNodes=18). Running the model below takes a short time (64.259 seconds). Running the same model using all teams takes a bit longer (1481.995 seconds).
fit1 <- sienaBayes(ir_algo, data=ir, effects=ir_effect, nwarm=10, nmain=25, nrunMHBatches=10)##
## Estimate initial global parameters
## Initial global estimates
## Estimates, standard errors and convergence t-ratios
##
## Estimate Standard Convergence
## Error t-ratio
## 1. rate constant IS rate (period 1) 98.5660 ( 231.5310 ) -2.9261
## 2. rate constant IS rate (period 2) 1.1200 ( 1.4645 ) -0.0513
## 3. rate constant IS rate (period 4) 61.6437 ( 139.6079 ) -2.0153
## 4. rate constant IS rate (period 5) 41.1782 ( 588.9581 ) -0.9998
## 5. rate constant IS rate (period 7) 25.6257 ( 1.2073 ) -0.7405
## 6. rate constant IS rate (period 8) 3.0758 ( 3.9893 ) -0.0071
## 7. eval outdegree (density) -3.6848 ( 3.8463 ) -1.4403
## 8. eval reciprocity 3.8725 ( 5.2318 ) 0.0176
## 9. eval val 5.3512 ( 6.5326 ) 3.2253
## 10. eval ae ego -0.7595 ( 1.7998 ) 0.5327
##
## Overall maximum convergence ratio: 8.3251
##
##
## Total of 1561 iteration steps.
##
##
##
## maximum initial global estimate is 98.56599
## Group 1
## Estimate initial parameters group 1
##
## Initial estimate obtained
## 107.656 0.500 -0.512 -2.189 5.351 -0.760
## Group 2
## Estimate initial parameters group 2
##
## Initial estimate obtained
## 64.234 37.949 -4.210 6.131 5.351 -0.760
## Group 3
## Estimate initial parameters group 3
##
## Initial estimate obtained
## 22.721 5.349 -2.425 2.645 5.351 -0.760
## Condition priorRatesFromData=2 impossible, changed to 1.
## Initial global model estimates
## Estimates, standard errors and convergence t-ratios
##
## Estimate Standard Convergence
## Error t-ratio
## 1. rate constant IS rate (period 1) 98.5660 ( 231.5310 ) -2.9261
## 2. rate constant IS rate (period 2) 1.1200 ( 1.4645 ) -0.0513
## 3. rate constant IS rate (period 4) 61.6437 ( 139.6079 ) -2.0153
## 4. rate constant IS rate (period 5) 41.1782 ( 588.9581 ) -0.9998
## 5. rate constant IS rate (period 7) 25.6257 ( 1.2073 ) -0.7405
## 6. rate constant IS rate (period 8) 3.0758 ( 3.9893 ) -0.0071
## 7. eval outdegree (density) -3.6848 ( 3.8463 ) -1.4403
## 8. eval reciprocity 3.8725 ( 5.2318 ) 0.0176
## 9. eval val 5.3512 ( 6.5326 ) 3.2253
## 10. eval ae ego -0.7595 ( 1.7998 ) 0.5327
##
## Overall maximum convergence ratio: 8.3251
##
##
## Total of 1561 iteration steps.
##
## 6.468
## improveMH
## Desired acceptances 25 .
## ..........
## 1 . 8.5 2.7 6.9 2.1 2.7
## multipliers 0.500 0.200 0.500 0.200 0.200
## scaleFactors 0.417 0.167 0.417 0.167 0.167
## ..........
## 2 . 7.9 10.6 11.7 4.1 6.5
## multipliers 0.500 0.500 0.500 0.200 0.500
## scaleFactors 0.208 0.083 0.208 0.033 0.083
## ..........
## 3 . 5.5 10.8 26.3 13.6 15.2
## multipliers 0.500 0.500 1.023 0.500 0.829
## scaleFactors 0.104 0.042 0.213 0.017 0.069
## ..........
## 4 . 13.8 24.6 21.3 14.4 15.1
## multipliers 0.500 0.993 0.939 0.500 0.839
## scaleFactors 0.052 0.041 0.200 0.008 0.058
## ..........
## 5 . 20.4 26.0 23.3 13.2 10.6
## multipliers 0.929 1.016 0.973 0.500 0.778
## scaleFactors 0.048 0.042 0.195 0.004 0.045
## ..........
## 6 . 21.4 22.5 19.5 14.2 8.9
## multipliers 0.946 0.963 0.919 0.500 0.762
## scaleFactors 0.046 0.041 0.179 0.002 0.034
## ..........
## 7 . 22.6 23.2 25.4 14.3 16.4
## multipliers 0.966 0.975 1.005 0.500 0.878
## scaleFactors 0.044 0.039 0.180 0.001 0.030
## ..........
## 8 . 22.7 29.2 27.3 21.3 22.2
## multipliers 0.969 1.057 1.032 0.950 0.962
## scaleFactors 0.043 0.042 0.186 0.001 0.029
## ..........
## 9 . 23.9 28.8 27.7 20.8 20.1
## multipliers 0.986 1.050 1.036 0.944 0.934
## scaleFactors 0.042 0.044 0.193 0.001 0.027
## fine tuning took 9 iterations.
## improveMH 22.157 seconds.
## .Warming step 1 ( 10 )
## Accepts 9 / 30
## .Warming step 2 ( 10 )
## Accepts 9 / 30
## .Warming step 3 ( 10 )
## Accepts 10 / 30
## .Warming step 4 ( 10 )
## Accepts 18 / 30
## .Warming step 5 ( 10 )
## Accepts 8 / 30
## .Warming step 6 ( 10 )
## Accepts 8 / 30
## .Warming step 7 ( 10 )
## Accepts 8 / 30
## .Warming step 8 ( 10 )
## Accepts 9 / 30
## .Warming step 9 ( 10 )
## Accepts 10 / 30
## .Warming step 10 ( 10 )
## Accepts 9 / 30
## [1] "end of warming"
## warming took 2.874 seconds.
## Parameter values after warming up
## 1 . 107.684 1.056 -0.158 -2.441 5.262 -0.092
## 2 . 55.183 38.286 -4.138 6.073 5.262 -0.092
## 3 . 22.546 5.874 -3.089 3.317 5.262 -0.092
##
## Second improveMH
## Desired acceptances 25 .
## ..........
## 1 . 19.4 15.5 27.7 14.9 9.4
## multipliers 0.870 0.780 1.062 0.500 0.500
## scaleFactors 0.037 0.034 0.205 0.000 0.014
## ..........
## 2 . 29.0 18.7 23.5 20.0 30.1
## multipliers 1.077 0.878 0.970 0.902 1.100
## scaleFactors 0.040 0.030 0.198 0.000 0.015
## ..........
## 3 . 27.0 32.0 21.7 22.4 18.9
## multipliers 1.035 1.122 0.942 0.954 0.893
## scaleFactors 0.041 0.034 0.187 0.000 0.013
## ..........
## 4 . 25.5 34.4 20.9 20.6 25.7
## multipliers 1.008 1.154 0.932 0.928 1.012
## scaleFactors 0.041 0.039 0.174 0.000 0.013
## ..........
## 5 . 26.0 26.2 22.3 22.7 24.0
## multipliers 1.015 1.018 0.959 0.964 0.984
## scaleFactors 0.042 0.040 0.167 0.000 0.013
## ..........
## 6 . 27.8 29.5 25.6 22.4 22.5
## multipliers 1.042 1.066 1.009 0.962 0.963
## scaleFactors 0.044 0.042 0.169 0.000 0.013
## fine tuning took 6 iterations.
## Second improveMH 18.282 seconds.
## .main 11 ( 35 )
## Mu = 60.081 9.142 -2.072 1.55
## Eta = 5.443 0.008
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 2562.9877 -37.4758 48.6765 -33.3434
## [2,] -37.4758 340.5773 -10.3205 13.1204
## [3,] 48.6765 -10.3205 2.7185 -2.4008
## [4,] -33.3434 13.1204 -2.4008 3.2732
##
## main 11 ( 35 ) Accepts 14 / 30
## .main 12 ( 35 )
## Mu = 65.463 16.362 -1.777 0.547
## Eta = 5.002 0.025
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 2223.4143 273.2853 19.0228 -70.2343
## [2,] 273.2853 499.5236 13.5227 -35.7717
## [3,] 19.0228 13.5227 1.7909 -3.0972
## [4,] -70.2343 -35.7717 -3.0972 8.3691
##
## main 12 ( 35 ) Accepts 17 / 30
## .main 13 ( 35 )
## Mu = 55.673 -3.936 -1.704 3.026
## Eta = 5.472 -0.41
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 1805.4771 194.0165 22.6238 -43.3879
## [2,] 194.0165 705.2253 -6.4457 -24.7245
## [3,] 22.6238 -6.4457 1.6956 -1.1956
## [4,] -43.3879 -24.7245 -1.1956 4.6249
##
## main 13 ( 35 ) Accepts 15 / 30
## .main 14 ( 35 )
## Mu = 35.119 21.978 -1.997 3.502
## Eta = 5.312 -0.787
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 2211.4800 934.1939 0.7696 6.6220
## [2,] 934.1939 1041.1349 -10.6270 58.8604
## [3,] 0.7696 -10.6270 2.6982 -2.8942
## [4,] 6.6220 58.8604 -2.8942 15.5941
##
## main 14 ( 35 ) Accepts 11 / 30
## .main 15 ( 35 )
## Mu = 68.519 40.797 -0.489 0.435
## Eta = 5.287 -0.884
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 2187.9418 45.8678 -7.0783 22.1127
## [2,] 45.8678 1231.1211 65.2484 -74.7619
## [3,] -7.0783 65.2484 6.9262 -9.6065
## [4,] 22.1127 -74.7619 -9.6065 15.1284
##
## main 15 ( 35 ) Accepts 17 / 30
## .main 16 ( 35 )
## Mu = -5.008 42.186 -3.495 2.045
## Eta = 5.679 -0.851
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 9272.258 -1392.260 143.784 -204.312
## [2,] -1392.260 864.151 -19.253 0.913
## [3,] 143.784 -19.253 4.474 -5.374
## [4,] -204.312 0.913 -5.374 9.355
##
## main 16 ( 35 ) Accepts 11 / 30
## .main 17 ( 35 )
## Mu = 11.281 43.125 -1.817 0.924
## Eta = 5.818 -0.959
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 5186.463 -729.732 59.009 -135.290
## [2,] -729.732 463.678 0.397 0.629
## [3,] 59.009 0.397 2.388 -2.797
## [4,] -135.290 0.629 -2.797 8.071
##
## main 17 ( 35 ) Accepts 15 / 30
## .main 18 ( 35 )
## Mu = 92.317 4.517 0.204 0.412
## Eta = 5.43 -0.877
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 1917.302 -508.170 104.430 -57.980
## [2,] -508.170 567.111 -33.359 14.130
## [3,] 104.430 -33.359 13.881 -6.884
## [4,] -57.980 14.130 -6.884 6.495
##
## main 18 ( 35 ) Accepts 14 / 30
## .main 19 ( 35 )
## Mu = 32.098 21.315 -6.521 7.811
## Eta = 4.909 -0.899
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 3109.153 -397.611 81.516 -136.320
## [2,] -397.611 650.024 -4.086 2.489
## [3,] 81.516 -4.086 14.588 -21.328
## [4,] -136.320 2.489 -21.328 37.765
##
## main 19 ( 35 ) Accepts 11 / 30
## .main 20 ( 35 )
## Mu = 72.631 40.304 -1.759 0.011
## Eta = 5.406 -0.631
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 1515.124 646.846 10.364 -52.964
## [2,] 646.846 898.438 7.460 -52.890
## [3,] 10.364 7.460 1.524 -2.477
## [4,] -52.964 -52.890 -2.477 7.410
##
## main 20 ( 35 ) Accepts 6 / 30
## .main 21 ( 35 )
## Mu = 33.227 -0.84 -4.115 2.884
## Eta = 5.385 -0.142
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 1505.943 45.768 26.055 -39.755
## [2,] 45.768 471.327 13.366 -21.199
## [3,] 26.055 13.366 2.821 -2.652
## [4,] -39.755 -21.199 -2.652 5.072
##
## main 21 ( 35 ) Accepts 10 / 30
## .main 22 ( 35 )
## Mu = 67.526 48.088 0.12 0.926
## Eta = 5.513 -0.005
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 1246.843 214.088 27.474 -28.455
## [2,] 214.088 875.895 76.901 -39.873
## [3,] 27.474 76.901 8.965 -3.882
## [4,] -28.455 -39.873 -3.882 5.288
##
## main 22 ( 35 ) Accepts 7 / 30
## .main 23 ( 35 )
## Mu = 51.45 24.25 -2.558 2.245
## Eta = 5.027 -0.242
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 1589.391 -19.698 46.946 -92.444
## [2,] -19.698 405.667 13.416 -37.314
## [3,] 46.946 13.416 5.147 -8.483
## [4,] -92.444 -37.314 -8.483 16.692
##
## main 23 ( 35 ) Accepts 15 / 30
## .main 24 ( 35 )
## Mu = 59.821 14.965 -0.999 -0.107
## Eta = 5.157 -0.432
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 2237.511 660.550 -11.565 -30.327
## [2,] 660.550 728.572 -18.770 -11.154
## [3,] -11.565 -18.770 3.344 -1.784
## [4,] -30.327 -11.154 -1.784 6.188
##
## main 24 ( 35 ) Accepts 12 / 30
## .main 25 ( 35 )
## Mu = 37.783 4.22 -2.997 3.099
## Eta = 5.875 -0.276
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 3387.000 158.018 84.065 -155.708
## [2,] 158.018 288.359 11.120 -14.886
## [3,] 84.065 11.120 4.636 -6.051
## [4,] -155.708 -14.886 -6.051 10.723
##
## main 25 ( 35 ) Accepts 11 / 30
## .main 26 ( 35 )
## Mu = 66.631 5.372 -1.258 1.04
## Eta = 5.214 0.122
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 4517.426 518.511 83.703 -170.816
## [2,] 518.511 549.756 2.632 -28.992
## [3,] 83.703 2.632 3.479 -3.774
## [4,] -170.816 -28.992 -3.774 8.920
##
## main 26 ( 35 ) Accepts 15 / 30
## .main 27 ( 35 )
## Mu = 67.007 7.227 0.184 -0.996
## Eta = 4.659 -0.491
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 4829.655 -402.744 118.559 -163.709
## [2,] -402.744 408.900 -13.374 5.339
## [3,] 118.559 -13.374 4.996 -5.615
## [4,] -163.709 5.339 -5.615 8.773
##
## main 27 ( 35 ) Accepts 17 / 30
## .main 28 ( 35 )
## Mu = 66.255 17.514 -2.069 3.018
## Eta = 4.967 -0.521
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 13862.997 -445.905 159.881 -102.649
## [2,] -445.905 158.617 -4.082 5.068
## [3,] 159.881 -4.082 3.013 -3.129
## [4,] -102.649 5.068 -3.129 8.254
##
## main 28 ( 35 ) Accepts 13 / 30
## .main 29 ( 35 )
## Mu = 135.073 21.306 -0.356 -1.793
## Eta = 5.173 -0.418
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 7841.699 -131.831 83.672 -286.607
## [2,] -131.831 467.080 -2.841 7.256
## [3,] 83.672 -2.841 2.618 -3.883
## [4,] -286.607 7.256 -3.883 12.550
##
## main 29 ( 35 ) Accepts 14 / 30
## .main 30 ( 35 )
## Mu = 60.439 24.043 -0.77 0.297
## Eta = 5.063 -0.266
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 2739.481 528.214 -25.670 -38.846
## [2,] 528.214 1348.651 4.557 -32.478
## [3,] -25.670 4.557 7.136 -4.532
## [4,] -38.846 -32.478 -4.532 5.756
##
## main 30 ( 35 ) Accepts 9 / 30
##
## Mu = 60.439 24.043 -0.77 0.297
## Eta = 5.063 -0.266
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 2739.481 528.214 -25.670 -38.846
## [2,] 528.214 1348.651 4.557 -32.478
## [3,] -25.670 4.557 7.136 -4.532
## [4,] -38.846 -32.478 -4.532 5.756
##
## .main 31 ( 35 )
## Mu = 50.752 -0.166 -3.357 1.398
## Eta = 4.764 0.153
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 7085.484 -246.648 34.065 29.466
## [2,] -246.648 1033.533 46.472 -23.755
## [3,] 34.065 46.472 4.269 -2.509
## [4,] 29.466 -23.755 -2.509 5.655
##
## main 31 ( 35 ) Accepts 9 / 30
## .main 32 ( 35 )
## Mu = 129.901 9.109 -1.95 0.478
## Eta = 5.385 0.319
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 4187.638 -573.299 -39.962 2.073
## [2,] -573.299 870.115 28.457 -50.584
## [3,] -39.962 28.457 3.287 -3.978
## [4,] 2.073 -50.584 -3.978 7.406
##
## main 32 ( 35 ) Accepts 17 / 30
## .main 33 ( 35 )
## Mu = 45.362 24.35 -1.635 -0.785
## Eta = 5.166 0.509
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 2174.856 -194.361 56.656 -75.177
## [2,] -194.361 246.624 -16.066 18.341
## [3,] 56.656 -16.066 6.762 -10.502
## [4,] -75.177 18.341 -10.502 19.076
##
## main 33 ( 35 ) Accepts 11 / 30
## .main 34 ( 35 )
## Mu = 96.093 25.623 -1.913 1.632
## Eta = 4.827 0.696
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 4227.004 788.493 35.317 -48.436
## [2,] 788.493 509.315 13.440 -7.154
## [3,] 35.317 13.440 3.301 -2.836
## [4,] -48.436 -7.154 -2.836 4.381
##
## main 34 ( 35 ) Accepts 8 / 30
## .main 35 ( 35 )
## Mu = 34.508 20.375 -2.125 0.742
## Eta = 4.871 0.439
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 2674.147 468.762 48.249 -115.126
## [2,] 468.762 563.602 -1.731 -3.261
## [3,] 48.249 -1.731 3.557 -7.447
## [4,] -115.126 -3.261 -7.447 21.841
##
## main 35 ( 35 ) Accepts 14 / 30
## Total duration 58.843 seconds.Of course, we want to see the results of the model. To do this, we have to modify the print.sienaBayes function as NA’s have crept into the output. In the function print.sienaBayes the parameters are rounded, which doesn’t work if a vector has numbers and NA. This is not recognized as a numeric vector but as a XXX, which the round function doesn’t accept. We will load the functions below, which will override the print function we loaded with the package. An alternative is to rename the function.
source("sienaprint_modified.R", echo=F)fit1## Note: this summary does not contain a convergence check.
