1 Scenario and Dataset

An organizational psychologist wants to know whether employees who perceive more social support at work go on to experience less job burnout, and, if so, whether that relationship runs through how well-balanced employees feel their work and personal life are, and through how much control employees feel they have over their own job.

You have anonymized survey data from 250 employees: perceived social support, perceived work-life balance, perceived job control, average weekly hours worked, and a job burnout score. The data is workplace_burnout_lab.csv.

Variable	Type	Description
employee_id	Integer	Anonymous employee identifier, 1-250
social_support	Continuous	Perceived workplace social support score, 0-100 (higher = more supported)
work_life_balance	Continuous	Perceived work-life balance score, 0-100 (mediator)
job_control	Continuous	Perceived control over one’s own job score, 0-100 (mediator)
weekly_hours	Continuous	Average hours worked per week over the preceding month (covariate, controlled on burnout)
burnout	Continuous	Job burnout score, 0-100 (higher = more burnout)

This practical builds a path model in stages – a total effect, a single-mediator model, and finally a two-parallel-mediator model – fit with lavaan, with bootstrapped confidence intervals for every indirect effect.

2 Questions

Work through the tasks below in order. Each part builds on the model from the part before it. Use workplace_burnout_lab.csv.

Part A – Getting to know the data

Load the dataset and report the sample size, and the mean and standard deviation of social_support, work_life_balance, job_control, weekly_hours, and burnout.
Produce scatterplots of work_life_balance against social_support and of job_control against social_support. Describe, in a sentence or two, what each plot suggests.

Part B – Research question 1: does perceived social support predict burnout at all?

Fit a simple linear regression predicting burnout from social_support alone. Report the coefficient, its significance test, and state what this coefficient represents in a mediation framework.
Interpret this coefficient in one sentence, being explicit that it says nothing yet about how or why social support might relate to burnout.

Part C – Research question 2: is the social-support-burnout relationship carried through work-life balance?

Specify a lavaan path model with work_life_balance as a single mediator between social_support and burnout, entering weekly_hours as a covariate on burnout. Label the \(a\), \(b\), and \(c'\) paths, and define the indirect and total effects using :=. Fit the model with se = "bootstrap" and bootstrap = 5000.
Report the \(a\)-path and \(b\)-path coefficients from the model summary, and state what each one means substantively.
Report the bootstrapped indirect effect (a \(\times\) b) and its percentile confidence interval. Does the interval exclude zero?
Compare the direct effect \(c'\) in this model to the total effect \(c\) from Question 3. Is the relationship between social support and burnout fully or partially mediated by work-life balance? Support your answer with a formal chi-square difference test comparing this model to a nested model in which \(c'\) is fixed to zero, not just by inspecting \(c'\)’s own \(p\)-value.

Part D – Research question 3: does adding job control as a second mediator change the picture?

Extend the model from Part C into a two-parallel-mediator model by adding job_control alongside work_life_balance, each with its own \(a\)-path from social_support and its own \(b\)-path to burnout. Label every path and define both specific indirect effects, their sum, and the total effect.
Report each specific indirect effect (via work_life_balance and via job_control) with its bootstrapped confidence interval.
Are the two specific indirect effects significantly different from each other? Define their difference with :=, report it with its bootstrapped 95% confidence interval, and state which mediator, if either, carries the larger indirect effect.
Is the direct effect \(c'\) still significant in this two-mediator model? Compare your conclusion about full versus partial mediation here to your conclusion in Question 8, and explain, in substantive terms, why adding a second mediator could change that conclusion.

Part E – Reporting

Build a single summary table listing every direct, specific indirect, total indirect, and total effect from both the single-mediator and two-mediator models, each with its bootstrapped 95% confidence interval.
Produce a path diagram of the two-mediator model showing the standardized path coefficients.
Write a short paragraph, as it might appear in a report to an HR director, summarizing what these models do and do not establish about the value of workplace social support, the role of work-life balance and job control, and the observational nature of this data (employees were not randomly assigned to different levels of social support).

3 Guided Walkthrough

This walkthrough builds the burnout path model in stages, from a bare total effect through a single-mediator model to a two-parallel-mediator model, testing the indirect effects at every stage.

