Lilian
Ribeiro Lacerda da Silva
University
of Araraquara, Brazil
E-mail: lilianrlacerda@gmail.com
Jorge
Alberto Achcar
University
of São Paulo, Brazil
E-mail: achcar@fmrp.usp.br
Jose
Luis Garcia Hermosilla
University
of Araraquara, Brazil
E-mail: jlghermosilla@hotmail.com
Submission: 3/31/2020
Revision: 5/13/2020
Accept: 6/3/2020
ABSTRACT
The main goal of this study is to describe the variability in work
ability over time and to verify the influences of professional and
sociodemographic variables. It is a longitudinal study conducted with 148
employees of an agricultural research company in a city located in the
countryside of São Paulo state, Brazil. The Work Ability Index (WAI)
questionnaire was applied to each individual in the sample in two times:
December 2018 and June 2019. Different statistical analyzes of the data were
performed using t-Student hypothesis tests for paired data, multiple linear
regression models with normal errors, logistic regression models and Bayesian
beta regression models assuming dependent WAI measures (the novelty of this
study). From the obtained results, it is concluded that the Work Ability Index
average decreases over time. Some covariates as education, physical activity,
position in the company, number of children and nature of task have some
influence on the variability of the WAI. The results of the data analysis show
that the most important factor affecting the workers WAI index in both times is
physical activity.
Keywords:
Ability to work; WAI questionnaire; longitudinal study; Bayesian analysis
1.
INTRODUCTION
The
ability to work is measured by the physical, mental and social conditions of
the worker (Moreira, 2013; Cordeiro & Araujo, 2016). It is also defined as
the balance between work and worker (Ilmarinen, 2006,
2007, 2009; Ahlstrom
et al., 2010; Seitsamo,
Tuomi & Martikainen,
2007). In order to maintain and promote work ability, it is important to avoid
occupational diseases, remoteness and early retirement, that is, actions that
are beneficial not only to the individual, but also to society (Martinez & Latorre, 2009; Martinez, Latorre & Fischer, 2010).
The
Work Ability Index (WAI) has been used by organizations as a relevant tool to
determine how well the worker is performing his activities, measuring his
physical, mental and social capacity, and promoting the improvement of the work
environment and to identify employees who need support (Silva Junior et al., 2013; Renosto et al., 2009; Tuomi et al., 2001; Tuomi et al., 2010; Martelin et al., 2008).
WAI
longitudinal studies are needed as a way to obtain more concrete results on the
availability for work of workers by analyzing its evolution and assessing the
real cause, by monitoring the population, as well as directing the company in
its strategies for maintaining and promoting the capacity to develop the work (Martinez, Latorre & Fischer; 2010;
Cordeiro & Araujo, 2016).
The
present study is aimed to describe the variability of WAI over time and to
analyze the influence of some socio-demographic and professional variables on
the evolution of WAI based on the obtained information of the workers sample
considered in the study.
2.
METHODS
It is a longitudinal study,
considering employees of an agricultural research company located in the city
of São Carlos, São Paulo State, Brazil. The company develops research in the
agricultural area, such as increased milk production, meat improvement, and
working with forages. The company structure is concentrated on a farm. In 2018,
the company had 149 active employees, but only 148 worked in the city of São
Carlos, so the survey was conducted with these 148 workers of the company.
The
research was authorized by the head of the organization and approved by the
Research Ethics Committee of the enterprise, since the study involves human
beings. The information on some covariates (a list of the covariates used in
the study is presented in an Appendix at
the end of this manuscript) associated to the WAI questionnaire were obtained
from the company's database, leading to the research input variables such as
gender (female or male), nature of the task (research, administrative, research
support and field), position (researcher, analyst, technician and assistant),
employment (effective or retired), length of employment (up to 10 years, 11 to
20 years, 21 to 30 years and over 30 years), marital status (married or
single), education (elementary school, high school, higher education, and
postgraduate), categorized age (31-40, 41-50, 51-60, and over 60), number of
children (if yes or no and how much if so) and another covariate related to the
frequency of physical activity practices (do not practice, rarely, a few times a month, every week and every
day). The importance to detect important factors affecting the workers WAI
indexes is the goal of many studies (Pohjonen, 2001).