##
## Groups:
## Data1 Data2 Data3
##
## Posterior means and standard deviations for global mean parameters
##
## Total number of runs in the results is 35 .
## Posterior means and standard deviations are averages over 25 MCMC runs (counted after thinning).
##
## Post. Post. cred. cred. p varying Post. cred. cred.
## mean s.d.m. from to s.d. from to
## 1. rate constant IS rate (period 1) 107.0316 ( 0.2165 ) NA NA NA
## 2. rate constant IS rate (period 2) 0.8344 ( 0.2601 ) NA NA NA
## 3. rate constant IS rate (period 4) 55.3001 ( 0.4332 ) NA NA NA
## 4. rate constant IS rate (period 5) 38.9371 ( 0.2727 ) NA NA NA
## 5. rate constant IS rate (period 7) 22.8303 ( 0.6003 ) NA NA NA
## 6. rate constant IS rate (period 8) 5.5880 ( 0.8878 ) NA NA NA
## 7. eval outdegree (density) -1.8889 ( 1.4798 ) -5.0775 0.1920 0.12 + 2.1910 1.2755 3.7635
## 8. eval reciprocity 1.3737 ( 1.9114 ) -1.3144 5.2257 0.84 + 3.2414 1.9844 5.3113
## 9. eval val 5.2322 ( 0.3174 ) 4.7216 5.8410 1.00 - NA NA NA
## 10. eval ae ego -0.2727 ( 0.4789 ) -0.9226 0.5839 0.32 - NA NA NA
##
## Posterior mean of global covariance matrix (varying parameters)
## 3843.9470 15.8751 48.4225 -80.8644
## 15.8751 647.4799 6.2414 -13.3061
## 48.4225 6.2414 4.8007 -5.1644
## -80.8644 -13.3061 -5.1644 10.5064
##
## Posterior standard deviations of elements of global covariance matrix
## 2949.5244 539.7733 50.4787 75.8764
## 539.7733 306.6939 25.5556 28.1338
## 50.4787 25.5556 3.3900 4.1670
## 75.8764 28.1338 4.1670 7.4675sink("results_of_model.txt", append=T)
fit1## Note: this summary does not contain a convergence check.
##
## Groups:
## Data1 Data2 Data3
##
## Posterior means and standard deviations for global mean parameters
##
## Total number of runs in the results is 35 .
## Posterior means and standard deviations are averages over 25 MCMC runs (counted after thinning).
##
## Post. Post. cred. cred. p varying Post. cred. cred.
## mean s.d.m. from to s.d. from to
## 1. rate constant IS rate (period 1) 107.0316 ( 0.2165 ) NA NA NA
## 2. rate constant IS rate (period 2) 0.8344 ( 0.2601 ) NA NA NA
## 3. rate constant IS rate (period 4) 55.3001 ( 0.4332 ) NA NA NA
## 4. rate constant IS rate (period 5) 38.9371 ( 0.2727 ) NA NA NA
## 5. rate constant IS rate (period 7) 22.8303 ( 0.6003 ) NA NA NA
## 6. rate constant IS rate (period 8) 5.5880 ( 0.8878 ) NA NA NA
## 7. eval outdegree (density) -1.8889 ( 1.4798 ) -5.0775 0.1920 0.12 + 2.1910 1.2755 3.7635
## 8. eval reciprocity 1.3737 ( 1.9114 ) -1.3144 5.2257 0.84 + 3.2414 1.9844 5.3113
## 9. eval val 5.2322 ( 0.3174 ) 4.7216 5.8410 1.00 - NA NA NA
## 10. eval ae ego -0.2727 ( 0.4789 ) -0.9226 0.5839 0.32 - NA NA NA
##
## Posterior mean of global covariance matrix (varying parameters)
## 3843.9470 15.8751 48.4225 -80.8644
## 15.8751 647.4799 6.2414 -13.3061
## 48.4225 6.2414 4.8007 -5.1644
## -80.8644 -13.3061 -5.1644 10.5064
##
## Posterior standard deviations of elements of global covariance matrix
## 2949.5244 539.7733 50.4787 75.8764
## 539.7733 306.6939 25.5556 28.1338
## 50.4787 25.5556 3.3900 4.1670
## 75.8764 28.1338 4.1670 7.4675sink()After you run a model, you should check convergence. The lines below will create a couple of plots. We are looking for any types of irregularities, upward, or downward trends. To run the convergence check we first need to load another R file with the necessary scripts. I did not want to see the output of running the file and hence I have added echo=F (You can write out TRUE or FALSE or add the shorthand T and F).
source("BayesPlots.R", echo=F)The following two lines of code will test convergence for every variable and for every team. If you want you can change folders before and after to save the files in a specific place or modify the function RateTracePlots and NonRateTracePlots to include an option for a file path.
RateTracePlots(fit1)
NonRateTracePlots(fit1)In your working directory you should now see 10 pictures (png files). Instructions about what these are in the BayesPlots.R file we loaded.
We are going to look at fit1_NRTP_1.png. First a bit of background. What did you do so far ? You run a number of Markov Chain Monte Carlo (MCMC) simulations using Bayesian regression. The goal of this is to find the values for your variables. The provided link provides an excellent explanation of how this is done. In this example, you ran 35 simulations (nwarm = 10 and nmain = 25). At the end of every simulation, your variables were given certain values. These values you see as dots on your graph. Convergence happens when the values are similar in each run of the simulation. With our current analysis, it is not possible to make any claims about that. Theta is to Bayesian calculation what beta is to classical frequentist calculations.
As with any other model, you can now decide to add or remove effects until you answered all your questions. For example, we can test for balance (transTrip). We’ll add the effects to our effect object ir_effect, and run the model using sienaBayes. We are using a new fit name fit2 so that we look again at the results we want, extract numbers from fit1. If you are running into memory problems, then you might want to overwrite the model. You could first save fit1 as an Rdata file (save(object, file = filepath)). We did a couple of changes to the sienaBayes call. We increased the length of the Markov Chain, by increasing nwarm and nmain, and asked for a silentstart to reduce the output we get in the console. Running this model takes 58 seconds.
ir_effect<-includeEffects(ir_effect, transTrip)## effectName include fix test initialValue parm
## 1 transitive triplets TRUE FALSE FALSE 0 0fit2 <- sienaBayes(ir_algo, data=ir, effects=ir_effect, nwarm=20, nmain=70, nrunMHBatches=10, silentstart=T)##