3.1 Understanding the problem

The organizational psychologist’s question has three layers, and each should be answered by a separate, explicit model rather than by fitting the most complicated model first and hoping to read everything off it at once. First, is there any relationship at all between perceived social support and burnout. Second, once work-life balance is placed between them as a hypothesized mediator, how much of that relationship runs through work-life balance, and does a direct path from social support to burnout remain once work-life balance is accounted for. Third, once job control is added as a second, parallel mediator, does the picture change – does the direct path shrink further, and how does the burden of explaining the social-support-burnout relationship divide between the two mediators.

3.2 Inspecting the data

d <- read.csv("data/workplace_burnout_lab.csv")
str(d)

## 'data.frame':    250 obs. of  6 variables:
##  $ employee_id      : int  1 2 3 4 5 6 7 8 9 10 ...
##  $ social_support   : num  70.9 47.2 48.3 52.2 58.9 40.3 54.1 35.4 52.2 54.1 ...
##  $ work_life_balance: num  48.1 43.9 54.6 56.3 51.6 71.3 46.6 38.5 48.1 60.5 ...
##  $ job_control      : num  52.5 51.2 27.9 42.3 59.4 38.9 45.8 29.8 41.3 41.6 ...
##  $ weekly_hours     : num  47.2 36.4 37.8 36.5 40.1 49.1 34.4 45.6 47.9 42.3 ...
##  $ burnout          : num  34.6 38.6 29.8 37.3 42.7 38.7 46 44.5 55.4 18.9 ...

d %>%
  summarise(n = n(),
            social_support_M = mean(social_support), social_support_SD = sd(social_support),
            work_life_balance_M = mean(work_life_balance), work_life_balance_SD = sd(work_life_balance),
            job_control_M = mean(job_control), job_control_SD = sd(job_control),
            weekly_hours_M = mean(weekly_hours), weekly_hours_SD = sd(weekly_hours),
            burnout_M = mean(burnout), burnout_SD = sd(burnout)) %>%
  kable(digits = 2)

n	social_support_M	social_support_SD	work_life_balance_M	work_life_balance_SD	job_control_M	job_control_SD	weekly_hours_M	weekly_hours_SD	burnout_M	burnout_SD
250	49.12	9.71	46.93	9.69	39.4	9.83	45	6.02	44.15	12.31

d %>%
  select(social_support, work_life_balance, job_control, weekly_hours, burnout) %>%
  cor() %>%
  kable(digits = 3)

	social_support	work_life_balance	job_control	weekly_hours	burnout
social_support	1.000	0.382	0.357	0.077	-0.259
work_life_balance	0.382	1.000	0.176	-0.025	-0.509
job_control	0.357	0.176	1.000	-0.050	-0.318
weekly_hours	0.077	-0.025	-0.050	1.000	0.411
burnout	-0.259	-0.509	-0.318	0.411	1.000

Social support correlates positively with both work-life balance and job control, and both of those correlate negatively with burnout – exactly the pattern a mediation hypothesis predicts. Weekly hours correlates only weakly with social support and with the two candidate mediators, but more noticeably with burnout itself, which is why it is entered as a covariate on the outcome rather than treated as another mediator.

d %>%
  select(social_support, work_life_balance, job_control) %>%
  pivot_longer(cols = c(work_life_balance, job_control),
               names_to = "mediator", values_to = "mediator_value") %>%
  mutate(mediator = recode(mediator,
                            work_life_balance = "Work-life balance",
                            job_control = "Job control")) %>%
  ggplot(aes(social_support, mediator_value)) +
  geom_point(alpha = 0.6, color = ntnublue) +
  geom_smooth(method = "lm", se = FALSE, color = red) +
  facet_wrap(~ mediator, scales = "free_y") +
  labs(x = "Perceived social support", y = "Mediator value",
       title = "a-paths: social support and each candidate mediator")

Both candidate mediators rise with perceived social support, roughly linearly, which is consistent with both being viable carriers of a social-support-to-burnout effect.

