BASED ON PAPER: Toward a Greater Understanding of How Dissatisfaction Drives Employee Turnover Author(s): Peter W. Hom and Angelo J. Kinicki.
Source: The Academy of Management Journal, Vol. 44, No. 5 (Oct., 2001), pp. 975-987 Published by: Academy of Management.
Stable URL: https://www.jstor.org/stable/3069441
This example sensitivity analysis uses the published data and model from Hom and Kinicki (2001). We create a covariance matrix from their data, set up lavaan models for their original model and the sensitivity model, run the analysis, and view the results.
# Load lavaan and SEMsens packages
require(lavaan)
require(SEMsens)
set.seed(1)Hom and Kinicki (2001) published correlations and standard deviations
for all indicator variables, so we use those to create a covariance
matrix covmat.
# Correlation matrix from published data
cormat <- diag(1,29) # start with the diagonal
cormat[lower.tri(cormat)] <- c( # add lower triangle data
.46,.22,.30,-.20,-.30,-.20,-.22,-.33,-.19,-.25,-.63,-.60,-.48,-.17,-.42,-.09,-.36,.09,
.04,-.12,0,-.20,-.20,-.43,-.33,-.49,-.18,-.03,.21,.30,-.15,-.25,-.10,-.20,-.31,-.15,
-.24,-.40,-.37,-.32,-.08,-.24,-.02,-.27,.06,.07,-.08,0,-.10,-.16,-.25,-.18,-.35,-.06,
-.05,.04,-.05,-.09,-.12,-.10,-.01,.03,.02,-.18,-.14,-.09,-.02,-.12,-.05,-.08,.03,.07,
-.08,-.06,-.10,-.07,-.10,-.03,-.11,.04,.03,-.07,-.24,0,-.12,-.50,-.32,-.45,-.38,-.29,
-.31,-.16,-.24,-.16,-.37,.12,.05,-.28,-.13,-.06,-.03,-.16,-.12,-.23,-.08,.06,.29,.31,
.10,.08,-.02,.07,.21,.24,.25,.06,.09,.04,.14,-.02,-.01,.10,.04,.04,.13,.19,.03,.18,
.14,-.04,.38,.41,.23,.13,.22,.36,.35,.35,.09,.14,.11,.14,-.09,-.04,.11,.04,.11,.15,
.30,.17,.33,.12,-.02,.31,.05,.03,.15,.22,.20,.21,-.05,.10,-.05,.03,-.04,-.06,.03,.05,
.03,.07,.24,.19,.23,.13,-.08,.17,.15,.19,.28,.23,.23,.04,.18,.08,.10,-.09,-.06,.07,
.01,.11,.08,.21,.20,.28,.06,-.03,.43,.56,.35,.32,.26,.16,.27,.13,.45,-.04,-.04,.16,
.07,.14,.15,.23,.12,.29,.09,-.07,.67,.24,.26,.27,.15,.21,.13,.25,-.10,-.02,.12,0,.12,
.10,.18,.21,.27,.17,-.06,.36,.32,.31,.11,.29,.16,.40,-.10,-.05,.22,.10,.17,.15,.27,
.23,.33,.17,-.08,.78,.77,.11,.49,.09,.40,-.23,-.14,.19,-.07,.29,.27,.57,.40,.68,.27,0,
.82,.10,.57,.08,.42,-.29,-.10,.13,-.12,.33,.31,.66,.46,.75,.32,.02,.10,.49,.08,.38,
-.31,-.11,.18,-.06,.33,.34,.54,.38,.67,.31,-.08,.14,.52,.20,.22,.31,.42,.39,.01,.01,
.07,.06,.13,-.03,.06,.14,.42,-.29,-.12,.24,-.06,.25,.25,.38,.28,.48,.18,-.01,.16,.16,
.28,.68,.48,.06,.10,.01,.12,.15,-.05,.04,.02,.03,.24,.11,.14,.16,.31,.22,.32,.09,-.01,
.37,.12,.18,-.20,-.15,-.22,-.08,-.23,-.11,.07,.13,.18,-.07,0,-.10,.04,-.06,-.03,.15,
.54,.11,.12,.07,.10,.16,-.01,-.02,-.06,-.01,-.09,-.05,-.10,-.14,.06,.57,.28,.17,.36,
.27,-.05,.32,.21,.36,.18,.05,.42,.68,.26,-.05,.55,.23,.04,.28,-.03,-.07
)
cormat[upper.tri(cormat)] <- t(cormat)[upper.tri(cormat)] # mirror lower to upper
# Standard deviations from published data
sds <- diag(c(1,.38,.73,.65,.58,.78,.75,.55,.59,.54,.45,.74,.85,.80,.57,
.74,.69,.42,.57,.63,.62,.70,1.01,.94,.65,.37,.73,.40,1))
# Create covariance matrix covmat with row and column names
covmat <- sds %*% cormat %*% sds
rownames(covmat) <- colnames(covmat) <- c(
"FACES","Duty","Team","Hours","Absent","Effort","Sick","Quality","Family",
"Community","Personal","Thoughts","SI","QI","Stress","Jobs","Costs",
"Benefits","Joblessness","Moving","Impact","Interference","V1","V2",
"Prepare","Look","Intensity","Resign","Unemployed"
)The SEMsens package requires both an original model and a sensitivity model that adds the phantom variables. These models are defined SEMsens using the lavaan model syntax.