## Estimate initial global parameters
## Initial global estimates
## Estimates, standard errors and convergence t-ratios
##
## Estimate Standard Convergence
## Error t-ratio
## 1. rate constant IS rate (period 1) 109.7747 ( 68.3731 ) -3.1624
## 2. rate constant IS rate (period 2) 0.9344 ( 1.3306 ) -0.0685
## 3. rate constant IS rate (period 4) 69.8081 ( 68.0915 ) -2.5458
## 4. rate constant IS rate (period 5) 33.6923 ( 110.1572 ) -0.7452
## 5. rate constant IS rate (period 7) 17.5704 ( 61.0063 ) -0.4217
## 6. rate constant IS rate (period 8) 2.9523 ( 3.0414 ) 0.0688
## 7. eval outdegree (density) -3.5084 ( 2.4914 ) -1.7725
## 8. eval reciprocity 2.8842 ( 2.1550 ) -0.4840
## 9. eval transitive triplets 0.5074 ( 0.5172 ) -0.5661
## 10. eval val 4.2113 ( 4.2279 ) 2.8314
## 11. eval ae ego -0.3657 ( 1.7087 ) 0.5262
##
## Overall maximum convergence ratio: 6.9309
##
##
## Total of 1692 iteration steps.
##
##
##
## maximum initial global estimate is 109.7747
## Group 1
## Estimate initial parameters group 1
##
## Initial estimate obtained
## 119.784 0.490 -2.024 -2.264 0.507 4.211 -0.366
## Group 2
## Estimate initial parameters group 2
##
## Initial estimate obtained
## 85.231 37.264 -3.156 3.257 0.507 4.211 -0.366
## Group 3
## Estimate initial parameters group 3
##
## Initial estimate obtained
## 19.834 2.698 -3.685 2.458 0.507 4.211 -0.366
## Condition priorRatesFromData=2 impossible, changed to 1.
## Initial global model estimates
## Estimates, standard errors and convergence t-ratios
##
## Estimate Standard Convergence
## Error t-ratio
## 1. rate constant IS rate (period 1) 109.7747 ( 68.3731 ) -3.1624
## 2. rate constant IS rate (period 2) 0.9344 ( 1.3306 ) -0.0685
## 3. rate constant IS rate (period 4) 69.8081 ( 68.0915 ) -2.5458
## 4. rate constant IS rate (period 5) 33.6923 ( 110.1572 ) -0.7452
## 5. rate constant IS rate (period 7) 17.5704 ( 61.0063 ) -0.4217
## 6. rate constant IS rate (period 8) 2.9523 ( 3.0414 ) 0.0688
## 7. eval outdegree (density) -3.5084 ( 2.4914 ) -1.7725
## 8. eval reciprocity 2.8842 ( 2.1550 ) -0.4840
## 9. eval transitive triplets 0.5074 ( 0.5172 ) -0.5661
## 10. eval val 4.2113 ( 4.2279 ) 2.8314
## 11. eval ae ego -0.3657 ( 1.7087 ) 0.5262
##
## Overall maximum convergence ratio: 6.9309
##
##
## Total of 1692 iteration steps.
##
## 8.893
## improveMH
## Desired acceptances 25 .
## ..........
## 1 . 3.1 32.4 6.1 3.1 3.0
## multipliers 0.200 1.171 0.500 0.200 0.200
## scaleFactors 0.143 0.836 0.357 0.143 0.143
## ..........
## 2 . 4.2 23.3 13.1 11.0 6.0
## multipliers 0.200 0.968 0.500 0.500 0.500
## scaleFactors 0.029 0.809 0.179 0.071 0.071
## ..........
## 3 . 22.4 23.1 23.1 11.6 12.4
## multipliers 0.955 0.966 0.966 0.500 0.500
## scaleFactors 0.027 0.782 0.173 0.036 0.036
## ..........
## 4 . 20.2 23.3 29.6 18.9 21.5
## multipliers 0.922 0.972 1.075 0.900 0.943
## scaleFactors 0.025 0.760 0.185 0.032 0.034
## ..........
## 5 . 23.7 27.4 29.2 13.8 23.2
## multipliers 0.980 1.037 1.065 0.827 0.973
## scaleFactors 0.025 0.788 0.198 0.027 0.033
## ..........
## 6 . 23.4 24.0 26.3 10.3 20.0
## multipliers 0.977 0.985 1.019 0.783 0.926
## scaleFactors 0.024 0.777 0.201 0.021 0.030
## ..........
## 7 . 23.9 24.7 21.5 9.5 18.4
## multipliers 0.984 0.995 0.951 0.780 0.907
## scaleFactors 0.024 0.773 0.191 0.016 0.027
## ..........
## 8 . 21.7 19.0 26.8 12.0 14.6
## multipliers 0.955 0.918 1.024 0.822 0.857
## scaleFactors 0.023 0.710 0.196 0.013 0.024
## ..........
## 9 . 23.7 17.8 30.9 12.4 12.6
## multipliers 0.982 0.905 1.079 0.832 0.835
## scaleFactors 0.022 0.642 0.211 0.011 0.020
## ..........
## 10 . 23.3 25.6 27.5 10.1 14.7
## multipliers 0.978 1.007 1.032 0.807 0.866
## scaleFactors 0.022 0.647 0.218 0.009 0.017
## ..........
## 11 . 22.7 23.9 27.9 18.5 16.8
## multipliers 0.971 0.986 1.037 0.918 0.896
## scaleFactors 0.021 0.638 0.226 0.008 0.015
## ..........
## 12 . 25.0 22.1 24.8 13.9 16.2
## multipliers 1.000 0.964 0.997 0.862 0.891
## scaleFactors 0.021 0.615 0.225 0.007 0.014
## ..........
## 13 . 26.3 27.7 20.5 21.9 17.7
## multipliers 1.015 1.033 0.945 0.963 0.912
## scaleFactors 0.021 0.635 0.213 0.007 0.012
## ..........
## 14 . 30.1 27.0 25.4 25.1 18.4
## multipliers 1.061 1.024 1.005 1.001 0.922
## scaleFactors 0.023 0.650 0.214 0.007 0.011
## fine tuning took 14 iterations.
## improveMH 42.559 seconds.
## .Warming step 1 ( 20 )
## Accepts 19 / 30
## .Warming step 2 ( 20 )
## Accepts 16 / 30
## .Warming step 3 ( 20 )
## Accepts 9 / 30
## .Warming step 4 ( 20 )
## Accepts 14 / 30
## .Warming step 5 ( 20 )
## Accepts 13 / 30
## .Warming step 6 ( 20 )
## Accepts 15 / 30
## .Warming step 7 ( 20 )
## Accepts 14 / 30
## .Warming step 8 ( 20 )
## Accepts 21 / 30
## .Warming step 9 ( 20 )
## Accepts 12 / 30
## .Warming step 10 ( 20 )
## Accepts 15 / 30
## .Warming step 11 ( 20 )
## Accepts 15 / 30
## .Warming step 12 ( 20 )
## Accepts 16 / 30
## .Warming step 13 ( 20 )
## Accepts 11 / 30
## .Warming step 14 ( 20 )
## Accepts 14 / 30
## .Warming step 15 ( 20 )
## Accepts 14 / 30
## .Warming step 16 ( 20 )
## Accepts 15 / 30
## .Warming step 17 ( 20 )
## Accepts 12 / 30
## .Warming step 18 ( 20 )
## Accepts 10 / 30
## .Warming step 19 ( 20 )
## Accepts 12 / 30
## .Warming step 20 ( 20 )
## Accepts 8 / 30
## [1] "end of warming"
## warming took 6.854 seconds.
## Parameter values after warming up
## 1 . 119.514 0.282 -1.936 -0.255 0.619 3.022 0.358
## 2 . 55.002 33.848 -3.303 3.527 0.619 3.022 0.358
## 3 . 20.833 2.166 -3.087 2.927 0.619 3.022 0.358
##
## Second improveMH
## Desired acceptances 25 .
## ..........
## 1 . 21.2 26.1 15.5 24.6 19.8
## multipliers 0.912 1.026 0.782 0.990 0.880
## scaleFactors 0.021 0.667 0.167 0.007 0.010
## ..........
## 2 . 24.9 27.1 23.2 25.4 21.4
## multipliers 0.998 1.040 0.964 1.007 0.930
## scaleFactors 0.021 0.693 0.161 0.007 0.009
## ..........
## 3 . 22.3 23.9 24.5 25.8 24.3
## multipliers 0.952 0.980 0.992 1.014 0.987
## scaleFactors 0.020 0.680 0.160 0.007 0.009
## fine tuning took 3 iterations.
## Second improveMH 8.678 seconds.
## .main 21 ( 90 )
## Mu = 96.332 31.631 -1.698 0.666
## Eta = 0.724 3.057 0.525
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 6423.2422 584.9054 52.7285 -110.9752
## [2,] 584.9054 707.3657 2.7611 -33.7286
## [3,] 52.7285 2.7611 1.1882 -1.4107
## [4,] -110.9752 -33.7286 -1.4107 4.1052
##
## main 21 ( 90 ) Accepts 11 / 30
## .main 22 ( 90 )
## Mu = 12.445 9.518 -3.423 3.604
## Eta = 0.63 3.152 0.955
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 5843.5821 1310.1028 125.6160 -167.2625
## [2,] 1310.1028 640.9783 41.2713 -56.5304
## [3,] 125.6160 41.2713 5.1536 -5.8505
## [4,] -167.2625 -56.5304 -5.8505 8.8677
##
## main 22 ( 90 ) Accepts 9 / 30
## .main 23 ( 90 )
## Mu = 42.101 45.224 -2.329 0.991
## Eta = 0.61 3.208 0.944
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 1992.9558 -278.2571 10.1120 -42.4710
## [2,] -278.2571 1127.8526 14.2256 15.9315
## [3,] 10.1120 14.2256 1.3987 0.2088
## [4,] -42.4710 15.9315 0.2088 3.8943
##
## main 23 ( 90 ) Accepts 12 / 30
## .main 24 ( 90 )
## Mu = 87.284 36.84 -2.177 1.692
## Eta = 0.636 3.463 0.938
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 3233.7348 384.9111 11.0100 -32.4533
## [2,] 384.9111 375.8406 -3.2391 7.3269
## [3,] 11.0100 -3.2391 1.6098 -1.5289
## [4,] -32.4533 7.3269 -1.5289 2.9613
##
## main 24 ( 90 ) Accepts 10 / 30
## .main 25 ( 90 )
## Mu = 70.438 18.305 -2.115 2.358
## Eta = 0.679 3.541 0.87
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 2935.1672 131.6599 -6.2507 -58.6239
## [2,] 131.6599 121.5569 0.5726 0.4744
## [3,] -6.2507 0.5726 2.3104 -1.1497
## [4,] -58.6239 0.4744 -1.1497 6.6024
##
## main 25 ( 90 ) Accepts 8 / 30
## .main 26 ( 90 )
## Mu = 63.417 32.023 -2.908 1.983
## Eta = 0.715 3.475 0.642
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 2461.4782 96.7916 9.5915 -51.4765
## [2,] 96.7916 551.9680 -16.8667 -24.5826
## [3,] 9.5915 -16.8667 2.0936 -0.2728
## [4,] -51.4765 -24.5826 -0.2728 3.9530
##
## main 26 ( 90 ) Accepts 20 / 30
## .main 27 ( 90 )
## Mu = 25.341 11.015 -3.985 3.148
## Eta = 0.678 3.063 0.493
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 3128.6067 576.2101 -32.4866 8.0802
## [2,] 576.2101 500.4019 -29.3727 22.7313
## [3,] -32.4866 -29.3727 7.0305 -5.5977
## [4,] 8.0802 22.7313 -5.5977 5.2315
##
## main 27 ( 90 ) Accepts 14 / 30
## .main 28 ( 90 )
## Mu = -27.19 5.553 -1.978 3.166
## Eta = 0.643 3.033 0.289
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 10527.9829 1878.3854 55.4597 -250.3731
## [2,] 1878.3854 1017.9363 7.2731 -56.1548
## [3,] 55.4597 7.2731 1.8839 -2.3177
## [4,] -250.3731 -56.1548 -2.3177 7.6626
##
## main 28 ( 90 ) Accepts 10 / 30
## .main 29 ( 90 )
## Mu = 59.949 33.455 -1.804 1.84
## Eta = 0.736 3.169 0.44
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 3832.7532 -585.4998 -67.3846 -46.5252
## [2,] -585.4998 818.3551 19.6853 -6.4835
## [3,] -67.3846 19.6853 4.7077 0.8587
## [4,] -46.5252 -6.4835 0.8587 2.2296
##
## main 29 ( 90 ) Accepts 7 / 30
## .main 30 ( 90 )
## Mu = 51.977 21.125 -2.867 3.094
## Eta = 0.711 3.31 0.519
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 3469.2825 418.1795 41.9798 -119.4906
## [2,] 418.1795 397.3684 5.1199 -9.3729
## [3,] 41.9798 5.1199 2.1572 -2.3217
## [4,] -119.4906 -9.3729 -2.3217 6.8547
##
## main 30 ( 90 ) Accepts 14 / 30
## .main 31 ( 90 )
## Mu = 95.029 17.798 -3.245 2.673
## Eta = 0.747 3.362 0.513
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 4149.1000 -281.0279 10.6908 -86.4962
## [2,] -281.0279 1262.6945 -20.4970 5.2351
## [3,] 10.6908 -20.4970 2.2472 -0.7172
## [4,] -86.4962 5.2351 -0.7172 4.4805
##
## main 31 ( 90 ) Accepts 11 / 30
## .main 32 ( 90 )
## Mu = 45.334 -3.338 -2.002 2.118
## Eta = 0.655 2.811 0.79
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 2109.0968 879.8126 3.9370 -39.6963
## [2,] 879.8126 1475.0510 48.9004 -45.4021
## [3,] 3.9370 48.9004 6.6354 -2.5863
## [4,] -39.6963 -45.4021 -2.5863 3.0536
##
## main 32 ( 90 ) Accepts 21 / 30
## .main 33 ( 90 )
## Mu = 127.038 39.755 -1.545 -0.21
## Eta = 0.684 2.978 0.577
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 4997.5212 648.6072 66.3903 -157.9086
## [2,] 648.6072 403.3040 8.0901 -26.0793
## [3,] 66.3903 8.0901 1.7452 -2.6768
## [4,] -157.9086 -26.0793 -2.6768 6.2041
##
## main 33 ( 90 ) Accepts 20 / 30
## .main 34 ( 90 )
## Mu = -62.029 16.614 -3.291 5.68
## Eta = 0.777 2.731 0.579
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 27967.7057 895.7162 198.2378 -745.8356
## [2,] 895.7162 591.2242 7.1659 -29.2825
## [3,] 198.2378 7.1659 1.9918 -5.6025
## [4,] -745.8356 -29.2825 -5.6025 20.7177
##
## main 34 ( 90 ) Accepts 10 / 30
## .main 35 ( 90 )
## Mu = 76.438 22.438 -3.149 1.739
## Eta = 0.869 2.582 0.304
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 10924.826 3091.449 58.629 -194.766
## [2,] 3091.449 1361.899 19.256 -71.161
## [3,] 58.629 19.256 1.137 -1.515
## [4,] -194.766 -71.161 -1.515 4.988
##
## main 35 ( 90 ) Accepts 11 / 30
## .main 36 ( 90 )
## Mu = 48.614 17.352 -1.338 1.379
## Eta = 0.859 2.659 0.415
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 2638.674 -165.726 -37.599 -26.161
## [2,] -165.726 288.102 -3.323 4.787
## [3,] -37.599 -3.323 3.716 -0.436
## [4,] -26.161 4.787 -0.436 2.721
##
## main 36 ( 90 ) Accepts 12 / 30
## .main 37 ( 90 )
## Mu = 22.976 28.69 -3.751 3.263
## Eta = 0.951 2.572 0.316
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 4718.306 8.492 62.273 -51.007
## [2,] 8.492 265.327 -1.830 -1.103
## [3,] 62.273 -1.830 1.811 -1.124
## [4,] -51.007 -1.103 -1.124 2.171
##
## main 37 ( 90 ) Accepts 7 / 30
## .main 38 ( 90 )
## Mu = 51.781 3.113 -1.494 4.65
## Eta = 0.907 2.489 0.386
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 3130.673 -267.929 22.008 -19.886
## [2,] -267.929 512.003 -15.014 -57.350
## [3,] 22.008 -15.014 2.058 0.990
## [4,] -19.886 -57.350 0.990 12.242
##
## main 38 ( 90 ) Accepts 12 / 30
## .main 39 ( 90 )
## Mu = 35.839 -8.662 -1.429 1.908
## Eta = 0.81 2.555 0.409
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 4025.277 784.127 -18.174 -37.609
## [2,] 784.127 1160.952 -11.112 10.709
## [3,] -18.174 -11.112 2.638 -1.673
## [4,] -37.609 10.709 -1.673 3.005
##
## main 39 ( 90 ) Accepts 12 / 30
## .main 40 ( 90 )
## Mu = 110.547 31.547 -1.218 0.952
## Eta = 0.895 2.424 0.594
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 8132.133 1215.885 78.290 -163.027
## [2,] 1215.885 555.838 14.448 -28.288
## [3,] 78.290 14.448 1.662 -2.063
## [4,] -163.027 -28.288 -2.063 4.773
##
## main 40 ( 90 ) Accepts 9 / 30
## .main 41 ( 90 )
## Mu = 66.075 21.211 -3.005 2.798
## Eta = 0.936 2.58 0.327
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 5450.450 1887.348 -30.093 -58.028
## [2,] 1887.348 962.154 -12.798 -15.475
## [3,] -30.093 -12.798 1.246 -0.532
## [4,] -58.028 -15.475 -0.532 2.867
##
## main 41 ( 90 ) Accepts 11 / 30
## .main 42 ( 90 )
## Mu = 113.013 -4.834 -0.305 0.518
## Eta = 1.045 2.753 0.46
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 12211.742 -813.775 224.234 -286.845
## [2,] -813.775 476.526 -39.581 39.036
## [3,] 224.234 -39.581 9.594 -8.839
## [4,] -286.845 39.036 -8.839 9.804
##
## main 42 ( 90 ) Accepts 11 / 30
## .main 43 ( 90 )
## Mu = 63.106 20.438 -2.628 1.959
## Eta = 1.002 2.608 0.917
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 3186.526 283.513 -10.093 -45.579
## [2,] 283.513 412.787 -6.650 8.605
## [3,] -10.093 -6.650 2.362 -1.127
## [4,] -45.579 8.605 -1.127 4.775
##
## main 43 ( 90 ) Accepts 14 / 30
## .main 44 ( 90 )
## Mu = 91.74 13.137 -2.591 1.745
## Eta = 1 2.333 0.883
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 9023.457 495.586 13.110 -104.530
## [2,] 495.586 422.879 5.804 3.198
## [3,] 13.110 5.804 1.686 -1.090
## [4,] -104.530 3.198 -1.090 4.040
##
## main 44 ( 90 ) Accepts 10 / 30
## .main 45 ( 90 )
## Mu = 148.005 40.24 -2.299 -1.954
## Eta = 1.013 2.429 1.069
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 4779.899 600.915 57.651 -194.225
## [2,] 600.915 275.654 6.148 -22.356
## [3,] 57.651 6.148 1.957 -3.933
## [4,] -194.225 -22.356 -3.933 11.951
##
## main 45 ( 90 ) Accepts 7 / 30
## .main 46 ( 90 )
## Mu = 40.754 25.871 -2.12 2.919
## Eta = 0.958 2.33 0.979
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 4531.660 1155.270 50.387 -24.868
## [2,] 1155.270 1135.057 24.773 25.698
## [3,] 50.387 24.773 4.107 -2.442
## [4,] -24.868 25.698 -2.442 5.132
##
## main 46 ( 90 ) Accepts 16 / 30
## .main 47 ( 90 )
## Mu = 75.091 14.077 -2.095 1.206
## Eta = 0.917 2.533 1.387
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 2163.811 -294.441 72.780 -43.551
## [2,] -294.441 515.311 -42.381 25.763
## [3,] 72.780 -42.381 7.780 -3.864
## [4,] -43.551 25.763 -3.864 3.702
##
## main 47 ( 90 ) Accepts 12 / 30
## .main 48 ( 90 )
## Mu = 89.875 10.567 -2.141 0.969
## Eta = 0.887 2.166 1.298
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 2777.744 830.505 43.859 -71.042
## [2,] 830.505 749.727 17.324 -12.097
## [3,] 43.859 17.324 1.614 -2.016
## [4,] -71.042 -12.097 -2.016 4.648
##
## main 48 ( 90 ) Accepts 14 / 30
## .main 49 ( 90 )
## Mu = 71.669 24.052 -1.381 1.565
## Eta = 0.912 2.198 1.136
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 3703.162 351.840 35.182 -78.033
## [2,] 351.840 355.478 -1.125 -10.145
## [3,] 35.182 -1.125 1.414 -1.494
## [4,] -78.033 -10.145 -1.494 3.385
##
## main 49 ( 90 ) Accepts 12 / 30
## .main 50 ( 90 )
## Mu = 33.871 20.577 -2.959 2.2
## Eta = 0.919 2.26 0.184
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 4201.240 829.981 29.415 27.787
## [2,] 829.981 521.847 -8.540 31.417
## [3,] 29.415 -8.540 2.300 -1.639
## [4,] 27.787 31.417 -1.639 3.306
##
## main 50 ( 90 ) Accepts 19 / 30
## .main 51 ( 90 )
## Mu = 65.201 27.751 -1.107 0.856
## Eta = 0.806 2.175 -0.132
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 3097.257 860.716 49.881 -51.473
## [2,] 860.716 526.141 16.090 -12.992
## [3,] 49.881 16.090 2.351 -1.865
## [4,] -51.473 -12.992 -1.865 2.398
##
## main 51 ( 90 ) Accepts 9 / 30
## .main 52 ( 90 )
## Mu = 33.254 14.815 -2.065 2.036
## Eta = 0.832 2.201 0.206
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 4823.614 401.997 68.391 -145.616