The
main response of interest was the WAI questionnaire response obtained for each
worker in the company. According to Tuomi, et al. (2010) the WAI reaches a value ranging
from 7 to 49 points, with 7 being the lowest rating and 49 the best rating of
the index. Through the obtained results, it is possible to classify the ability
to work as low, moderate, good and optimal. The WAI was applied in two times:
December, 2018 and June, 2019 which characterizes longitudinal data. Several
statistical techniques were used to analyze the WAI data. Initially it was used
a standard statistical analysis for paired data to compare the WAI means in the
two times.
The
dataset was also analyzed using independent standard multiple linear regression
models (Montgomery & Runger, 2010; Draper &
Smith, 1981), leading to an analysis of the joint effect of covariates with the
response given by the WAI assuming a transformation of the WAI data in the two
periods (December 2018 and June 2019 denoted as WAI1 and WAI2),
given by,
·
Y1=[(WAI1
-7)/42] (Y1 is defined
in the interval [0,1])
·
Y2=[(WAI2 -7)/42]
(Y2 is defined in the interval [0,1]) (1)
In
addition to the use of a multiple linear regression model, a statistical
treatment of the data was also performed using a logistic regression model,
where the WAI response was categorized into a binary form, another way to
analyze the relationship between the covariates and the WAI response. This type
of regression model is used when the response variable is categorized into two
classes usually referred to as success and failure (Bernoulli independent trials),
quantified with values 1 and 0 (Montgomery & Runger,
2010). In the study, the optimal and good WAI indexes were coded by the value 1
(success) and the low and moderate WAI indexes were coded by the value 0
(failure).
Finally,
as the novel part of this study, it was assumed a Bayesian beta regression
model (Ferrari
& Cribari-Neto, 2004; Jorgensen, 1997) assuming
dependent WAI measures. Since the WAI scores range is defined
in the interval [7, 49], it was assumed the transformation (1) of the data to a
[0,1] scale, where beta regression models were used in the data analysis
assuming independent and dependent structures under a Bayesian approach (Box & Tiao,
1973). To capture the possible dependence between the repeated WAI measures it
was considered the introduction of a latent variable in the regression models
and the use of hierarchical Bayesian models using MCMC (Markov Chain Monte
Carlo) methods (Gelfand & Smith, 1990; Chib
& Greenberg, 1995).
2.1.
A Beta regression model
Since Y1 and Y2 introduced by
(1) are defined in the interval [0,1], it is assumed beta probability
distributions for each random variable,
given by the density probability function,
f(y/a,b) = c ya-1(1-y)b-1 ,
0 < y < 1 (2)
where c is a beta function defined by, c = B(a,b) = Γ(a+b)/Γ(a)Γ(b)
where Γ(v) = (gamma function). The Beta distribution is
denoted by Y Beta(a,b).The mean and variance of the beta
distribution are given respectively by,
μ = E(Y) = a/(a+b),
and
(3)
σ2 = var(Y)
= ab/[(a+b)2(a+b+1)
In
presence of a vector of covariates associated to each unit, it is assumed a
regression model considering a reparametrized form for the beta distribution
with density (2) given by, μ = a/(a+b) and Φ = a + b (Ferrari & Cribari-Neto,
2004; Jorgensen, 1997). In this way we have,
a = Φμ , b = (1 – μ)Φ , E(Y) = μ and var(Y)
= V(μ)/(1 + Φ) where V(μ) = μ(1 – μ), so that μ is the mean
of the response variable and Φ can be interpreted as a precision parameter in
the sense that, for fixed μ, the larger the value of Φ, the smaller the variance of Y.
The density of the random variable Y
can be written, in the new parameterization, as,
f(y/ μ, Φ) = yΦμ -1 (1 – y)(1 – μ)Φ -1 (4)
where 0 < μ < 1 and Φ > 0.