We first define the original model:
# Original model from Hom and Kinicki (2001)
model <- "JSat =~ FACES + Duty + Team
IC =~ Family + Personal + Community
JAvoid =~ Quality + Absent + Effort + Sick
WC =~ QI + Thoughts + SI
WEU =~ Stress + Benefits + Impact + Jobs
JSearch =~ Prepare + Look + Intensity
CA =~ V1 + V2
Turnover =~ Resign
Resign ~~ 0*Resign
UR =~ Unemployed
Unemployed ~~ 0*Unemployed
JSat ~ IC
JAvoid ~ JSat
WC ~ JAvoid + JSat + IC
WEU ~ WC + JSat + UR
JSearch ~ WEU
CA ~ JSearch
Turnover ~ CA + WC + UR"For the sensitivity model, we use the same model definition as the original model but add one phantom variable with paths phantom1, phantom2, etc. to each of the latent variables in the original model.
# Sensitivity model
sens.model <- "JSat =~ FACES + Duty + Team
IC =~ Family + Personal + Community
JAvoid =~ Quality + Absent + Effort + Sick
WC =~ QI + Thoughts + SI
WEU =~ Stress + Benefits + Impact + Jobs
JSearch =~ Prepare + Look + Intensity
CA =~ V1 + V2
Turnover =~ Resign
Resign ~~ 0*Resign
UR =~ Unemployed
Unemployed ~~ 0*Unemployed
JSat ~ IC
JAvoid ~ JSat
WC ~ JAvoid + JSat + IC
WEU ~ WC + JSat + UR
JSearch ~ WEU
CA ~ JSearch
Turnover ~ CA + WC + UR
IC ~ phantom1*phantom
UR ~ phantom2*phantom
JSat ~ phantom3*phantom
JAvoid ~ phantom4*phantom
WC ~ phantom5*phantom
WEU ~ phantom6*phantom
JSearch ~ phantom7*phantom
CA ~ phantom8*phantom
Turnover ~ phantom9*phantom
phantom =~ 0
phantom ~~ 1*phantom"Before running the analysis, we need to identify the rows in a lavaan parameter table that include the paths we are interested in looking at in the analysis. To save space, only the most relevant section of the parameter table is displayed below.
ptab = lavaanify(model = model, auto = TRUE, model.type="sem")
ptab[26:40,1:4]## id lhs op rhs
## 26 26 Unemployed ~~ Unemployed
## 27 27 JSat ~ IC
## 28 28 JAvoid ~ JSat
## 29 29 WC ~ JAvoid
## 30 30 WC ~ JSat
## 31 31 WC ~ IC
## 32 32 WEU ~ WC
## 33 33 WEU ~ JSat
## 34 34 WEU ~ UR
## 35 35 JSearch ~ WEU
## 36 36 CA ~ JSearch
## 37 37 Turnover ~ CA
## 38 38 Turnover ~ WC
## 39 39 Turnover ~ UR
## 40 40 FACES ~~ FACESFor this example, we are interested in all the paths between latent variables. These are located on rows 27 to 39 in the parameter table for this model. That information will be used in the next step for the analysis.
The sa.aco function is used to run the sensitivity
analysis.
my.sa <- sa.aco(model = model, sens.model = sens.model, sample.cov = covmat,
sample.nobs = 410, opt.fun = 3, paths = 27:39,
seed = 1, k = 5, max.iter = 20)We specified the original model (model), the sensitivity
model (sens.model), the covariance matrix
(sample.cov), the number of observations in the sample
(sample.nobs), the number of sensitivity parameters
included (n.of.sens.pars), a preset optimization function
(opt.fun), the paths from the previous step
(paths), and a seed for reproducibility
(seed).
Note: We only used k = 5 and
max.iter = 20 so the analysis would run quickly for
illustration purposes. For actual analyses, please specify these
parameters as larger numbers (e.g., the default values are
k = 50 and max.iter = 1000).