## [2,] 401.997 338.163 4.036 -20.591
## [3,] 68.391 4.036 3.084 -3.909
## [4,] -145.616 -20.591 -3.909 8.497
##
## main 52 ( 90 ) Accepts 16 / 30
## .main 53 ( 90 )
## Mu = 106.603 21.195 -1.991 0.992
## Eta = 0.739 2.149 -0.291
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 8784.665 -504.770 36.921 -79.317
## [2,] -504.770 804.965 4.404 0.302
## [3,] 36.921 4.404 2.183 -2.212
## [4,] -79.317 0.302 -2.212 3.284
##
## main 53 ( 90 ) Accepts 6 / 30
## .main 54 ( 90 )
## Mu = 66.717 24.905 -2.517 2.347
## Eta = 0.753 2.372 -0.408
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 5875.743 649.639 35.547 -71.727
## [2,] 649.639 441.663 -5.262 -3.881
## [3,] 35.547 -5.262 1.610 -1.253
## [4,] -71.727 -3.881 -1.253 2.276
##
## main 54 ( 90 ) Accepts 12 / 30
## .main 55 ( 90 )
## Mu = 57.232 15.662 -1.847 1.191
## Eta = 0.744 2.587 -0.483
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 3607.543 -44.522 28.015 -33.380
## [2,] -44.522 299.277 -4.974 1.121
## [3,] 28.015 -4.974 0.882 -0.579
## [4,] -33.380 1.121 -0.579 1.670
##
## main 55 ( 90 ) Accepts 12 / 30
## .main 56 ( 90 )
## Mu = 94.637 33.074 -1.266 -0.447
## Eta = 0.731 2.433 -0.317
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 6400.681 825.684 3.419 -117.399
## [2,] 825.684 299.259 2.360 -17.157
## [3,] 3.419 2.360 2.777 -2.484
## [4,] -117.399 -17.157 -2.484 6.742
##
## main 56 ( 90 ) Accepts 10 / 30
## .main 57 ( 90 )
## Mu = 47.127 0.178 -2.731 1.105
## Eta = 0.71 2.353 -0.299
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 3263.230 -527.317 15.606 -40.865
## [2,] -527.317 405.311 -2.424 16.250
## [3,] 15.606 -2.424 2.010 -1.483
## [4,] -40.865 16.250 -1.483 4.732
##
## main 57 ( 90 ) Accepts 21 / 30
## .main 58 ( 90 )
## Mu = 24.631 14.383 -2.645 1.827
## Eta = 0.675 2.419 -0.367
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 7711.528 257.717 -8.810 -87.221
## [2,] 257.717 488.683 -12.660 5.808
## [3,] -8.810 -12.660 2.313 -1.806
## [4,] -87.221 5.808 -1.806 3.863
##
## main 58 ( 90 ) Accepts 12 / 30
## .main 59 ( 90 )
## Mu = 30.284 21.766 -1.572 2.733
## Eta = 0.73 2.446 -0.451
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 1771.196 16.500 20.780 -31.997
## [2,] 16.500 453.145 -15.389 6.863
## [3,] 20.780 -15.389 2.552 -1.496
## [4,] -31.997 6.863 -1.496 2.729
##
## main 59 ( 90 ) Accepts 16 / 30
## .main 60 ( 90 )
## Mu = 53.071 -2.983 -2.732 1.869
## Eta = 0.835 2.447 -0.384
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 3085.972 653.272 -6.269 -14.839
## [2,] 653.272 932.438 9.884 1.378
## [3,] -6.269 9.884 1.437 -0.728
## [4,] -14.839 1.378 -0.728 2.549
##
## main 60 ( 90 ) Accepts 11 / 30
## .main 61 ( 90 )
## Mu = 106.712 29.73 -1.567 0.469
## Eta = 0.815 2.662 -0.531
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 3263.613 209.724 57.993 -26.390
## [2,] 209.724 668.734 -11.523 3.209
## [3,] 57.993 -11.523 3.331 -1.674
## [4,] -26.390 3.209 -1.674 3.669
##
## main 61 ( 90 ) Accepts 13 / 30
## .main 62 ( 90 )
## Mu = 42.149 8.137 -2.232 0.962
## Eta = 0.783 2.472 -0.368
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 1887.208 55.185 2.750 -9.352
## [2,] 55.185 173.867 4.108 0.136
## [3,] 2.750 4.108 1.890 -0.880
## [4,] -9.352 0.136 -0.880 1.782
##
## main 62 ( 90 ) Accepts 13 / 30
## .main 63 ( 90 )
## Mu = -35.347 12.927 -1.703 3.086
## Eta = 0.875 2.49 -0.149
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 8679.347 -941.287 -20.616 -153.244
## [2,] -941.287 338.005 -3.731 21.906
## [3,] -20.616 -3.731 2.367 -0.609
## [4,] -153.244 21.906 -0.609 3.703
##
## main 63 ( 90 ) Accepts 11 / 30
## .main 64 ( 90 )
## Mu = 94.468 26.252 -2.188 1.147
## Eta = 0.899 2.557 -0.006
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 3876.208 494.529 98.934 -72.195
## [2,] 494.529 423.628 13.525 -8.139
## [3,] 98.934 13.525 6.063 -3.950
## [4,] -72.195 -8.139 -3.950 3.413
##
## main 64 ( 90 ) Accepts 13 / 30
## .main 65 ( 90 )
## Mu = 89.704 9.736 -2.087 1.427
## Eta = 0.898 2.674 0.318
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 2869.561 167.230 8.090 -15.554
## [2,] 167.230 1131.143 -24.686 58.195
## [3,] 8.090 -24.686 2.797 -2.311
## [4,] -15.554 58.195 -2.311 5.351
##
## main 65 ( 90 ) Accepts 13 / 30
## .main 66 ( 90 )
## Mu = 70.682 22.032 -4.295 2.371
## Eta = 0.864 2.624 0.471
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 2595.216 746.188 -12.259 -3.738
## [2,] 746.188 1500.086 -15.126 8.458
## [3,] -12.259 -15.126 2.975 -1.784
## [4,] -3.738 8.458 -1.784 1.991
##
## main 66 ( 90 ) Accepts 11 / 30
## .main 67 ( 90 )
## Mu = 14.116 9.926 -2.2 2.523
## Eta = 0.879 2.761 0.28
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 6069.272 -332.451 112.413 -115.030
## [2,] -332.451 1203.795 -41.213 9.180
## [3,] 112.413 -41.213 4.785 -3.294
## [4,] -115.030 9.180 -3.294 7.371
##
## main 67 ( 90 ) Accepts 16 / 30
## .main 68 ( 90 )
## Mu = 109.773 40.695 -2.673 1.442
## Eta = 0.857 3.056 0.38
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 11362.919 1222.894 -20.009 51.374
## [2,] 1222.894 371.851 -3.958 11.675
## [3,] -20.009 -3.958 0.953 -0.476
## [4,] 51.374 11.675 -0.476 2.797
##
## main 68 ( 90 ) Accepts 16 / 30
## .main 69 ( 90 )
## Mu = 52.034 29.944 -2.326 2.17
## Eta = 0.869 3.044 0.083
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 4919.990 -317.449 27.030 -109.324
## [2,] -317.449 340.476 -3.636 0.856
## [3,] 27.030 -3.636 1.535 -1.209
## [4,] -109.324 0.856 -1.209 5.480
##
## main 69 ( 90 ) Accepts 9 / 30
## .main 70 ( 90 )
## Mu = 76.178 19.709 -2.299 1.233
## Eta = 0.879 2.83 0.159
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 4132.855 538.882 22.128 -90.430
## [2,] 538.882 952.996 -1.966 -16.644
## [3,] 22.128 -1.966 1.577 -0.772
## [4,] -90.430 -16.644 -0.772 3.154
##
## main 70 ( 90 ) Accepts 12 / 30
## .main 71 ( 90 )
## Mu = 41.489 45.224 -3.629 3.391
## Eta = 0.826 3.032 0.12
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 3223.650 248.372 34.057 10.264
## [2,] 248.372 667.352 -11.302 23.499
## [3,] 34.057 -11.302 2.843 -0.392
## [4,] 10.264 23.499 -0.392 2.601
##
## main 71 ( 90 ) Accepts 14 / 30
## .main 72 ( 90 )
## Mu = 100.477 22.154 -1.065 -0.681
## Eta = 0.929 3.203 0.846
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 6246.689 2439.855 30.470 29.032
## [2,] 2439.855 2587.787 -3.940 51.845
## [3,] 30.470 -3.940 1.605 -1.487
## [4,] 29.032 51.845 -1.487 3.639
##
## main 72 ( 90 ) Accepts 12 / 30
## .main 73 ( 90 )
## Mu = 47.342 9.482 -1.021 1.46
## Eta = 0.81 3.059 0.726
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 6659.874 473.584 -145.018 -78.689
## [2,] 473.584 476.671 -7.286 -6.930
## [3,] -145.018 -7.286 6.424 2.215
## [4,] -78.689 -6.930 2.215 1.517
##
## main 73 ( 90 ) Accepts 9 / 30
## .main 74 ( 90 )
## Mu = 55.082 7.729 -2.124 1.469
## Eta = 0.957 3.116 0.882
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 4878.660 682.505 20.263 -54.300
## [2,] 682.505 1893.108 15.399 12.421
## [3,] 20.263 15.399 1.138 -0.249
## [4,] -54.300 12.421 -0.249 1.632
##
## main 74 ( 90 ) Accepts 12 / 30
## .main 75 ( 90 )
## Mu = 36.805 21.448 -1.474 -0.318
## Eta = 0.846 3.011 0.709
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 2612.057 -283.297 -30.725 -17.649
## [2,] -283.297 296.919 10.666 4.638
## [3,] -30.725 10.666 2.708 -0.484
## [4,] -17.649 4.638 -0.484 2.363
##
## main 75 ( 90 ) Accepts 15 / 30
## .main 76 ( 90 )
## Mu = 4.579 15.758 -5.395 2.19
## Eta = 0.836 2.934 0.793
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 5221.194 -12.562 89.356 -135.860
## [2,] -12.562 647.635 -11.336 -1.688
## [3,] 89.356 -11.336 3.757 -1.643
## [4,] -135.860 -1.688 -1.643 5.586
##
## main 76 ( 90 ) Accepts 8 / 30
##
## Mu = 4.579 15.758 -5.395 2.19
## Eta = 0.836 2.934 0.793
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 5221.194 -12.562 89.356 -135.860
## [2,] -12.562 647.635 -11.336 -1.688
## [3,] 89.356 -11.336 3.757 -1.643
## [4,] -135.860 -1.688 -1.643 5.586
##
## .main 77 ( 90 )
## Mu = 44.316 38.732 -2.305 1.028
## Eta = 0.803 2.876 0.62
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 4419.706 -863.607 -20.010 -8.684
## [2,] -863.607 724.676 12.683 -5.390
## [3,] -20.010 12.683 1.404 -0.505
## [4,] -8.684 -5.390 -0.505 1.350
##
## main 77 ( 90 ) Accepts 10 / 30
## .main 78 ( 90 )
## Mu = 36.642 32.269 -3.035 1.759
## Eta = 0.779 2.926 0.791
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 3184.072 -50.098 6.332 18.624
## [2,] -50.098 822.701 -20.958 10.554
## [3,] 6.332 -20.958 1.912 -1.817
## [4,] 18.624 10.554 -1.817 5.228
##
## main 78 ( 90 ) Accepts 13 / 30
## .main 79 ( 90 )
## Mu = 41.541 46.499 -2.284 0.404
## Eta = 0.744 2.994 0.697
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 3152.949 -111.079 -40.600 35.784
## [2,] -111.079 1350.337 42.808 -36.419
## [3,] -40.600 42.808 3.477 -2.315
## [4,] 35.784 -36.419 -2.315 2.715
##
## main 79 ( 90 ) Accepts 15 / 30
## .main 80 ( 90 )
## Mu = 139.099 25.624 -2.866 0.205
## Eta = 0.768 3.536 0.781
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 5568.024 -376.144 -47.291 -4.069
## [2,] -376.144 879.571 9.477 -30.527
## [3,] -47.291 9.477 1.649 -0.360
## [4,] -4.069 -30.527 -0.360 2.888
##
## main 80 ( 90 ) Accepts 13 / 30
## .main 81 ( 90 )
## Mu = 48.082 17.743 -3.481 0.347
## Eta = 0.743 3.191 0.879
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 2794.385 -91.387 34.297 -21.412
## [2,] -91.387 521.013 3.983 11.559
## [3,] 34.297 3.983 1.953 -0.177
## [4,] -21.412 11.559 -0.177 1.267
##
## main 81 ( 90 ) Accepts 12 / 30
## .main 82 ( 90 )
## Mu = 61.013 15.118 -1.298 0.316
## Eta = 0.757 3.317 0.897
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 13204.431 3419.694 -4.399 -167.147
## [2,] 3419.694 3542.289 -22.614 -60.796
## [3,] -4.399 -22.614 3.375 -0.174
## [4,] -167.147 -60.796 -0.174 2.981
##
## main 82 ( 90 ) Accepts 10 / 30
## .main 83 ( 90 )
## Mu = 51.672 27.184 -3.021 2.059
## Eta = 0.795 3.601 0.049
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 24959.641 664.062 714.428 -631.745
## [2,] 664.062 286.337 19.805 -19.304
## [3,] 714.428 19.805 22.514 -18.768
## [4,] -631.745 -19.304 -18.768 16.636
##
## main 83 ( 90 ) Accepts 17 / 30
## .main 84 ( 90 )
## Mu = 56.486 14.911 -2.323 0.422
## Eta = 0.725 3.49 0.148
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 1442.553 469.464 6.525 -1.232
## [2,] 469.464 857.986 -1.717 5.049
## [3,] 6.525 -1.717 1.748 -1.026
## [4,] -1.232 5.049 -1.026 1.589
##
## main 84 ( 90 ) Accepts 10 / 30
## .main 85 ( 90 )
## Mu = 39.628 15.954 -1.301 0.467
## Eta = 0.763 3.327 0.136
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 2845.430 23.998 10.558 0.505
## [2,] 23.998 342.399 0.441 -4.301
## [3,] 10.558 0.441 1.886 -0.925
## [4,] 0.505 -4.301 -0.925 1.514
##
## main 85 ( 90 ) Accepts 11 / 30
## .main 86 ( 90 )
## Mu = 30.797 2.677 -3.213 1.773
## Eta = 0.803 3.109 0.086
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 2405.055 -161.522 9.608 -13.395
## [2,] -161.522 738.540 -15.914 15.391
## [3,] 9.608 -15.914 10.433 -1.769
## [4,] -13.395 15.391 -1.769 1.606
##
## main 86 ( 90 ) Accepts 14 / 30
## .main 87 ( 90 )
## Mu = 62.636 11.913 -1.714 -0.289
## Eta = 0.855 3.086 0.187
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 4409.268 1434.577 7.020 -13.677
## [2,] 1434.577 919.057 -11.616 7.664
## [3,] 7.020 -11.616 2.121 -1.571
## [4,] -13.677 7.664 -1.571 1.881
##
## main 87 ( 90 ) Accepts 8 / 30
## .main 88 ( 90 )
## Mu = 107.304 21.619 -1.555 1.033
## Eta = 0.693 3.134 0.168
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 6062.620 572.824 49.166 32.619
## [2,] 572.824 327.467 11.258 4.339
## [3,] 49.166 11.258 1.773 0.267
## [4,] 32.619 4.339 0.267 1.379
##
## main 88 ( 90 ) Accepts 9 / 30
## .main 89 ( 90 )
## Mu = 89.57 23.027 -2.883 0.099
## Eta = 0.74 2.885 0.281
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 4492.714 -97.332 -18.719 -77.712
## [2,] -97.332 418.473 -16.801 -3.195
## [3,] -18.719 -16.801 6.415 1.906
## [4,] -77.712 -3.195 1.906 3.143
##
## main 89 ( 90 ) Accepts 14 / 30
## .main 90 ( 90 )
## Mu = 43.682 19.923 -1.941 1.892
## Eta = 0.798 2.703 0.584
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 11278.916 737.977 9.176 -231.797
## [2,] 737.977 702.190 1.375 14.266
## [3,] 9.176 1.375 0.736 -0.236
## [4,] -231.797 14.266 -0.236 7.895
##
## main 90 ( 90 ) Accepts 12 / 30
## Total duration 90.474 seconds.fit2## Note: this summary does not contain a convergence check.
##
## Groups:
## Data1 Data2 Data3
##
## Posterior means and standard deviations for global mean parameters
##
## Total number of runs in the results is 90 .
## Posterior means and standard deviations are averages over 70 MCMC runs (counted after thinning).
##
## Post. Post. cred. cred. p varying Post. cred. cred.
## mean s.d.m. from to s.d. from to
## 1. rate constant IS rate (period 1) 119.5287 ( 0.2406 ) NA NA NA
## 2. rate constant IS rate (period 2) 1.1878 ( 0.4506 ) NA NA NA
## 3. rate constant IS rate (period 4) 46.9808 ( 3.8093 ) NA NA NA
## 4. rate constant IS rate (period 5) 38.8507 ( 2.7244 ) NA NA NA
## 5. rate constant IS rate (period 7) 22.9111 ( 1.1408 ) NA NA NA
## 6. rate constant IS rate (period 8) 2.8329 ( 0.9853 ) NA NA NA
## 7. eval outdegree (density) -2.3035 ( 0.8653 ) -4.0700 -1.0527 0.00 + 1.7671 0.9661 3.1345
## 8. eval reciprocity 1.5854 ( 1.2479 ) -0.5111 3.8917 0.91 + 2.1287 1.1710 3.6675
## 9. eval transitive triplets 0.8093 ( 0.1012 ) 0.6344 1.0048 1.00 - NA NA NA
## 10. eval val 2.8158 ( 0.3923 ) 2.1727 3.5372 1.00 - NA NA NA
## 11. eval ae ego 0.4032 ( 0.4618 ) -0.4599 1.1802 0.81 - NA NA NA
##
## Posterior mean of global covariance matrix (varying parameters)
## 5511.5899 431.5112 33.7989 -83.1591
## 431.5112 729.4225 -0.8178 -3.5153
## 33.7989 -0.8178 3.1226 -1.8292
## -83.1591 -3.5153 -1.8292 4.5312
##
## Posterior standard deviations of elements of global covariance matrix
## 4516.6248 808.7176 98.2830 126.3042
## 808.7176 549.0415 17.3128 24.7918
## 98.2830 17.3128 3.0793 2.6822
## 126.3042 24.7918 2.6822 3.4359sink("results_of_model.txt", append=T)
fit2## Note: this summary does not contain a convergence check.
##
## Groups:
## Data1 Data2 Data3
##
## Posterior means and standard deviations for global mean parameters
##
## Total number of runs in the results is 90 .
## Posterior means and standard deviations are averages over 70 MCMC runs (counted after thinning).
##
## Post. Post. cred. cred. p varying Post. cred. cred.
## mean s.d.m. from to s.d. from to
## 1. rate constant IS rate (period 1) 119.5287 ( 0.2406 ) NA NA NA
## 2. rate constant IS rate (period 2) 1.1878 ( 0.4506 ) NA NA NA
## 3. rate constant IS rate (period 4) 46.9808 ( 3.8093 ) NA NA NA
## 4. rate constant IS rate (period 5) 38.8507 ( 2.7244 ) NA NA NA
## 5. rate constant IS rate (period 7) 22.9111 ( 1.1408 ) NA NA NA
## 6. rate constant IS rate (period 8) 2.8329 ( 0.9853 ) NA NA NA
## 7. eval outdegree (density) -2.3035 ( 0.8653 ) -4.0700 -1.0527 0.00 + 1.7671 0.9661 3.1345
## 8. eval reciprocity 1.5854 ( 1.2479 ) -0.5111 3.8917 0.91 + 2.1287 1.1710 3.6675
## 9. eval transitive triplets 0.8093 ( 0.1012 ) 0.6344 1.0048 1.00 - NA NA NA
## 10. eval val 2.8158 ( 0.3923 ) 2.1727 3.5372 1.00 - NA NA NA
## 11. eval ae ego 0.4032 ( 0.4618 ) -0.4599 1.1802 0.81 - NA NA NA
##
## Posterior mean of global covariance matrix (varying parameters)
## 5511.5899 431.5112 33.7989 -83.1591
## 431.5112 729.4225 -0.8178 -3.5153
## 33.7989 -0.8178 3.1226 -1.8292
## -83.1591 -3.5153 -1.8292 4.5312
##
## Posterior standard deviations of elements of global covariance matrix
## 4516.6248 808.7176 98.2830 126.3042
## 808.7176 549.0415 17.3128 24.7918
## 98.2830 17.3128 3.0793 2.6822
## 126.3042 24.7918 2.6822 3.4359sink()Again, we’ll be inspecting the convergence plots.
RateTracePlots(fit2)
NonRateTracePlots(fit2)Wow, that backfired. There is a slight backward trend for information retrieval estimates for t1 in Group 1. The estimates for the dyadic and individual covariates are also fluctuating. If this would happen, you should first test the robustness of these results by modifying the parameters for the Markov Chain. For example, you could run: fit3 <- sienaBayes(ir_algo, data=ir, effects=ir_effect, nwarm=20, nmain=100, nrunMHBatches=10, silentstart=T, initgainGlobal = 0, initgainGroupwise = 0).