Assuming the presence of a covariate
vector x = (x1, x2,...,
xp)’ with p covariates associated to each
WAI observation, it is assumed the following regression model for the mean (Cepeda-Cuervo, Achcar & Lopera, 2013),
log[μ/(1- μ)] = logit (μ) = β’x (5)
where β = (β1, β2,..., βp)’ is a vector of regression parameters.
This modeling approach was proposed by Cepeda and Gamerman (2005)
considering the joint modeling of the mean and variance or dispersion
parameters in the biparametric exponential family,
including joint modeling of the mean and dispersion parameters in the beta
distribution, under a Bayesian approach. The use of Bayesian methods has been
extensively used in data analysis given the great flexibility of fit by
combining a likelihood function with a prior distribution based on the Bayes
formula (Box & Tiao, 1973) which could be informative using prior
information of experts or non-informative when there is little prior
information on the parameters of the proposed model.
In this study, it is introduced a Bayesian analysis for
the WAI data assuming bivariate regression models. The dependence between the
observed proportions is considered using
hierarchical Bayesian models (Gelman et al., 2004) to capture the possible
dependence between the two WAI measures. Combining the joint prior distribution for the parameters of
the model, β
= (β1, β2,..., βp)’ and Φ, with the likelihood function based on the reparametrized form of the beta
density given by (4), the joint posterior distribution for β and Φ is determined from the Bayes formula
(Box & Tiao, 1973).
The posterior summaries of interest are obtained using Markov Chain Monte Carlo
(MCMC) simulation methods as the popular Gibbs sampling algorithm or the
Metropolis-Hastings algorithm (Gelfand & Smith,
1990; Chib & Greenberg, 1995) using the free
existing OpenBugs software (Lunn
et al., 2000).
3.
COMPANY CHARACTERIZATION AND RESULTS
The
company subject to this study has a predominantly older working class, with
approximately 67% of its employees aged 41-60 and over 83% of workers aged over
41 years. This is partly due to the human resources policy that the company, of
a public nature, has been adopting as a result of the budgetary restrictions
imposed by the federal government, which no longer opens job vacancies for the
replacement and renewal of its staff.
The
last recruitment that the company opened was in in the year of 2009. Another
aspect that deserves attention in this regard is the accumulation of activities
for workers who stay and assume other responsibilities due to retirement and
dismissal of many employees. In the organization, there is a predominance of male workers,
composed of 68.24% of the employees, while 31.76% are female. This
characteristic is attributed to activities performed in the agricultural sector,
such as animal handling, operation and maintenance of agricultural tractors,
and even in the field of research, where the concentration of men is usually
higher than that of women.
Related
to education, 52.03% of the workers have graduate education, a necessary level
of education for a company whose main activity is research. However,
approximately 10% of workers have only elementary school and perform field
activities to maintain the farm. Of the company's workers, 73.65% are married
and 76.35% have at least one child. A relevant fact is that some workers have
family ties with other workers, that is, in the company there are couples,
brothers, brothers-in-law, who work together.
The
company also provides homes for some field workers and their families. In
general, 29% of the workers have up to 10 years in the job company, 26% have
from 11 to 20 years, 23% from 21 to 30 years and 22% over 30 years. Regarding
the type of the worker employment, about 78% of respondents are permanent
employees of the company and 22%, although still working, are retired workers.
This is a relevant information for the organization's managers, as about 20% of
workers can leave the job as soon as they want.
With
reference to the positions of the participants, 35% are assistants, 28% are
researchers, 25% are analysts and 12% are technicians and at all job levels
there are a lack of employees. However, a major concern of the company is in
relation to assistant workers, who work directly in the field, because even
with the opening of new recruitments there is difficulty in hiring this type of
worker in São Paulo state.