The sens.tables function helps summarize the results of
a sensitivity analysis. We specify path = TRUE to only
obtain results for the structural paths.
my.sa.results = sens.tables(my.sa, path=TRUE) # get results
my.sa.results = lapply(my.sa.results, round, digits = 3) # round results (optional)The tables contain several categories of results. Each is displayed below.
The sens.summary table contains the estimates and p
values for each path in the original model as well as the mean, minimum,
and maximum values for the paths that were estimated during the
sensitivity analysis.
my.sa.results$sens.summary## model.est model.pvalue mean.est.sens min.est.sens max.est.sens
## JSat~IC -0.401 0.000 -0.579 -1.023 -0.336
## JAvoid~JSat -0.529 0.000 -0.499 -0.660 -0.129
## WC~JSat -0.637 0.000 -0.484 -0.645 -0.270
## Turnover~UR -0.065 0.155 -0.075 -0.256 0.129
## WEU~UR -0.018 0.575 -0.039 -0.225 0.028
## WC~JAvoid 0.139 0.034 0.080 -0.046 0.141
## WEU~JSat -0.093 0.202 0.112 -1.309 2.226
## WC~IC 0.144 0.004 0.154 -0.066 0.551
## Turnover~CA 0.190 0.002 0.211 0.129 0.304
## Turnover~WC 0.245 0.000 0.414 -0.660 1.628
## JSearch~WEU 0.883 0.000 0.588 0.032 2.124
## CA~JSearch 0.520 0.000 0.669 0.167 1.004
## WEU~WC 0.903 0.000 1.208 -2.875 6.782The phan.paths table contains the mean, minimum, and
maximum of the sensitivity parameters from the analysis
my.sa.results$phan.paths## mean.phan min.phan max.phan
## WEU~phantom -2.310 -4.965 -0.670
## JSat~phantom -0.458 -0.837 -0.047
## UR~phantom -0.305 -0.686 0.285
## CA~phantom -0.230 -0.481 0.280
## IC~phantom -0.180 -0.965 0.813
## WC~phantom 0.115 -1.103 0.694
## JAvoid~phantom 0.277 -0.148 0.805
## JSearch~phantom 0.332 -0.894 1.499
## Turnover~phantom 0.553 -1.105 1.795The phan.min table provides the set of tested
sensitivity parameter values for each path that resulted in the smallest
coefficient value for the path.
my.sa.results$phan.min## IC~phantom UR~phantom JSat~phantom JAvoid~phantom WC~phantom
## JSat~IC -0.965 -0.595 -0.384 0.123 0.409
## JAvoid~JSat -0.514 0.285 -0.837 -0.148 0.694
## WC~JAvoid -0.514 0.285 -0.837 -0.148 0.694
## WC~JSat -0.965 -0.595 -0.384 0.123 0.409
## WC~IC -0.295 0.001 -0.497 0.151 -1.103
## WEU~WC -0.295 0.001 -0.497 0.151 -1.103
## WEU~JSat -0.295 0.001 -0.497 0.151 -1.103
## WEU~UR 0.060 -0.531 -0.524 0.453 0.169
## JSearch~WEU -0.295 0.001 -0.497 0.151 -1.103
## CA~JSearch -0.295 0.001 -0.497 0.151 -1.103
## Turnover~CA -0.514 0.285 -0.837 -0.148 0.694
## Turnover~WC -0.514 0.285 -0.837 -0.148 0.694
## Turnover~UR 0.813 -0.686 -0.047 0.805 0.408
## WEU~phantom JSearch~phantom CA~phantom Turnover~phantom
## JSat~IC -0.714 1.499 -0.423 -0.194
## JAvoid~JSat -4.965 0.935 -0.389 1.254
## WC~JAvoid -4.965 0.935 -0.389 1.254
## WC~JSat -0.714 1.499 -0.423 -0.194
## WC~IC -3.900 -0.894 -0.481 1.795
## WEU~WC -3.900 -0.894 -0.481 1.795
## WEU~JSat -3.900 -0.894 -0.481 1.795
## WEU~UR -1.301 -0.675 0.280 1.014
## JSearch~WEU -3.900 -0.894 -0.481 1.795
## CA~JSearch -3.900 -0.894 -0.481 1.795
## Turnover~CA -4.965 0.935 -0.389 1.254
## Turnover~WC -4.965 0.935 -0.389 1.254
## Turnover~UR -0.670 0.794 -0.135 -1.105Likewise, the phan.max table provides the set of tested
sensitivity parameter values for each path that resulted in the
largest coefficient value for the path.