To inspect the model, run convergence test you can load the saved model fit3.
fit3 <- sienaBayes(ir_algo, data=ir, effects=ir_effect, nwarm=20, nmain=100, nrunMHBatches=10, silentstart=T, initgainGlobal = 0, initgainGroupwise = 0)##
## Estimate initial global parameters
## Initial global estimates
## Estimates, standard errors and convergence t-ratios
##
## Estimate Standard Convergence
## Error t-ratio
## 1. rate constant IS rate (period 1) 4.3692 ( 10.2626 ) -1.8751
## 2. rate constant IS rate (period 2) 0.6769 ( 0.5432 ) 0.6313
## 3. rate constant IS rate (period 4) 2.4800 ( 2.8170 ) -0.3819
## 4. rate constant IS rate (period 5) 1.9077 ( 1.7775 ) 0.0458
## 5. rate constant IS rate (period 7) 3.8571 ( 2.8085 ) -0.5161
## 6. rate constant IS rate (period 8) 1.6316 ( 0.9991 ) 0.8605
## 7. eval outdegree (density) -0.3923 ( 0.4346 ) -1.0031
## 8. eval reciprocity 0.0000 ( 0.5714 ) -2.4987
## 9. eval transitive triplets 0.0000 ( 0.4003 ) -2.5169
## 10. eval val 0.0000 ( 0.2502 ) -3.6571
## 11. eval ae ego 0.0000 ( 0.5586 ) -0.8766
##
## Overall maximum convergence ratio: 6.0166
##
##
## Total of 500 iteration steps.
##
##
##
## maximum initial global estimate is 4.369231
## Group 1
## Estimate initial parameters group 1
##
## Initial estimate obtained
## 4.369 0.677 -0.392 0.000 0.000 0.000 0.000
## Group 2
## Estimate initial parameters group 2
##
## Initial estimate obtained
## 2.480 1.908 -0.392 0.000 0.000 0.000 0.000
## Group 3
## Estimate initial parameters group 3
##
## Initial estimate obtained
## 3.857 1.632 -0.392 0.000 0.000 0.000 0.000
## Condition priorRatesFromData=2 impossible, changed to 1.
## Initial global model estimates
## Estimates, standard errors and convergence t-ratios
##
## Estimate Standard Convergence
## Error t-ratio
## 1. rate constant IS rate (period 1) 4.3692 ( 10.2626 ) -1.8751
## 2. rate constant IS rate (period 2) 0.6769 ( 0.5432 ) 0.6313
## 3. rate constant IS rate (period 4) 2.4800 ( 2.8170 ) -0.3819
## 4. rate constant IS rate (period 5) 1.9077 ( 1.7775 ) 0.0458
## 5. rate constant IS rate (period 7) 3.8571 ( 2.8085 ) -0.5161
## 6. rate constant IS rate (period 8) 1.6316 ( 0.9991 ) 0.8605
## 7. eval outdegree (density) -0.3923 ( 0.4346 ) -1.0031
## 8. eval reciprocity 0.0000 ( 0.5714 ) -2.4987
## 9. eval transitive triplets 0.0000 ( 0.4003 ) -2.5169
## 10. eval val 0.0000 ( 0.2502 ) -3.6571
## 11. eval ae ego 0.0000 ( 0.5586 ) -0.8766
##
## Overall maximum convergence ratio: 6.0166
##
##
## Total of 500 iteration steps.
##
## 2.84
## improveMH
## Desired acceptances 25 .
## ..........
## 1 . 29.1 26.9 30.4 19.3 24.1
## multipliers 1.095 1.045 1.125 0.869 0.979
## scaleFactors 0.782 0.746 0.804 0.621 0.699
## ..........
## 2 . 26.0 31.5 23.8 17.6 21.2
## multipliers 1.020 1.125 0.977 0.856 0.926
## scaleFactors 0.798 0.840 0.786 0.532 0.647
## ..........
## 3 . 23.3 26.0 25.8 18.5 20.1
## multipliers 0.969 1.018 1.015 0.887 0.914
## scaleFactors 0.773 0.855 0.797 0.472 0.592
## ..........
## 4 . 25.7 26.3 25.7 20.3 22.8
## multipliers 1.012 1.021 1.011 0.923 0.965
## scaleFactors 0.783 0.873 0.806 0.435 0.571
## ..........
## 5 . 27.4 24.3 26.3 21.1 22.1
## multipliers 1.036 0.989 1.020 0.939 0.956
## scaleFactors 0.811 0.863 0.822 0.409 0.545
## fine tuning took 5 iterations.
## improveMH 6.551 seconds.
## .Warming step 1 ( 20 )
## Accepts 10 / 30
## .Warming step 2 ( 20 )
## Accepts 12 / 30
## .Warming step 3 ( 20 )
## Accepts 11 / 30
## .Warming step 4 ( 20 )
## Accepts 16 / 30
## .Warming step 5 ( 20 )
## Accepts 14 / 30
## .Warming step 6 ( 20 )
## Accepts 10 / 30
## .Warming step 7 ( 20 )
## Accepts 14 / 30
## .Warming step 8 ( 20 )
## Accepts 10 / 30
## .Warming step 9 ( 20 )
## Accepts 14 / 30
## .Warming step 10 ( 20 )
## Accepts 16 / 30
## .Warming step 11 ( 20 )
## Accepts 12 / 30
## .Warming step 12 ( 20 )
## Accepts 11 / 30
## .Warming step 13 ( 20 )
## Accepts 16 / 30
## .Warming step 14 ( 20 )
## Accepts 11 / 30
## .Warming step 15 ( 20 )
## Accepts 13 / 30
## .Warming step 16 ( 20 )
## Accepts 18 / 30
## .Warming step 17 ( 20 )
## Accepts 17 / 30
## .Warming step 18 ( 20 )
## Accepts 13 / 30
## .Warming step 19 ( 20 )
## Accepts 15 / 30
## .Warming step 20 ( 20 )
## Accepts 13 / 30
## [1] "end of warming"
## warming took 2.992 seconds.
## Parameter values after warming up
## 1 . 5.137 1.812 -0.139 -0.282 0.270 1.429 1.290
## 2 . 1.122 2.484 -0.996 1.120 0.270 1.429 1.290
## 3 . 2.516 1.066 -0.447 0.476 0.270 1.429 1.290
##
## Second improveMH
## Desired acceptances 25 .
## ..........
## 1 . 27.4 25.5 31.7 23.5 22.9
## multipliers 1.056 1.013 1.155 0.965 0.952
## scaleFactors 0.857 0.874 0.950 0.395 0.519
## ..........
## 2 . 26.7 25.8 26.3 19.7 25.0
## multipliers 1.033 1.015 1.026 0.897 1.001
## scaleFactors 0.885 0.887 0.975 0.354 0.520
## ..........
## 3 . 23.3 21.8 26.7 22.8 21.6
## multipliers 0.970 0.945 1.030 0.962 0.941
## scaleFactors 0.858 0.838 1.004 0.341 0.489
## fine tuning took 3 iterations.
## Second improveMH 3.55 seconds.
## .main 21 ( 120 )
## Mu = 3.522 1.742 -0.549 0.653
## Eta = 0.21 1.188 0.48
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 6.6647 -2.5921 3.1843 -1.5951
## [2,] -2.5921 1.3409 -1.2034 0.7781
## [3,] 3.1843 -1.2034 2.4437 -0.7574
## [4,] -1.5951 0.7781 -0.7574 1.7885
##
## main 21 ( 120 ) Accepts 13 / 30
## .main 22 ( 120 )
## Mu = 1.876 2.652 -1.824 1.901
## Eta = 0.131 1.25 0.646
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 2.8526 0.7545 0.2567 0.9669
## [2,] 0.7545 1.1921 -0.5722 1.5446
## [3,] 0.2567 -0.5722 1.4547 -1.7320
## [4,] 0.9669 1.5446 -1.7320 3.8439
##
## main 22 ( 120 ) Accepts 14 / 30
## .main 23 ( 120 )
## Mu = 2.868 1.173 -0.75 0.652
## Eta = -0.002 1.11 0.259
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 0.7241 -0.2387 0.0209 -0.0846
## [2,] -0.2387 0.6993 -0.5136 0.3453
## [3,] 0.0209 -0.5136 1.2183 -1.0895
## [4,] -0.0846 0.3453 -1.0895 2.5215
##
## main 23 ( 120 ) Accepts 16 / 30
## .main 24 ( 120 )
## Mu = 4.214 1.726 0.482 0.89
## Eta = -0.525 1.154 -0.074
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 3.1273 -1.8508 1.2797 0.3220
## [2,] -1.8508 1.3677 -0.8526 -0.2081
## [3,] 1.2797 -0.8526 1.8027 -1.5158
## [4,] 0.3220 -0.2081 -1.5158 4.9738
##
## main 24 ( 120 ) Accepts 15 / 30
## .main 25 ( 120 )
## Mu = 3.855 1.72 -1.289 1.582
## Eta = 0.13 1.41 -0.041
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 1.5597 -0.2358 1.2543 -0.2232
## [2,] -0.2358 0.6127 0.5921 -0.2876
## [3,] 1.2543 0.5921 3.8435 -1.6805
## [4,] -0.2232 -0.2876 -1.6805 1.7927
##
## main 25 ( 120 ) Accepts 14 / 30
## .main 26 ( 120 )
## Mu = 3.333 3.332 -1.868 2.64
## Eta = 0.412 1.517 -0.063
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 2.4196 -0.8162 -1.7699 0.4889
## [2,] -0.8162 0.8663 0.3163 0.4319
## [3,] -1.7699 0.3163 2.5017 -0.9321
## [4,] 0.4889 0.4319 -0.9321 1.9321
##
## main 26 ( 120 ) Accepts 13 / 30
## .main 27 ( 120 )
## Mu = 2.524 3.383 -0.597 1.104
## Eta = 0.096 1.57 -1.357
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 26.8726 -13.3009 7.7139 12.5459
## [2,] -13.3009 6.8454 -4.1573 -6.1050
## [3,] 7.7139 -4.1573 5.5916 3.9749
## [4,] 12.5459 -6.1050 3.9749 7.4964
##
## main 27 ( 120 ) Accepts 20 / 30
## .main 28 ( 120 )
## Mu = 3.059 2.77 -1.207 0.264
## Eta = 0.014 1.503 -1.234
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 0.8837 -0.4800 1.4052 -0.7117
## [2,] -0.4800 0.8672 -1.6188 1.2289
## [3,] 1.4052 -1.6188 7.6008 -4.2553
## [4,] -0.7117 1.2289 -4.2553 3.9911
##
## main 28 ( 120 ) Accepts 17 / 30
## .main 29 ( 120 )
## Mu = 3.512 1.965 -2.398 0.952
## Eta = 0.116 1.185 -1.516
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 3.1909 -2.6929 0.7209 -1.2923
## [2,] -2.6929 2.6323 -0.4715 1.3874
## [3,] 0.7209 -0.4715 2.0880 -0.3496
## [4,] -1.2923 1.3874 -0.3496 1.5176
##
## main 29 ( 120 ) Accepts 11 / 30
## .main 30 ( 120 )
## Mu = 2.184 3.32 -0.534 -0.214
## Eta = 0.032 1.281 -2.198
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 0.6989 -0.4233 -0.3658 0.4892
## [2,] -0.4233 0.5870 0.0447 -0.1469
## [3,] -0.3658 0.0447 4.2883 -1.9332
## [4,] 0.4892 -0.1469 -1.9332 1.7118
##
## main 30 ( 120 ) Accepts 12 / 30
## .main 31 ( 120 )
## Mu = 3.592 2.786 -1.218 1.177
## Eta = 0.014 1.414 -1.221
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 2.5896 -1.9745 1.4532 0.7320
## [2,] -1.9745 1.9011 -1.1648 -0.3759
## [3,] 1.4532 -1.1648 2.6193 0.8180
## [4,] 0.7320 -0.3759 0.8180 0.8088
##
## main 31 ( 120 ) Accepts 18 / 30
## .main 32 ( 120 )
## Mu = 3.846 2.127 -1.506 0.008
## Eta = -0.301 1.927 -2.385
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 2.2073 -1.2628 1.3559 -0.5296
## [2,] -1.2628 1.4432 -1.3364 0.8210
## [3,] 1.3559 -1.3364 3.1180 0.2019
## [4,] -0.5296 0.8210 0.2019 2.3887
##
## main 32 ( 120 ) Accepts 14 / 30
## .main 33 ( 120 )
## Mu = 6.167 1.444 0.826 -0.704
## Eta = -0.534 1.824 -1.904
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 8.8117 -3.5678 7.7490 -9.5162
## [2,] -3.5678 1.8782 -3.2405 4.3057
## [3,] 7.7490 -3.2405 8.4741 -8.5633
## [4,] -9.5162 4.3057 -8.5633 12.0873
##
## main 33 ( 120 ) Accepts 13 / 30
## .main 34 ( 120 )
## Mu = 2.177 2.497 -0.773 1.613
## Eta = -0.527 1.94 -1.852
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 1.6668 0.6340 0.8039 -0.8724
## [2,] 0.6340 1.4344 0.3577 -0.3297
## [3,] 0.8039 0.3577 2.7561 -2.3389
## [4,] -0.8724 -0.3297 -2.3389 2.9449
##
## main 34 ( 120 ) Accepts 15 / 30
## .main 35 ( 120 )
## Mu = 3.451 3.448 -0.314 -1.149
## Eta = -0.496 1.887 -1.996
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 2.0804 -1.0272 0.2627 -0.8546
## [2,] -1.0272 1.3574 -0.2870 0.5262
## [3,] 0.2627 -0.2870 1.4661 -1.5395
## [4,] -0.8546 0.5262 -1.5395 2.9289
##
## main 35 ( 120 ) Accepts 16 / 30
## .main 36 ( 120 )
## Mu = 3.115 2.601 -0.316 1.131
## Eta = -0.258 1.413 -1.09
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 3.0578 -2.0417 0.9178 -1.6785
## [2,] -2.0417 3.2197 -1.0550 1.0439
## [3,] 0.9178 -1.0550 1.0277 -1.5200
## [4,] -1.6785 1.0439 -1.5200 5.1683
##
## main 36 ( 120 ) Accepts 9 / 30
## .main 37 ( 120 )
## Mu = 3.292 2.231 -0.586 0.79
## Eta = -0.264 1.707 -0.93
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 2.6543 -2.4527 -1.0590 1.5091
## [2,] -2.4527 2.8571 1.0722 -1.4004
## [3,] -1.0590 1.0722 1.5862 -1.5430
## [4,] 1.5091 -1.4004 -1.5430 2.4994
##
## main 37 ( 120 ) Accepts 16 / 30
## .main 38 ( 120 )
## Mu = 3.265 2.387 -0.325 1.609
## Eta = -0.311 1.602 -1.135
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 1.5426 -0.2692 -1.4747 0.6214
## [2,] -0.2692 0.4444 0.0773 0.3685
## [3,] -1.4747 0.0773 2.3500 -0.6727
## [4,] 0.6214 0.3685 -0.6727 2.5151
##
## main 38 ( 120 ) Accepts 11 / 30
## .main 39 ( 120 )
## Mu = 2.52 2.282 -0.448 0.863
## Eta = -0.282 0.953 -0.261
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 1.1784 -0.5281 -0.1710 0.3819
## [2,] -0.5281 0.4574 -0.0856 -0.2372
## [3,] -0.1710 -0.0856 0.9691 -0.7465
## [4,] 0.3819 -0.2372 -0.7465 1.8734
##
## main 39 ( 120 ) Accepts 12 / 30
## .main 40 ( 120 )
## Mu = 2.978 1.374 0.04 0.722
## Eta = -0.305 1.251 -0.489
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 2.1053 -1.5159 0.6432 0.9717
## [2,] -1.5159 1.8015 -0.8792 -0.5792
## [3,] 0.6432 -0.8792 1.1533 -0.1708
## [4,] 0.9717 -0.5792 -0.1708 1.3119
##
## main 40 ( 120 ) Accepts 12 / 30
## .main 41 ( 120 )
## Mu = 3.425 1.465 -0.056 -0.089
## Eta = -0.242 1.23 0.137
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 3.710 -2.255 -1.823 -0.200
## [2,] -2.255 1.644 1.270 0.034
## [3,] -1.823 1.270 1.459 0.216
## [4,] -0.200 0.034 0.216 0.961
##
## main 41 ( 120 ) Accepts 11 / 30
## .main 42 ( 120 )
## Mu = 3.152 1.507 -2.024 0.674
## Eta = 0.155 1.287 -1.952
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 0.973 -0.704 -1.478 -0.239