So
one of the great challenges of the company is the mechanization of some
activities, facing the containment of expenses. Regarding the nature of the
task, there is 30% of people working in the administrative area of
the company, 28% working in the research area, 28% working in the
field and 14% working in the research support. Although the company has as its
purpose the research, being a public company, the processes have been very bureaucratic
and therefore there is concentration of workers in the administrative area. The
company has been working to improve and unify some systems to reduce rework and
make activities less bureaucratic.
The
first WAI dataset here denoted as WAI1 was collected in December,
2018 with the participation of the 148 employees of the company. The second WAI
dataset here denoted as WAI2 was collected in June, 2019, six months
after the first collection with the participation of the same 148 individuals,
that is, there was no dropout. With the obtained dataset
initially was performed a paired data analysis to verify if there is
statistical difference between the WAI means in the two considered times. Table
1 shows the obtained inference results
(use of a paired Student-t test and the Minitab® software).
Table 1: Paired data analysis for WAI1 and WAI2
WAI |
Sample
Average |
St-Deviation |
p-value |
WAI1 |
40.561 |
4.756 |
0.046 |
WAI2 |
39.882 |
4.999 |
Source: The authors (2020)
From
the results presented in Table 1, it is observed that the means for WAI1
and WAI2 are different, since the p-value is 0.046 < 0.05
(significance level set at 5%). In addition, it is observed that the sample
average of WAI1 is higher
than the sample average of WAI2, that is, it is possible to conclude
that there was a significant variability in the work ability index with a
decrease in the mean of WAI over time.
Another
statistical analysis was considered using independent multiple linear
regression models relating all covariates with the WAI transformed responses
(1) for each period. Tables 2 and 3 (use of the Minitab® software)
show the obtained inference results (F-statistics and p-values associated to
each regression parameter). The required assumptions for the use of linear
regression models with normal errors (normality and constant variance for the
residuals) were verified from standard residual plots.
As
observed in the results presented in Table 2, WAI1 is statistically
affected by physical activity, with p-value equal to 0.006 < 0.05, and by
the number of children, with p-value equal to 0.054 (close to 0.05), assuming
the usual significance level equal to 5%. The other covariates considered in
the study (age, gender, education, marital status, nature of the job, job
title, employment relationship, and length of employment) do not show
significant effects on the WAI1 response (p-value > 0.05).
The
least squares estimator for the regression parameter associated with the number
of children (use of a dummy variable in the multiple linear regression model (Draper
& Smith, 1981) to compare workers without children with those who have at
least one child, where the reference is not having children) is given by 0.0580
which shows that WAI1 increases for those who have at least one
child compared to those who have no children.
Table 2: Results of multiple linear
regression analysis with response Y1
( WAI1)
Variables |
F-Statistics |
p-value |
|
Socio-demographics |
Age |
0.46 |
0.501 |
Gender |
0.04 |
0.836 |
|
Education |
0.43 |
0.731 |
|
Marital status |
0.03 |
0.856 |
|
Number of Chidren |
2.61 |
0.054 |
|
Physical activity |
3.84 |
0.006 |
|
|
|
|
|
Professionals |
Nature of task |
0.36 |
0.785 |
Position |
1.17 |
0.325 |
|
Employment bond |
0.15 |
0.695 |
|
Company Time |
1.30 |
0.277 |
Source: The authors (2020)
Regarding
to physical activity, the least squares estimator of the corresponding
regression parameter (use of dummy variables where the reference is the one who
practices physical activity every day) is equal to - 0.0691, implying that WAI1
index has a significative
decreasing for those who do not practice physical activity or practice few
physical activities when compared to those who practice physical activity every
day.
Considering
the WAI2 response, the only covariate that shows a significative effect on the response is physical activity,
with p-value equal to 0.003 < 0.05, as observed in Table 3. The least
squares estimator for the associated regression parameter for physical activity
(use of a dummy variable) is given by - 0.1494 showing that WAI2
significantly decreases among those who
do not engage in physical activity or have few physical activity compared to those who practice physical
activities every day.