my.sa.results$phan.max## IC~phantom UR~phantom JSat~phantom JAvoid~phantom WC~phantom
## JSat~IC 0.060 -0.531 -0.524 0.453 0.169
## JAvoid~JSat 0.813 -0.686 -0.047 0.805 0.408
## WC~JAvoid 0.060 -0.531 -0.524 0.453 0.169
## WC~JSat -0.295 0.001 -0.497 0.151 -1.103
## WC~IC -0.965 -0.595 -0.384 0.123 0.409
## WEU~WC -0.514 0.285 -0.837 -0.148 0.694
## WEU~JSat -0.514 0.285 -0.837 -0.148 0.694
## WEU~UR 0.813 -0.686 -0.047 0.805 0.408
## JSearch~WEU -0.965 -0.595 -0.384 0.123 0.409
## CA~JSearch 0.060 -0.531 -0.524 0.453 0.169
## Turnover~CA 0.813 -0.686 -0.047 0.805 0.408
## Turnover~WC -0.295 0.001 -0.497 0.151 -1.103
## Turnover~UR 0.060 -0.531 -0.524 0.453 0.169
## WEU~phantom JSearch~phantom CA~phantom Turnover~phantom
## JSat~IC -1.301 -0.675 0.280 1.014
## JAvoid~JSat -0.670 0.794 -0.135 -1.105
## WC~JAvoid -1.301 -0.675 0.280 1.014
## WC~JSat -3.900 -0.894 -0.481 1.795
## WC~IC -0.714 1.499 -0.423 -0.194
## WEU~WC -4.965 0.935 -0.389 1.254
## WEU~JSat -4.965 0.935 -0.389 1.254
## WEU~UR -0.670 0.794 -0.135 -1.105
## JSearch~WEU -0.714 1.499 -0.423 -0.194
## CA~JSearch -1.301 -0.675 0.280 1.014
## Turnover~CA -0.670 0.794 -0.135 -1.105
## Turnover~WC -3.900 -0.894 -0.481 1.795
## Turnover~UR -1.301 -0.675 0.280 1.014The final table p.paths provides the sensitivity
parameters that lead to a change in significance for each path according
to the significance level specified in the sens.tables
function. We used the default significance level of .05 for that. The
first column contains the original p values and the second contains the
changed p values that are obtained with the listed phantom variable path
coefficients. The NAs occur when there is no change in p value for any
of the tested phantom variable path coefficients.
my.sa.results$p.paths## p.value p.changed IC~phantom UR~phantom JSat~phantom JAvoid~phantom
## WEU~UR 0.575 0.000 0.060 -0.531 -0.524 0.453
## WEU~JSat 0.202 0.032 0.813 -0.686 -0.047 0.805
## Turnover~UR 0.155 0.048 -0.965 -0.595 -0.384 0.123
## WC~IC 0.004 0.053 0.813 -0.686 -0.047 0.805
## JSearch~WEU 0.000 0.430 -0.295 0.001 -0.497 0.151
## JSat~IC 0.000 NA NA NA NA NA
## JAvoid~JSat 0.000 NA NA NA NA NA
## WC~JAvoid 0.034 NA NA NA NA NA
## WC~JSat 0.000 NA NA NA NA NA
## WEU~WC 0.000 NA NA NA NA NA
## CA~JSearch 0.000 NA NA NA NA NA
## Turnover~CA 0.002 NA NA NA NA NA
## Turnover~WC 0.000 NA NA NA NA NA
## WC~phantom WEU~phantom JSearch~phantom CA~phantom Turnover~phantom
## WEU~UR 0.169 -1.301 -0.675 0.280 1.014
## WEU~JSat 0.408 -0.670 0.794 -0.135 -1.105
## Turnover~UR 0.409 -0.714 1.499 -0.423 -0.194
## WC~IC 0.408 -0.670 0.794 -0.135 -1.105
## JSearch~WEU -1.103 -3.900 -0.894 -0.481 1.795
## JSat~IC NA NA NA NA NA
## JAvoid~JSat NA NA NA NA NA
## WC~JAvoid NA NA NA NA NA
## WC~JSat NA NA NA NA NA
## WEU~WC NA NA NA NA NA
## CA~JSearch NA NA NA NA NA
## Turnover~CA NA NA NA NA NA
## Turnover~WC NA NA NA NA NALeite, W., Shen, Z., Marcoulides, K., Fish, C., & Harring, J. (2022). Using ant colony optimization for sensitivity analysis in structural equation modeling. Structural Equation Modeling: A Multidisciplinary Journal, 29 (1), 47-56.