## [2,] -0.704 0.693 1.355 0.249
## [3,] -1.478 1.355 4.757 0.820
## [4,] -0.239 0.249 0.820 0.496
##
## main 42 ( 120 ) Accepts 9 / 30
## .main 43 ( 120 )
## Mu = 3.361 1.815 0.066 0.005
## Eta = -0.114 1.083 -1.364
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 1.654 -0.408 0.170 0.537
## [2,] -0.408 0.447 0.063 -0.257
## [3,] 0.170 0.063 1.842 -0.111
## [4,] 0.537 -0.257 -0.111 1.347
##
## main 43 ( 120 ) Accepts 12 / 30
## .main 44 ( 120 )
## Mu = 2.417 2.685 -0.007 -0.243
## Eta = -0.24 1.375 -0.353
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 1.241 -0.703 -0.342 -0.219
## [2,] -0.703 0.903 -0.168 0.331
## [3,] -0.342 -0.168 1.017 -0.401
## [4,] -0.219 0.331 -0.401 1.317
##
## main 44 ( 120 ) Accepts 14 / 30
## .main 45 ( 120 )
## Mu = 2.38 1.961 0.334 1.87
## Eta = -0.733 1.489 -0.328
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 3.155 -1.586 0.868 -2.946
## [2,] -1.586 1.297 -0.235 1.335
## [3,] 0.868 -0.235 1.032 -0.932
## [4,] -2.946 1.335 -0.932 3.650
##
## main 45 ( 120 ) Accepts 15 / 30
## .main 46 ( 120 )
## Mu = 3.263 1.895 -1.66 1.296
## Eta = -0.52 1.098 -0.765
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 1.037 -0.279 0.303 -0.121
## [2,] -0.279 0.417 -0.382 -0.320
## [3,] 0.303 -0.382 1.528 -0.024
## [4,] -0.121 -0.320 -0.024 1.449
##
## main 46 ( 120 ) Accepts 14 / 30
## .main 47 ( 120 )
## Mu = 3.966 1.392 -1.916 1.843
## Eta = -0.292 0.846 -1.075
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 6.540 -2.253 -5.268 1.922
## [2,] -2.253 0.938 2.088 -0.777
## [3,] -5.268 2.088 10.473 -4.038
## [4,] 1.922 -0.777 -4.038 3.473
##
## main 47 ( 120 ) Accepts 15 / 30
## .main 48 ( 120 )
## Mu = 1.993 2.279 -1.287 0.208
## Eta = -0.273 1.179 -0.101
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 2.720 -1.120 2.106 0.206
## [2,] -1.120 0.794 -0.978 -0.794
## [3,] 2.106 -0.978 3.418 0.935
## [4,] 0.206 -0.794 0.935 3.629
##
## main 48 ( 120 ) Accepts 11 / 30
## .main 49 ( 120 )
## Mu = 2.658 1.377 -1.789 1.267
## Eta = -0.151 1.046 -0.158
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 2.929 -3.814 -0.731 4.586
## [2,] -3.814 6.167 0.905 -8.210
## [3,] -0.731 0.905 1.520 -0.599
## [4,] 4.586 -8.210 -0.599 13.186
##
## main 49 ( 120 ) Accepts 8 / 30
## .main 50 ( 120 )
## Mu = 0.936 2.58 -0.162 -0.46
## Eta = 0.119 1.051 -0.085
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 1.316 -0.920 0.393 0.336
## [2,] -0.920 1.311 -0.502 -0.045
## [3,] 0.393 -0.502 0.797 -0.239
## [4,] 0.336 -0.045 -0.239 1.018
##
## main 50 ( 120 ) Accepts 11 / 30
## .main 51 ( 120 )
## Mu = 2.311 2.066 0.319 0.625
## Eta = 0.417 1.312 1.59
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 3.712 -3.003 0.277 -0.718
## [2,] -3.003 2.817 0.212 1.138
## [3,] 0.277 0.212 2.396 1.004
## [4,] -0.718 1.138 1.004 2.306
##
## main 51 ( 120 ) Accepts 14 / 30
## .main 52 ( 120 )
## Mu = 3.323 1.913 -1.955 0.767
## Eta = 0.882 1.477 2.023
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 0.811 -0.250 -0.259 0.204
## [2,] -0.250 0.183 -0.142 -0.093
## [3,] -0.259 -0.142 1.689 -0.467
## [4,] 0.204 -0.093 -0.467 1.891
##
## main 52 ( 120 ) Accepts 12 / 30
## .main 53 ( 120 )
## Mu = 4.61 1.243 -1.039 0.037
## Eta = 0.479 1.736 1.213
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 9.251 -6.820 5.170 0.550
## [2,] -6.820 5.679 -4.020 -0.649
## [3,] 5.170 -4.020 4.426 0.411
## [4,] 0.550 -0.649 0.411 1.222
##
## main 53 ( 120 ) Accepts 16 / 30
## .main 54 ( 120 )
## Mu = 4.958 1.036 -2.161 -1.246
## Eta = 0.62 1.719 1.321
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 3.619 -1.689 -0.538 -2.776
## [2,] -1.689 1.357 0.310 1.987
## [3,] -0.538 0.310 0.698 0.398
## [4,] -2.776 1.987 0.398 4.114
##
## main 54 ( 120 ) Accepts 11 / 30
## .main 55 ( 120 )
## Mu = 2.984 2.121 -0.037 0.198
## Eta = 0.578 1.477 1.333
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 9.381 -3.707 2.555 -6.304
## [2,] -3.707 1.819 -0.905 2.597
## [3,] 2.555 -0.905 1.775 -2.052
## [4,] -6.304 2.597 -2.052 5.772
##
## main 55 ( 120 ) Accepts 12 / 30
## .main 56 ( 120 )
## Mu = 3.009 1.95 -1.206 0.026
## Eta = 0.744 1.748 2.686
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 1.255 -0.461 0.232 0.338
## [2,] -0.461 0.365 0.010 0.056
## [3,] 0.232 0.010 1.354 -0.273
## [4,] 0.338 0.056 -0.273 1.804
##
## main 56 ( 120 ) Accepts 16 / 30
## .main 57 ( 120 )
## Mu = 4.171 1.895 -0.971 0.801
## Eta = 0.739 1.706 2.15
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 1.233 -0.358 0.326 -0.225
## [2,] -0.358 0.229 -0.089 0.144
## [3,] 0.326 -0.089 0.608 -0.069
## [4,] -0.225 0.144 -0.069 0.863
##
## main 57 ( 120 ) Accepts 15 / 30
## .main 58 ( 120 )
## Mu = 3.176 2.114 -1.072 -0.23
## Eta = -0.084 1.407 2.365
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 1.671 -0.753 1.152 0.308
## [2,] -0.753 0.608 -0.750 -0.002
## [3,] 1.152 -0.750 1.734 0.043
## [4,] 0.308 -0.002 0.043 0.733
##
## main 58 ( 120 ) Accepts 20 / 30
## .main 59 ( 120 )
## Mu = 4.184 2.151 0.785 -0.642
## Eta = -0.345 1.579 1.426
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 1.553 0.040 0.561 0.078
## [2,] 0.040 0.334 0.082 -0.001
## [3,] 0.561 0.082 2.052 -0.819
## [4,] 0.078 -0.001 -0.819 1.134
##
## main 59 ( 120 ) Accepts 14 / 30
## .main 60 ( 120 )
## Mu = 2.784 1.817 -0.292 -0.191
## Eta = -0.46 1.772 0.847
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 2.349 -0.710 0.511 -0.308
## [2,] -0.710 0.394 -0.105 0.346
## [3,] 0.511 -0.105 0.891 0.555
## [4,] -0.308 0.346 0.555 1.615
##
## main 60 ( 120 ) Accepts 9 / 30
## .main 61 ( 120 )
## Mu = 2.944 1.663 -0.134 -1.633
## Eta = -0.589 2.367 0.419
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 1.898 -0.914 -0.088 -0.327
## [2,] -0.914 0.833 -0.381 -0.088
## [3,] -0.088 -0.381 1.550 0.998
## [4,] -0.327 -0.088 0.998 1.299
##
## main 61 ( 120 ) Accepts 12 / 30
## .main 62 ( 120 )
## Mu = 1.958 1.893 0.796 -1.091
## Eta = -0.495 1.787 1.669
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 0.976 -0.397 -0.008 0.111
## [2,] -0.397 0.580 0.028 0.078
## [3,] -0.008 0.028 2.398 -0.507
## [4,] 0.111 0.078 -0.507 0.974
##
## main 62 ( 120 ) Accepts 14 / 30
## .main 63 ( 120 )
## Mu = 2.615 1.62 -0.262 -1.425
## Eta = -0.074 1.924 0.799
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 1.700 -0.914 0.166 -0.115
## [2,] -0.914 0.885 -0.415 0.190
## [3,] 0.166 -0.415 1.047 -0.180
## [4,] -0.115 0.190 -0.180 1.027
##
## main 63 ( 120 ) Accepts 13 / 30
## .main 64 ( 120 )
## Mu = 3.165 1.674 -0.128 0.212
## Eta = -0.149 1.859 1.423
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 7.407 -3.625 -0.066 1.109
## [2,] -3.625 2.154 0.090 -0.506
## [3,] -0.066 0.090 0.642 0.103
## [4,] 1.109 -0.506 0.103 0.740
##
## main 64 ( 120 ) Accepts 19 / 30
## .main 65 ( 120 )
## Mu = 2.903 1.174 -1.418 -0.582
## Eta = 0.377 1.828 0.864
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 0.813 -0.508 0.285 -0.161
## [2,] -0.508 1.010 0.247 0.522
## [3,] 0.285 0.247 1.105 0.466
## [4,] -0.161 0.522 0.466 1.145
##
## main 65 ( 120 ) Accepts 12 / 30
## .main 66 ( 120 )
## Mu = 1.954 2.22 -2.127 -1.026
## Eta = 0.654 2.02 1.037
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 1.590 -1.062 0.254 -0.058
## [2,] -1.062 0.832 -0.183 0.130
## [3,] 0.254 -0.183 1.285 0.167
## [4,] -0.058 0.130 0.167 1.161
##
## main 66 ( 120 ) Accepts 13 / 30
## .main 67 ( 120 )
## Mu = 3.464 1.445 0.57 0.28
## Eta = -0.193 1.904 1.144
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 1.954 -0.717 2.453 0.361
## [2,] -0.717 0.414 -0.911 -0.169
## [3,] 2.453 -0.911 5.143 0.572
## [4,] 0.361 -0.169 0.572 1.038
##
## main 67 ( 120 ) Accepts 19 / 30
## .main 68 ( 120 )
## Mu = 4.373 1.246 0.304 -0.973
## Eta = -0.319 1.811 1.196
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 1.918 -0.985 0.692 0.152
## [2,] -0.985 0.683 -0.451 -0.305
## [3,] 0.692 -0.451 1.000 -0.030
## [4,] 0.152 -0.305 -0.030 0.899
##
## main 68 ( 120 ) Accepts 11 / 30
## .main 69 ( 120 )
## Mu = 2.393 2.355 -0.275 0.285
## Eta = 0.165 1.658 0.374
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 4.370 -3.473 1.380 -1.960
## [2,] -3.473 3.240 -1.245 2.164
## [3,] 1.380 -1.245 1.815 -0.974
## [4,] -1.960 2.164 -0.974 2.520
##
## main 69 ( 120 ) Accepts 9 / 30
## .main 70 ( 120 )
## Mu = 2.68 1.374 0.444 0.29
## Eta = -0.034 1.465 0.218
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 2.077 -1.458 0.437 0.228
## [2,] -1.458 1.545 -0.780 0.126
## [3,] 0.437 -0.780 1.605 -0.647
## [4,] 0.228 0.126 -0.647 0.724
##
## main 70 ( 120 ) Accepts 10 / 30
## .main 71 ( 120 )
## Mu = 3.29 2.57 -0.179 0.576
## Eta = 0.03 1.724 -0.819
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 1.853 -1.734 0.047 -0.664
## [2,] -1.734 1.847 -0.045 0.639
## [3,] 0.047 -0.045 0.675 -0.360
## [4,] -0.664 0.639 -0.360 1.411
##
## main 71 ( 120 ) Accepts 17 / 30
## .main 72 ( 120 )
## Mu = 4.359 1.433 -0.931 1.18
## Eta = 0.431 1.473 -1.087
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 1.668 -0.840 0.132 -0.108
## [2,] -0.840 1.037 0.131 0.111
## [3,] 0.132 0.131 0.553 -0.113
## [4,] -0.108 0.111 -0.113 0.757
##
## main 72 ( 120 ) Accepts 18 / 30
## .main 73 ( 120 )
## Mu = 3.314 2.363 -1.12 0.817
## Eta = 0.284 1.692 -0.465
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 1.786 -1.052 -0.293 -0.211
## [2,] -1.052 1.601 -0.725 0.721
## [3,] -0.293 -0.725 2.002 -1.082
## [4,] -0.211 0.721 -1.082 1.157
##
## main 73 ( 120 ) Accepts 10 / 30
## .main 74 ( 120 )
## Mu = 3.093 3.101 -0.863 0.891
## Eta = 0.292 1.381 -0.435
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 2.319 -0.891 0.361 -0.422
## [2,] -0.891 2.076 -1.104 0.914
## [3,] 0.361 -1.104 1.159 -0.718
## [4,] -0.422 0.914 -0.718 1.149
##
## main 74 ( 120 ) Accepts 8 / 30
## .main 75 ( 120 )
## Mu = 6.214 1.266 0.096 -0.179
## Eta = 0.056 1.626 -0.698
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 4.608 -1.916 -0.619 0.477
## [2,] -1.916 1.591 0.293 -0.685
## [3,] -0.619 0.293 0.911 0.033
## [4,] 0.477 -0.685 0.033 1.911
##
## main 75 ( 120 ) Accepts 9 / 30
## .main 76 ( 120 )
## Mu = 3.552 3.302 -0.945 0.769
## Eta = -0.244 1.68 -1.079
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 2.012 -1.944 -1.388 -0.024
## [2,] -1.944 3.266 0.311 0.465
## [3,] -1.388 0.311 3.065 -0.375
## [4,] -0.024 0.465 -0.375 0.431
##
## main 76 ( 120 ) Accepts 10 / 30
## .main 77 ( 120 )
## Mu = 3.307 2.216 -2.123 1.671
## Eta = -0.26 1.58 -0.622
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 0.846 -1.140 -0.080 -0.728
## [2,] -1.140 2.617 1.446 1.242
## [3,] -0.080 1.446 5.371 -1.170
## [4,] -0.728 1.242 -1.170 5.057
##
## main 77 ( 120 ) Accepts 13 / 30
## .main 78 ( 120 )
## Mu = 4.367 1.352 -0.252 -0.012
## Eta = -0.913 1.523 0.649
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 1.549 -1.299 -0.104 0.597
## [2,] -1.299 3.554 -0.891 1.049
## [3,] -0.104 -0.891 1.470 -0.514
## [4,] 0.597 1.049 -0.514 2.142
##
## main 78 ( 120 ) Accepts 15 / 30
## .main 79 ( 120 )
## Mu = 2.439 3.545 0.114 0.391
## Eta = -0.444 1.815 -0.35
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 2.193 -2.471 -0.663 -0.968
## [2,] -2.471 3.508 0.911 1.223
## [3,] -0.663 0.911 0.759 0.399
## [4,] -0.968 1.223 0.399 1.206
##
## main 79 ( 120 ) Accepts 21 / 30
## .main 80 ( 120 )
## Mu = 2.261 3.009 -1.285 0.685
## Eta = -0.447 1.69 0.432
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 4.795 -4.522 4.191 -0.184
## [2,] -4.522 4.878 -4.222 0.090
## [3,] 4.191 -4.222 5.486 -0.373
## [4,] -0.184 0.090 -0.373 0.385
##
## main 80 ( 120 ) Accepts 12 / 30
## .main 81 ( 120 )
## Mu = 3.093 2.192 -0.51 0.221
## Eta = -0.389 1.985 0.051
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 0.947 -0.623 0.134 0.243
## [2,] -0.623 1.285 -0.933 0.244
## [3,] 0.134 -0.933 1.628 -0.463
## [4,] 0.243 0.244 -0.463 0.914
##
## main 81 ( 120 ) Accepts 17 / 30
## .main 82 ( 120 )
## Mu = 3.884 1.175 -0.533 0.189
## Eta = -0.232 1.957 0.07
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 1.053 -0.605 -0.286 -0.135