A
third statistical analysis of the data was performed considering a logistic
regression model, where WAI values were categorized with values 1 (optimal and
good) and 0 (low and moderate), where maximum likelihood estimates (use of
iterative numerical methods) for the regression parameters were obtained using
the Minitab® software. Table 4 shows the p-values associated to each
regression parameter.
Table 3: Results of
Multiple Linear Regression with response Y2
(WAI2)
Variables |
F-Snedecor |
p-value |
|
Sociodemographics |
Age |
2.33 |
0.129 |
Gender |
3.03 |
0.084 |
|
Schooling |
1.11 |
0.346 |
|
Marital status |
0.81 |
0.370 |
|
Number of Chidren |
2.10 |
0.104 |
|
Physical activity |
4.28 |
0.003 |
|
|
|
|
|
Professionals |
Nature of task |
2.37 |
0.074 |
Position |
0.11 |
0.956 |
|
Employment bond |
0.13 |
0.716 |
|
Company Time |
0.48 |
0.696 |
Source: The authors (2020)
Table
4. Binary
Logistic Regression Results for WAI1 and WAI2
Covariates |
p-value (WAI1) |
p-value (WAI2) |
Age |
0.183 |
0.257 |
Gender |
0.905 |
0.435 |
Schooling |
0.069 |
0.022 |
Marital status |
0.364 |
0.396 |
Number
of Chidren |
0.148 |
0.612 |
Physical activity |
0.039 |
0.005 |
Nature
of task |
0.148 |
0.073 |
Position |
0.012 |
0.260 |
Employment bond |
0.351 |
0.831 |
Company Time |
0.739 |
0.566 |
Source:
The authors (2020)
From
the results of Table 4, it is observed that there is statistical dependence of
the binary WAI1 with physical activity and position (p-values <
0.05), and binary WAI2 with education and physical activity
(p-values < 0.05).
3.1.
Use of a Beta regression model under
a Bayesian approach for the dependent WAI indexes
Since the two WAI indexes are
evaluated to the same individual, it is possible to have some dependence
between WAI1 and WAI2 (WAI1 measured in
December, 2018 and WAI2 measured in June, 2019). Figure 1 shows the
scatter plot of WAI1 versus WAI2, from where it is
observed an approximately linear relation between the WAI1 and WAI2
indexes indicating dependence. The sample Pearson correlation coefficient between WAI1 and WAI2 is given to 0.647 (p-value <
0.001) indicating a significate correlation between the two responses measured
for each individual. This result shows the need of better regression modeling
approach in the data analysis incorporating the dependence structure. In this
way, it is assumed a hierarchical Bayesian model to jointly analyze the WAI1
and WAI2 indexes.
Figure
1: Scatterplot of WAI1 versus WAI2
Considering
the regression models defined by (4) and (5), it is assumed dummy variables
related to the unordered categorical variables given by nature of the task (reference is research)
and position (reference is researcher). The physical activity was measured in
the two times of WAI measures (December 2018 and June 2019) also in the
transformed form Y1 and Y2 introduced in (1). For a
Bayesian analysis of the data, it was considered the introduction of a latent
variable Wi assuming a normal distribution with mean zero and
variance , that is, N(0, ) to capture the possible
dependence between the two WAI measures, that is,
logit (μri) = βr0 + βr1genderi+ βr2 educationi + βr3agei + βr4 marital.statusi + βr5 number.childreni + βr6 physical.activityi + βr7 employment.bondi + βr8 company.timei+
βr9 nature.administrativei+ βr10 nature.research.supporti + βr11 nature.fieldi +
βr12 analyst.positioni + βr13 technical.positioni+ βr14 assistant.positioni + wi (6)
where
r = 1 (WAI1 measured in December 2018) and r = 2 (WAI2 measured in June 2019)
for i = 1,2,…, 148. The covariate age is considered
in a standardized form (age -average)/SD.
For a hierarchical Bayesian analysis
of the model it is assumed normal prior distributions with means equal to zero
and fixed values for the variances for all regression parameters and an uniform
U(0,10) prior distribution for the parameter ζ = 1/ . Posterior summaries of
interest were obtained using the OpenBugs software
(LUNN et al., 2000) using standard MCMC procedures. It was generated 111,000
samples for each parameter of interest where the 11,000 first simulated samples
were discarded as a burn-in period, which is usually used to minimize the
effect of the initial values.