## [2,] -0.605 0.654 0.282 0.255
## [3,] -0.286 0.282 0.932 0.163
## [4,] -0.135 0.255 0.163 0.560
##
## main 82 ( 120 ) Accepts 19 / 30
## .main 83 ( 120 )
## Mu = 2.738 1.921 -0.025 1.553
## Eta = -0.275 1.845 0.393
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 1.422 -1.110 0.572 0.250
## [2,] -1.110 1.451 -0.865 -0.308
## [3,] 0.572 -0.865 1.873 -0.090
## [4,] 0.250 -0.308 -0.090 0.813
##
## main 83 ( 120 ) Accepts 12 / 30
## .main 84 ( 120 )
## Mu = 2.786 1.472 0.137 -0.114
## Eta = -0.487 1.728 -0.201
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 2.441 -1.393 0.410 0.890
## [2,] -1.393 1.976 -0.961 0.580
## [3,] 0.410 -0.961 1.601 -0.228
## [4,] 0.890 0.580 -0.228 3.215
##
## main 84 ( 120 ) Accepts 17 / 30
## .main 85 ( 120 )
## Mu = 3.286 2.094 -0.47 0.785
## Eta = -0.422 1.586 0.223
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 0.790 -0.341 0.381 -0.299
## [2,] -0.341 0.927 -1.164 -0.218
## [3,] 0.381 -1.164 5.050 0.195
## [4,] -0.299 -0.218 0.195 0.812
##
## main 85 ( 120 ) Accepts 15 / 30
## .main 86 ( 120 )
## Mu = 3.422 2.514 -0.838 0.423
## Eta = -0.338 1.454 -0.348
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 2.284 -1.398 -0.438 -0.544
## [2,] -1.398 1.688 0.019 0.691
## [3,] -0.438 0.019 0.663 0.189
## [4,] -0.544 0.691 0.189 0.925
##
## main 86 ( 120 ) Accepts 10 / 30
## .main 87 ( 120 )
## Mu = 4.316 0.634 -0.535 1.396
## Eta = -0.214 1.271 -0.051
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 0.740 -0.601 0.162 0.116
## [2,] -0.601 1.364 -0.506 -0.674
## [3,] 0.162 -0.506 0.754 0.138
## [4,] 0.116 -0.674 0.138 1.437
##
## main 87 ( 120 ) Accepts 10 / 30
## .main 88 ( 120 )
## Mu = 3.729 1.743 -1.109 -0.286
## Eta = 0.037 1.121 0.039
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 0.785 -0.216 -0.588 -0.013
## [2,] -0.216 0.766 0.008 -0.182
## [3,] -0.588 0.008 1.153 0.046
## [4,] -0.013 -0.182 0.046 1.203
##
## main 88 ( 120 ) Accepts 11 / 30
## .main 89 ( 120 )
## Mu = 3.518 2.394 -1.01 0.873
## Eta = 0.198 1.154 0.103
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 0.892 -0.497 -0.363 0.237
## [2,] -0.497 1.578 -0.255 0.035
## [3,] -0.363 -0.255 0.897 -0.032
## [4,] 0.237 0.035 -0.032 0.734
##
## main 89 ( 120 ) Accepts 13 / 30
## .main 90 ( 120 )
## Mu = 3.547 1.89 -1.082 0.942
## Eta = 0.211 0.655 0.173
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 2.912 -0.556 0.564 -0.457
## [2,] -0.556 1.103 -0.468 0.252
## [3,] 0.564 -0.468 1.604 -0.275
## [4,] -0.457 0.252 -0.275 0.565
##
## main 90 ( 120 ) Accepts 13 / 30
## .main 91 ( 120 )
## Mu = 3.408 1.495 -0.736 0.691
## Eta = -0.013 0.642 -0.28
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 2.493 -0.897 0.748 -0.848
## [2,] -0.897 0.745 -0.118 0.169
## [3,] 0.748 -0.118 1.349 -0.827
## [4,] -0.848 0.169 -0.827 1.163
##
## main 91 ( 120 ) Accepts 19 / 30
## .main 92 ( 120 )
## Mu = 1.969 2.059 -1.324 1.252
## Eta = 0.18 0.976 0.645
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 1.422 -0.726 0.384 0.002
## [2,] -0.726 0.727 -0.415 0.884
## [3,] 0.384 -0.415 1.337 -2.344
## [4,] 0.002 0.884 -2.344 6.454
##
## main 92 ( 120 ) Accepts 9 / 30
## .main 93 ( 120 )
## Mu = 2.845 2.024 -0.908 0.719
## Eta = 0.345 1.502 1.389
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 1.283 -0.217 1.153 -1.133
## [2,] -0.217 0.390 -0.324 0.111
## [3,] 1.153 -0.324 1.775 -1.322
## [4,] -1.133 0.111 -1.322 1.944
##
## main 93 ( 120 ) Accepts 12 / 30
## .main 94 ( 120 )
## Mu = 3.084 2.486 -0.434 -0.062
## Eta = 0.39 1.499 0.938
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 0.776 -0.402 0.099 -0.394
## [2,] -0.402 0.773 -0.329 0.545
## [3,] 0.099 -0.329 0.851 -0.692
## [4,] -0.394 0.545 -0.692 1.634
##
## main 94 ( 120 ) Accepts 15 / 30
## .main 95 ( 120 )
## Mu = 4.403 0.938 1.411 -0.629
## Eta = -0.389 1.773 -0.118
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 2.332 -1.656 1.544 -1.065
## [2,] -1.656 1.545 -1.128 0.695
## [3,] 1.544 -1.128 1.556 -0.612
## [4,] -1.065 0.695 -0.612 1.395
##
## main 95 ( 120 ) Accepts 13 / 30
## .main 96 ( 120 )
## Mu = 2.487 2.391 0.225 0.137
## Eta = -0.226 1.928 -0.579
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 1.390 -0.996 0.086 -0.252
## [2,] -0.996 0.849 0.063 0.219
## [3,] 0.086 0.063 2.625 -1.545
## [4,] -0.252 0.219 -1.545 1.929
##
## main 96 ( 120 ) Accepts 13 / 30
## .main 97 ( 120 )
## Mu = 3.466 1.936 0.519 -1.811
## Eta = 0.014 1.54 0.413
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 1.747 -1.238 0.154 -0.899
## [2,] -1.238 1.494 -0.124 0.983
## [3,] 0.154 -0.124 0.690 -0.548
## [4,] -0.899 0.983 -0.548 2.243
##
## main 97 ( 120 ) Accepts 13 / 30
## .main 98 ( 120 )
## Mu = 1.441 2.205 -0.326 -0.915
## Eta = -0.191 1.44 0.634
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 1.300 -0.666 0.029 0.121
## [2,] -0.666 0.916 -0.728 1.228
## [3,] 0.029 -0.728 2.257 -2.195
## [4,] 0.121 1.228 -2.195 3.898
##
## main 98 ( 120 ) Accepts 13 / 30
## .main 99 ( 120 )
## Mu = 2.593 2.86 0.843 -0.785
## Eta = -0.107 1.534 1.457
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 1.470 -0.579 0.979 -1.215
## [2,] -0.579 1.012 0.705 -0.044
## [3,] 0.979 0.705 4.097 -2.931
## [4,] -1.215 -0.044 -2.931 3.491
##
## main 99 ( 120 ) Accepts 15 / 30
## .main 100 ( 120 )
## Mu = 1.85 2.792 0.298 0.503
## Eta = -0.18 1.052 1.958
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 1.813 -0.913 -0.481 -0.431
## [2,] -0.913 0.959 0.195 0.579
## [3,] -0.481 0.195 1.134 0.360
## [4,] -0.431 0.579 0.360 2.486
##
## main 100 ( 120 ) Accepts 14 / 30
##
## Mu = 1.85 2.792 0.298 0.503
## Eta = -0.18 1.052 1.958
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 1.813 -0.913 -0.481 -0.431
## [2,] -0.913 0.959 0.195 0.579
## [3,] -0.481 0.195 1.134 0.360
## [4,] -0.431 0.579 0.360 2.486
##
## .main 101 ( 120 )
## Mu = 2.049 4.34 1.585 -0.312
## Eta = -0.561 1.433 2.389
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 1.124 -1.333 1.061 0.506
## [2,] -1.333 3.059 -1.400 0.191
## [3,] 1.061 -1.400 3.250 0.292
## [4,] 0.506 0.191 0.292 2.597
##
## main 101 ( 120 ) Accepts 15 / 30
## .main 102 ( 120 )
## Mu = 3.748 2.432 -0.039 -0.155
## Eta = -0.458 1.918 2.637
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 2.938 1.495 0.528 3.145
## [2,] 1.495 3.368 0.467 4.001
## [3,] 0.528 0.467 0.981 0.984
## [4,] 3.145 4.001 0.984 6.685
##
## main 102 ( 120 ) Accepts 16 / 30
## .main 103 ( 120 )
## Mu = 2.872 3.76 -0.358 -0.241
## Eta = -0.765 1.85 1.312
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 2.580 -0.749 1.259 0.074
## [2,] -0.749 1.879 -0.518 0.587
## [3,] 1.259 -0.518 1.697 0.131
## [4,] 0.074 0.587 0.131 0.989
##
## main 103 ( 120 ) Accepts 19 / 30
## .main 104 ( 120 )
## Mu = 3.112 3.033 -1.281 -1.025
## Eta = -0.588 1.705 1.589
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 2.924 1.381 -0.823 1.001
## [2,] 1.381 3.037 -0.992 1.994
## [3,] -0.823 -0.992 1.796 -1.117
## [4,] 1.001 1.994 -1.117 2.305
##
## main 104 ( 120 ) Accepts 14 / 30
## .main 105 ( 120 )
## Mu = 3 2.706 -0.85 2.033
## Eta = -1.066 2.302 1.67
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 1.762 -0.293 -0.713 -0.066
## [2,] -0.293 1.105 -0.014 0.783
## [3,] -0.713 -0.014 2.471 -2.614
## [4,] -0.066 0.783 -2.614 6.004
##
## main 105 ( 120 ) Accepts 15 / 30
## .main 106 ( 120 )
## Mu = 3.797 3.25 0.347 -1.319
## Eta = -1.012 2.036 2.174
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 3.056 -2.863 -1.351 0.971
## [2,] -2.863 6.022 4.354 -3.260
## [3,] -1.351 4.354 5.553 -3.049
## [4,] 0.971 -3.260 -3.049 2.823
##
## main 106 ( 120 ) Accepts 16 / 30
## .main 107 ( 120 )
## Mu = 2.533 3.165 -0.281 0.352
## Eta = -0.77 2.242 2.775
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 2.128 -0.344 0.799 -0.608
## [2,] -0.344 0.901 0.072 -0.129
## [3,] 0.799 0.072 0.925 -0.179
## [4,] -0.608 -0.129 -0.179 0.834
##
## main 107 ( 120 ) Accepts 19 / 30
## .main 108 ( 120 )
## Mu = 5.011 1.766 0.482 -1.17
## Eta = -0.906 1.674 1.932
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 1.529 -0.469 0.523 0.113
## [2,] -0.469 0.857 0.004 0.003
## [3,] 0.523 0.004 0.946 0.485
## [4,] 0.113 0.003 0.485 2.280
##
## main 108 ( 120 ) Accepts 19 / 30
## .main 109 ( 120 )
## Mu = 4.19 2.727 -0.087 -0.87
## Eta = -0.772 1.532 2.123
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 1.639 -0.763 0.846 -0.321
## [2,] -0.763 1.741 -0.033 0.258
## [3,] 0.846 -0.033 2.186 -0.028
## [4,] -0.321 0.258 -0.028 0.683
##
## main 109 ( 120 ) Accepts 10 / 30
## .main 110 ( 120 )
## Mu = 2.867 3.105 -0.722 0.367
## Eta = -0.683 1.323 1.901
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 1.304 -0.637 0.305 -0.246
## [2,] -0.637 0.507 -0.104 -0.002
## [3,] 0.305 -0.104 1.546 -0.601
## [4,] -0.246 -0.002 -0.601 0.898
##
## main 110 ( 120 ) Accepts 17 / 30
## .main 111 ( 120 )
## Mu = 1.829 2.513 0.222 0.149
## Eta = -0.795 1.691 0.957
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 0.983 -0.250 -0.032 -0.163
## [2,] -0.250 0.512 -0.069 -0.141
## [3,] -0.032 -0.069 0.813 -0.075
## [4,] -0.163 -0.141 -0.075 1.041
##
## main 111 ( 120 ) Accepts 16 / 30
## .main 112 ( 120 )
## Mu = 1.737 3.947 0.755 -0.252
## Eta = -0.485 2.134 0.726
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 1.209 -1.205 -0.233 0.053
## [2,] -1.205 1.618 0.131 0.055
## [3,] -0.233 0.131 0.715 -0.253
## [4,] 0.053 0.055 -0.253 0.884
##
## main 112 ( 120 ) Accepts 14 / 30
## .main 113 ( 120 )
## Mu = 3.797 1.991 1.384 -0.152
## Eta = -0.876 2.438 -0.627
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 2.469 -2.187 2.418 0.578
## [2,] -2.187 2.809 -2.794 -1.008
## [3,] 2.418 -2.794 4.873 0.749
## [4,] 0.578 -1.008 0.749 1.457
##
## main 113 ( 120 ) Accepts 12 / 30
## .main 114 ( 120 )
## Mu = 3.802 1.463 -0.326 -0.491
## Eta = -0.417 2.319 -0.077
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 1.035 -1.012 0.317 -0.658
## [2,] -1.012 1.412 -0.779 1.096
## [3,] 0.317 -0.779 1.412 -0.858
## [4,] -0.658 1.096 -0.858 1.588
##
## main 114 ( 120 ) Accepts 10 / 30
## .main 115 ( 120 )
## Mu = 3.373 2.378 0.262 0.01
## Eta = -0.419 1.754 -0.675
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 1.119 -0.340 0.186 0.211
## [2,] -0.340 0.603 -0.023 0.265
## [3,] 0.186 -0.023 0.592 0.136
## [4,] 0.211 0.265 0.136 1.107
##
## main 115 ( 120 ) Accepts 15 / 30
## .main 116 ( 120 )
## Mu = 2.649 2.313 0.831 -0.793
## Eta = -0.75 1.7 -1.035
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 2.264 -0.593 0.381 0.004
## [2,] -0.593 1.952 -0.380 -0.196
## [3,] 0.381 -0.380 1.354 -0.339
## [4,] 0.004 -0.196 -0.339 0.862
##
## main 116 ( 120 ) Accepts 12 / 30
## .main 117 ( 120 )
## Mu = 2.765 3.282 -0.198 -0.174
## Eta = -0.674 1.407 -0.667
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 1.016 0.080 -0.526 0.215
## [2,] 0.080 1.953 -1.222 0.266
## [3,] -0.526 -1.222 1.669 -0.069
## [4,] 0.215 0.266 -0.069 0.870
##
## main 117 ( 120 ) Accepts 9 / 30
## .main 118 ( 120 )
## Mu = 3.545 2.45 -1.473 1.693
## Eta = -0.661 1.506 -1.523
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 1.912 -1.751 2.187 -2.704
## [2,] -1.751 2.243 -1.823 2.918
## [3,] 2.187 -1.823 5.821 -5.986
## [4,] -2.704 2.918 -5.986 7.870
##
## main 118 ( 120 ) Accepts 10 / 30
## .main 119 ( 120 )
## Mu = 3.313 2.72 1.487 0.253
## Eta = -1.065 1.67 -0.765
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 2.277 -2.130 0.300 -1.420
## [2,] -2.130 2.576 0.029 0.956
## [3,] 0.300 0.029 1.203 -0.289
## [4,] -1.420 0.956 -0.289 2.353
##
## main 119 ( 120 ) Accepts 9 / 30
## .main 120 ( 120 )
## Mu = 3.047 2.8 -0.12 0.77
## Eta = -0.275 1.267 0.726
## Sigma =
## [,1] [,2] [,3] [,4]
## [1,] 3.013 -1.370 1.643 0.594
## [2,] -1.370 1.011 -0.873 -0.181
## [3,] 1.643 -0.873 1.586 0.113
## [4,] 0.594 -0.181 0.113 1.238
##
## main 120 ( 120 ) Accepts 19 / 30
## Total duration 30.546 seconds.RateTracePlots(fit3)
NonRateTracePlots(fit3)fit3## Note: this summary does not contain a convergence check.
##
## Groups:
## Data1 Data2 Data3
##
## Posterior means and standard deviations for global mean parameters
##
## Total number of runs in the results is 120 .
## Posterior means and standard deviations are averages over 100 MCMC runs (counted after thinning).
##
## Post. Post. cred. cred. p varying Post. cred. cred.
## mean s.d.m. from to s.d. from to
## 1. rate constant IS rate (period 1) 3.7095 ( 0.9551 ) NA NA NA
## 2. rate constant IS rate (period 2) 2.0008 ( 0.7819 ) NA NA NA
## 3. rate constant IS rate (period 4) 3.0673 ( 0.8553 ) NA NA NA
## 4. rate constant IS rate (period 5) 2.3651 ( 0.7830 ) NA NA NA
## 5. rate constant IS rate (period 7) 3.2798 ( 0.8262 ) NA NA NA
## 6. rate constant IS rate (period 8) 1.9778 ( 0.7611 ) NA NA NA
## 7. eval outdegree (density) -0.4579 ( 0.8721 ) -2.1248 1.3979 0.28 + 1.4767 0.7901 2.5991
## 8. eval reciprocity 0.2788 ( 0.8998 ) -1.3746 1.8866 0.63 + 1.5113 0.7257 2.7735
## 9. eval transitive triplets -0.1933 ( 0.4258 ) -0.9651 0.6983 0.33 - NA NA NA
## 10. eval val 1.5605 ( 0.3529 ) 0.8966 2.3112 1.00 - NA NA NA
## 11. eval ae ego 0.2167 ( 1.2107 ) -1.9751 2.5192 0.53 - NA NA NA
##
## Posterior mean of global covariance matrix (varying parameters)
## 2.5390 -1.3046 0.4977 -0.1076
## -1.3046 1.6172 -0.3787 0.2259
## 0.4977 -0.3787 2.1808 -0.6187
## -0.1076 0.2259 -0.6187 2.2839
##
## Posterior standard deviations of elements of global covariance matrix
## 3.0014 1.6994 1.6107 1.9682
## 1.6994 1.3020 1.1220 1.4474
## 1.6107 1.1220 1.7889 1.4673
## 1.9682 1.4474 1.4673 2.1804If this is all the data that you have, I would suggest trying to add simple network effects, increase the Markov Chain, but to not have high hopes to ever get good results. Three teams with 5 people is a very small dataset.
We analyzed information exchange in several emergency care teams. These teams were operating in the local simulation center and practicing a specific procedure (ABCDE). All training sessions were recorded and manually coded. A training session had most often 4 team members (main nurse, supporting nurse, doctor, and specialist). The specialist was only called in to transfer the simulated patient from the emergency care room to the care-giving unit. More information about the context is available in The Main Nurse as a Linchpin in Emergency Care Teams.
The variables we collected through coding the videos were information retrieval and information allocation (dependent variables), and three forms of higher order processing of information (summarizing, elaboration, and decision-making). Our coding schema also included exchanges between a human and a machine, when for example, a nurse is working on a machine. Additionally we collected the following variables using a survey: Awareness of team member’s expertise (knowing; independent variable), the importance team member’s attach to each other’s expertise (valuing, independent variable), how adaptive individuals are (adaptive expertise; independent variable), their emotional attachment to their group (social identity; independent variable), and background variables (gender, age, nationality, job role, tenure, number of training session, department; control variable).
We analyzed the data using relational event modeling. For the chapter mentioned above we created some specific scripts to deal with self-loops, valued independent data etc. Below I created a simpler script to demonstrate how to run a REM>
For this workshop we will be focusing
In general, the steps are: 1. Import the data 2. Specify independent, dependent variables 3. Select the effects and specify the model 4. Test goodness of fit
library(relevent)## Loading required package: trust## Loading required package: sna## Loading required package: statnet.common##
## Attaching package: 'statnet.common'## The following object is masked from 'package:base':
##
## order## Loading required package: network## network: Classes for Relational Data
## Version 1.13.0 created on 2015-08-31.
## copyright (c) 2005, Carter T. Butts, University of California-Irvine
## Mark S. Handcock, University of California -- Los Angeles
## David R. Hunter, Penn State University
## Martina Morris, University of Washington
## Skye Bender-deMoll, University of Washington
## For citation information, type citation("network").
## Type help("network-package") to get started.## sna: Tools for Social Network Analysis
## Version 2.4 created on 2016-07-23.
## copyright (c) 2005, Carter T. Butts, University of California-Irvine
## For citation information, type citation("sna").
## Type help(package="sna") to get started.## Loading required package: coda## relevent: Relational Event Models
## Version 1.0-4 created on March 9, 2015.
## copyright (c) 2007, Carter T. Butts, University of California-
## Irvine
## For citation information, type citation("relevent").
## Type help(package="relevent") to get started.library(informR)## Loading required package: abind## informR: Sequence Statistics for Relational Event Models
## Version 1.0-5 created on 2015-03-09.
## copyright (c) 2010, Christopher Steven Marcum, University of California-
## Irvine
## For citation information, type citation("informR").
## Type help(package="informR") to get started.source("rem_data_loading.R", echo=F)rem can be applied to egocentric relational event data but requires that the user supplies the necessary statistics. On the other hand, rem.dyad is less flexible, but has more built-in functionalities (and hence requires less coding). The function takes the form of rem.dyad(edgelist, n, effects = NULL, ordinal = TRUE. To run it, you need to define an edgelist, the number of senders and receivers, an optional list of effects, and indicate if the timing is ordinal (TRUE) or if the exact timing of events should be used (ordinal=FALSE). The edgelist is a 3-column matrix which contains information about the timing, sender, and receiver. The data needs to be sorted by time.
nbr_send_rec = c(unique(remj[remj$Observation == 10,2]), unique(remj[remj$Observation == 10,(3)]))
nbr_send_rec## [1] 10 8 1 5 2 6 3 4fit1 <- rem.dyad(remj[remj$Observation == 10,(1:3)], n = length(nbr_send_rec), ordinal=FALSE)
summary(fit1)## Relational Event Model (Temporal Likelihood)
##
## Null model object.
##
## Null deviance: 3124.23 on 255 degrees of freedom
## Residual deviance: 3124.23 on 255 degrees of freedom
## Chi-square: 0 on 0 degrees of freedom, asymptotic p-value 1
## AIC: 3126.23 AICC: 3124.245 BIC: 3129.771The model fit1 only includes the fixed effect. Not interesting at all. We are going to add a bunch of effects.
fit2 <- rem.dyad(remj[remj$Observation == 10,(1:3)], n = length(nbr_send_rec), ordinal=FALSE, effects= c("FESnd","FERec", "PSAB-BA", "PSAB-XA")) ## Computing preliminary statistics
## Fitting model
## Obtaining goodness-of-fit statisticssummary(fit2)## Relational Event Model (Temporal Likelihood)
##
## Estimate
## FESnd.2 -0.0006
## FESnd.3 0.0004
## FESnd.4 -0.0017
## FESnd.5 -0.0014
## FESnd.6 0.0001
## FESnd.7 -0.0001
## FESnd.8 0.0003
## FERec.2 0.0007
## FERec.3 -0.0018
## FERec.4 0.0002
## FERec.5 -0.0007
## FERec.6 -0.0009
## FERec.7 0.0013
## FERec.8 0.0001
## PSAB-BA -0.0002
## PSAB-XA -0.0007
## Null deviance: 3124.23 on 255 degrees of freedom
## Residual deviance: -4.631688e+77 on 240 degrees of freedom
## Chi-square: 4.631688e+77 on 15 degrees of freedom, asymptotic p-value 0
## AIC: -4.631688e+77 AICC: -4.631688e+77 BIC: -4.631688e+77In my analysis I also wanted to take the type of event into account. Hence, I wanted to make a difference between information allocation, information retrieval, summarizing, elaboration, and decision making. I also had individual variables I wanted to include. For these reasons I used rem.
The function rem requires a different set of arguments rem(eventlist, statslist, supplist = NULL, timing = c("ordinal", "interval"). The first, eventlist is a 2-column matrix (or list) with the time of an event and the event type. This is the file evlj. If you inspect its type (class(evlj)) and its structure (str(evlj)), you’ll see that it is a list with 31 items. Each item in the list is a matrix with 2 columns. The first column in the matrix is a series of numbers, the event types, the second column contains the timing.
evlj$eventlist$`1`[1:10,]## [,1] [,2]
## [1,] 0 0.00001
## [2,] 11 19.95292
## [3,] 12 22.45043
## [4,] 11 23.99704
## [5,] 5 29.57855
## [6,] 9 32.31916
## [7,] 1 34.75897
## [8,] 6 34.95038
## [9,] 2 36.16269
## [10,] 1 37.26560evlj$event.key## id event.type
## [1,] "a" "8.8"
## [2,] "b" "1.5"
## [3,] "c" "5.1"
## [4,] "d" "2.1"
## [5,] "e" "1.2"
## [6,] "f" "1.10"
## [7,] "g" "2.6"
## [8,] "h" "1.6"
## [9,] "i" "6.1"
## [10,] "j" "5.10"
## [11,] "k" "6.2"
## [12,] "l" "2.5"
## [13,] "m" "5.2"
## [14,] "n" "1.3"
## [15,] "o" "2.10"
## [16,] "p" "3.10"
## [17,] "q" "3.6"
## [18,] "r" "2.3"
## [19,] "s" "6.3"
## [20,] "t" "3.2"
## [21,] "u" "3.5"
## [22,] "v" "5.3"
## [23,] "w" "3.1"
## [24,] "x" "4.10"
## [25,] "y" "3.4"
## [26,] "z" "4.3"
## [27,] "A" "4.6"
## [28,] "B" "6.4"
## [29,] "C" "4.5"
## [30,] "D" "5.4"
## [31,] "E" "9.9"
## [32,] "F" "7.7"
## [33,] "G" "2.4"
## [34,] "H" "4.2"
## [35,] "I" "4.1"
## [36,] "J" "1.4"This list was created by calling gen.evl(eventlist, null.events=NULL). Eventlist is a 2 or 3 column matrix. Running gen.evl gives you an eventlist (a sequence of numbers indicating the events that occurred) and an event.key.
The function rem also requires that you provide a statslist. This is a file containing some statistics about your data. The code below creates such as statslist for the fixed sender effects. Think of these as your intercepts only for sending information.
#Intercepts et cetera
evlj.ints <- gen.intercepts(evlj, contr = F)
nj<-7
njn<-c(1,2,3,4,5,6,10)
sformlistj <- c(
lapply(2:(nj-1), function(z){
str <- paste("^",njn[z], ".", sep="")
grep(str, evlj$event.key[ ,2])
# put in the square brackets, all events which are between real people.
# the 2 stands for the event.key not event.id
}),
lapply(2:nj, function(z){
str <- paste(".", njn[z],"$", sep = "")
grep(str, evlj$event.key[, 2])
})
)
b1j<-list()
b1.lj<-list()
FEsj<-list()
for(h in 1:length(evlj$eventlist)){
b1j[[h]] <- lapply(sformlistj, function(x) evlj.ints[[h]][[1]][, , evlj$event.key[x,2]])
b1.lj[[h]] <- lapply(b1j[[h]], apply, MARGIN = 1:2, sum)
FEsj[[h]] <- array(unlist(b1.lj[[h]]), dim = c(nrow(b1.lj[[h]][[1]]), ncol(b1.lj[[h]][[1]]),
length(b1.lj[[h]])))
dimnames(FEsj[[h]]) <- list(dimnames(b1j[[h]][[1]])[[1]], dimnames(b1j[[h]][[1]])[[2]],
c(paste("FESnd", njn[-c(1,7)], sep="."),paste("FERec", njn[-1], sep=".")))
}
#Simple Fixed Effects for Sender and Receiver
FEsj<-sfl2statslist(FEsj)Now we have the statslist. The supplist has been created when loading the data. The goal of the supplist is to indicate which events could have been observed and which not. For example, in my setting the doctor entered the emergency care room at a later stage. This means that it was impossible to observe any interaction with the doctor before that. My event list contains an event ‘doctor enters the room’ (aka handover between nurse and doctor). We used this event to indicate when interaction with the doctor was possible.
fit1.rem is running a simple fixed effect model. This is the null model only including intercepts.
#Model 1 Fixed Effects for Sender and Receiver (pooled likelihood)
fit1.rem<-rem(evlj$eventlist,FEsj,timing="interval",estimator="MLE",supplist=supplistj)
summary(fit1.rem)## Egocentric Relational Event Model (Interval Likelihood)
##
## MLE Std.Err Z value Pr(>|z|)
## FESnd.2 -2.737658 0.015226 -179.80 < 2.2e-16 ***
## FESnd.3 -2.591566 0.014188 -182.66 < 2.2e-16 ***
## FESnd.4 -4.284953 0.032379 -132.34 < 2.2e-16 ***
## FESnd.5 -3.481403 0.022142 -157.23 < 2.2e-16 ***
## FESnd.6 -3.902952 0.028064 -139.07 < 2.2e-16 ***
## FERec.2 -3.016525 0.017835 -169.13 < 2.2e-16 ***
## FERec.3 -2.930825 0.017165 -170.75 < 2.2e-16 ***
## FERec.4 -4.531038 0.037141 -121.99 < 2.2e-16 ***
## FERec.5 -3.185861 0.019290 -165.15 < 2.2e-16 ***
## FERec.6 -3.938522 0.028070 -140.31 < 2.2e-16 ***
## FERec.10 -2.770828 0.015499 -178.78 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Null deviance: 106703.6 on 9557 degrees of freedom
## Residual deviance: 116213.4 on 9546 degrees of freedom
## Chi-square: -9509.75 on 11 degrees of freedom, asymptotic p-value 1
## AIC: 116235.4 AICC: 116235.4 BIC: 116314.2Now we will be including a participation shift event. 10 is a special ‘ego actor’: The team. When team members engaged in exchanges such as summarizing information, elaboration of information, and decision-making it was difficult to decide who the receiver of this information exchange is. Therefore, we coded them all to be directed at the team (actor 10). For this reason, actor 10 cannot send out information exchanges.
#Ignore null events and events involving 10, who cannot by construct reply.
nevs<-grep(paste(c(paste("(",evlj$null.events,")",sep=""),"(10)"),collapse="|"),evlj$event.key[,2])
evk.ex<-cbind(evlj$event.key[-nevs,1],do.call("rbind",strsplit(evlj$event.key[-nevs,2],"\\.")))
#Match AB->BA turn taking PShifts
tr1<-cbind(evk.ex[,1],evk.ex[sapply(paste(evk.ex[,2],evk.ex[,3],sep="."),function(x) which(x==paste(evk.ex[,3],evk.ex[,2],sep="."))),1])
tr2<-paste(tr1[,1],tr1[,2],sep="")
tr.sfl<-glb.sformlist(evlj,sforms=list(tr2),new.names="PS-ABBA",interval=TRUE,cond=FALSE)
FEsTr<-slbind(tr.sfl,FEsj)
#FEsTr<-slbind(tr.sfl,KWSnd1)
fit2.rem <- rem(evlj$eventlist, FEsTr, supplist=supplistj,estimator = "MLE",timing="interval")
summary(fit2.rem)## Egocentric Relational Event Model (Interval Likelihood)
##
## MLE Std.Err Z value Pr(>|z|)
## FESnd.2 -3.050740 0.015931 -191.49 < 2.2e-16 ***
## FESnd.3 -2.848682 0.014727 -193.44 < 2.2e-16 ***
## FESnd.4 -4.288418 0.032372 -132.47 < 2.2e-16 ***
## FESnd.5 -3.666170 0.022332 -164.17 < 2.2e-16 ***
## FESnd.6 -4.044053 0.028155 -143.64 < 2.2e-16 ***
## FERec.2 -3.302272 0.018360 -179.86 < 2.2e-16 ***
## FERec.3 -3.114472 0.017412 -178.87 < 2.2e-16 ***
## FERec.4 -4.515115 0.037135 -121.59 < 2.2e-16 ***
## FERec.5 -3.322871 0.019414 -171.16 < 2.2e-16 ***
## FERec.6 -4.047708 0.028122 -143.93 < 2.2e-16 ***
## FERec.10 -2.736799 0.015484 -176.75 < 2.2e-16 ***
## PS-ABBA 1.934131 0.015255 126.79 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Null deviance: 106703.6 on 9557 degrees of freedom
## Residual deviance: 110630.8 on 9545 degrees of freedom
## Chi-square: -3927.161 on 12 degrees of freedom, asymptotic p-value 1
## AIC: 110654.8 AICC: 110654.8 BIC: 110740.8A quick note about the interpretation of the results. The estimates are hazard rates. You could take the exponential of them (exp(-2.85)) to get log values. In that way, you can say thinks like “the likelihood that the doctor (actor 3) will send information is 95 per cent (exp(-2.85) less likely than that the main nurse will send information”. Why the main nurse? You have to specify a base level. We picked the main nurse as this actor initiates the interaction. However, we could have also picked someone else. The danger with using log likelihoods when discussing your results is that others might not view it as a longitudinal study. An alternative is to talk about hazard rates. You would then say something like “The rate at which the doctor sends information is 95 % less fast than the rate of sending information from the main nurse.”