The posterior summaries of interest were based on 1,000
samples, taking every 100th sample to have approximately
uncorrelated values. Convergence of the MCMC algorithm was monitored by usual
time series plots for the simulated samples and also using some existing
Bayesian convergence methods. Table 5
shows the posterior summaries of interest (posterior means, posterior standard
deviations and 80% credible for each parameter).
Table 5: Posterior summaries (responses Y1
and Y2)
mean |
sd |
Lower c.i. |
Upper c.i. |
|
β10 |
1.328 |
0.4015 |
0.8523 |
1.866 |
β11 |
0.01228 |
0.08055 |
-0.0846 |
0.1169 |
β110 |
-0.009842 |
0.08272 |
-0.1171 |
0.09526 |
β111 |
-0.01167 |
0.09183 |
-0.1314 |
0.1039 |
β112 |
0.02969 |
0.08552 |
-0.07832 |
0.1369 |
β113 |
-0.002856 |
0.09292 |
-0.1184 |
0.122 |
β114 |
-0.03509 |
0.08989 |
-0.1487 |
0.07978 |
β12 |
0.0653 |
0.07076 |
-0.02587 |
0.1575 |
β13 |
-0.04396 |
0.06782 |
-0.1303 |
0.04054 |
β14 |
-0.04536 |
0.08139 |
-0.1485 |
0.05345 |
β15 |
0.08419 |
0.06043 |
0.005568 |
0.1604 |
β16 |
-0.08535 |
0.04569 |
-0.1414 |
-0.02792 |
β17 |
0.03183 |
0.08927 |
-0.08592 |
0.1475 |
β18 |
0.06387 |
0.06131 |
-0.01083 |
0.142 |
β19 |
0.02236 |
0.08075 |
-0.08632 |
0.1229 |
β20 |
0.7473 |
0.3891 |
0.255 |
1.284 |
β21 |
0.1026 |
0.07719 |
0.0277 |
0.1966 |
β210 |
-0.01129 |
0.08847 |
-0.1247 |
0.1023 |
β211 |
-0.03078 |
0.08808 |
-0.1396 |
0.08387 |
β212 |
0.009325 |
0.08248 |
-0.1005 |
0.112 |
β213 |
-0.02793 |
0.08693 |
-0.1396 |
0.08502 |
β214 |
0.02925 |
0.08975 |
-0.08504 |
0.1407 |
β22 |
0.1229 |
0.06164 |
0.04698 |
0.1992 |
β23 |
0.06301 |
0.06873 |
-0.02559 |
0.1521 |
β24 |
0.09413 |
0.08072 |
-0.00686 |
0.1953 |
β25 |
0.02963 |
0.05819 |
-0.04703 |
0.1035 |
β26 |
-0.06776 |
0.04216 |
-0.1222 |
-0.01324 |
β27 |
0.01286 |
0.08837 |
-0.0989 |
0.1257 |
β28 |
0.03506 |
0.06075 |
-0.04348 |
0.1102 |
β29 |
0.05104 |
0.08285 |
-0.05611 |
0.1555 |
φ1 |
22.31 |
4.296 |
17.1 |
27.68 |
φ2 |
30.26 |
6.129 |
22.75 |
38.41 |
ζ |
1.663 |
0.2591 |
1.34 |
2.013 |
Source: The authors (2020)
From
the results of Table 5, we get the following interpretations:
·
The
covariates number of children and physical activity affect the mean of WAI1 (in December 2018), since the zero value is not
included in the 80% credible intervals for the regression parameter β15 and β16 .
·
The
covariates gender, education and physical activity affect the mean of WAI2 (in June 2019), since the zero value is not included
in the 80% credible intervals for the regression parameters β21 , β22 and β26 .
Table
6 shows a summary of the obtained inference results assuming the different
statistical models used in this study.
Table 6: Significate covariates in the regression models (*5%) and (**10%)
Independent
classical multiple regression model in the responses Y1 and Y2 |
Y1 (WAI1) Number of children*,
physical activity* Y2 (WAI2) Gender**, physical
activity*, nature of task** |
Binary
regression on binary WAI indexes |
WAI1 Schooling
degree**, physical activity*, position in company WAI2 Schooling degree*,
physical activity*, nature of task** |
Dependent Bayesian Beta regression model in the responses Y1
and Y2 |
Y1 (WAI1) Number of children,
physical activity Y2 (WAI2) Gender, physical
activity, schooling degree |
Source: The authors (2020)
4.
DISCUSSION OF THE OBTAINED RESULTS
AND CONCLUDING REMARKS
From
the obtained results using different statistical models, it is possible to see
that the most important factor affecting WAI1 and WAI2 is physical activity (1: every day;
2: every week; 3: few times a month; 4:
rarely; 5: do not practice physical activity). This effect is illustrated in
Figure 2 from where it is possible to observe larger WAI values for workers
that have physical activity every day and smaller WAI values for workers that
do not practice physical activity in both times.
From
Figure 3, it is possible to observe that WAI values are affected by the number of children in time 1 (WAI1)
but is not affected by the number of children in time 2 (WAI2). This
is in agreement with the results presented in Table 6. In Figures 4 and 5, it
is possible to observe that WAI values are affected by gender (larger WAI value
in time 2 for males) and education in
times 1 (WAI1) and 2 (WAI2)
where it is observed larger values of WAI for higher levels of education (see
Appendix with the levels of the covariates). These results are also in
agreement with the results presented in Table 6.
Figure
2: Scatterplot of WAI1 and WAI2 versus physical activity
Figure
3: Scatterplot of WAI1 and WAI2 versus number of children
Figure
4: Scatterplot of WAI1 and WAI2 versus gender
Figure
5. Scatterplot of WAI1 and WAI2 versus level of education
From
these results, it is possible to see that the use of different statistical
analysis assumed in this study were very important to detect the factors
(covariates) affecting the work capacity of workers in the agriculture company
in both times where WAI index was evaluated for each worker.
It
is also important to point out that the use of beta regression models under a
Bayesian approach could be a suitable alternative in the data analysis of
longitudinal WAI data in presence of covariates, especially considering the
introduction of a latent variable which captures the possible dependence for
the repeated data (longitudinal data). The reparametrized form of the beta
distribution (4) (Ferrari & Cribari-Neto, 2004;
Jorgensen, 1997) gives easy interpretations. Posterior summaries of interest
can be easily obtained using MCMC (Markov Chain Monte Carlo) methods especially
from the free available software OpenBugs which only
requires the definition of the likelihood function and the prior distributions
for the parameters of the model.
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APPENDIX 1 (LEVELS OF THE COVARIATES
USED IN THE STUDY)
·
Gender: 1-Female ; 2 - Male
·
Education degree: 1 - Elementary School; 2
- High School; 3 – Undergraduate; 4 - Graduate
·
Age: in years
·
Categorized Age: 1 - 31 to 40 years; 2 -
41 to 50 years; 3 - 51 to 60 years old; 4 - Over 60
·
Marital status: 1 - Single; 2 - Married
·
Number of children: 0 - None; 1 – one; 2 –
two; 3 - Three or more
·
Physical Activity: 1 - Every day; 2 -
Every week; 3 - A few times a month; 4 - Rarely; 5 - Do not practice physical
activity
· Nature of the
task: 1 – Research; 2 – Administrative; 3 - Research Support; 4 - Field
·
Position: 1 - Researcher; 2 - Analyst; 3 –
Technical; 4 - Assistant
·
Employment Bond: 1 - Effective; 2 -
Retired by the National Security Institute
·
Company Time: 1 - Up to 10 years; 2 - 11 to 20
years; 3 - 21 to 30 years; 4 - Over 30 years