3.3 Identifying the appropriate method

Each research question above concerns a directional chain of relationships among continuous variables, not just a single predictor-outcome pair, which is exactly the setting for path analysis: a system of regression equations fit simultaneously, with indirect effects defined as products of paths. Every model below is fit with lavaan::sem(), using se = "bootstrap" so that every indirect effect gets a percentile bootstrap confidence interval rather than relying on the (often poorly-behaved) normal-theory standard error of a product of coefficients.

3.4 Stage 1 – does perceived social support predict burnout at all? (total effect)

fit_total <- lm(burnout ~ social_support, data = d)
summary(fit_total)

## 
## Call:
## lm(formula = burnout ~ social_support, data = d)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -43.64  -7.33   0.01   8.59  29.65 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)     60.2762     3.8943   15.48  < 2e-16 ***
## social_support  -0.3282     0.0778   -4.22  3.4e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 11.9 on 248 degrees of freedom
## Multiple R-squared:  0.067,  Adjusted R-squared:  0.0632 
## F-statistic: 17.8 on 1 and 248 DF,  p-value: 3.43e-05

confint(fit_total)

##                  2.5 % 97.5 %
## (Intercept)    52.6060 67.946
## social_support -0.4814 -0.175

Each additional point of perceived social support is associated with a -0.328-point change in burnout, on average (-0.328 is negative, so more perceived support goes with less burnout), and this total effect is statistically significant. This coefficient, conventionally labeled \(c\), is the relationship the rest of this walkthrough will decompose. It says nothing yet about the route that relationship takes.

3.5 Stage 2 – is the social-support-burnout relationship carried through work-life balance? (simple mediation)

model2 <- '
  burnout ~ b*work_life_balance + cprime*social_support + weekly_hours
  work_life_balance ~ a*social_support

  indirect := a*b
  total := indirect + cprime
'
fit2 <- sem(model2, data = d, se = "bootstrap", bootstrap = 5000)
summary(fit2, standardized = TRUE, fit.measures = TRUE)

## lavaan 0.6-21 ended normally after 1 iteration
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                         6
## 
##   Number of observations                           250
## 
## Model Test User Model:
##                                                       
##   Test statistic                                 0.877
##   Degrees of freedom                                 1
##   P-value (Chi-square)                           0.349
## 
## Model Test Baseline Model:
## 
##   Test statistic                               180.660
##   Degrees of freedom                                 5
##   P-value                                        0.000
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    1.000
##   Tucker-Lewis Index (TLI)                       1.004
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)              -1813.863
##   Loglikelihood unrestricted model (H1)      -1813.424
##                                                       
##   Akaike (AIC)                                3639.726
##   Bayesian (BIC)                              3660.854
##   Sample-size adjusted Bayesian (SABIC)       3641.834
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.000
##   90 Percent confidence interval - lower         0.000
##   90 Percent confidence interval - upper         0.163
##   P-value H_0: RMSEA <= 0.050                    0.484
##   P-value H_0: RMSEA >= 0.080                    0.357
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.021
## 
## Parameter Estimates:
## 
##   Standard errors                            Bootstrap
##   Number of requested bootstrap draws             5000
##   Number of successful bootstrap draws            5000
## 
## Regressions:
##                       Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   burnout ~                                                                
##     wrk_lf_    (b)      -0.578    0.066   -8.768    0.000   -0.578   -0.459
##     scl_spp (cprm)      -0.148    0.064   -2.335    0.020   -0.148   -0.118
##     wkly_hr              0.837    0.108    7.759    0.000    0.837    0.413
##   work_life_balance ~                                                      
##     scl_spp    (a)       0.381    0.056    6.822    0.000    0.381    0.382
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .burnout          86.059    6.791   12.672    0.000   86.059    0.582
##    .work_life_blnc   79.847    7.111   11.229    0.000   79.847    0.854
## 
## Defined Parameters:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     indirect         -0.220    0.041   -5.334    0.000   -0.220   -0.175
##     total            -0.368    0.072   -5.149    0.000   -0.368   -0.293

pe2 <- parameterEstimates(fit2, ci = TRUE, boot.ci.type = "perc")
pe2 %>% kable(digits = 3)

lhs	op	rhs	label	est	se	z	pvalue	ci.lower	ci.upper
burnout	~	work_life_balance	b	-0.578	0.066	-8.768	0.00	-0.709	-0.451
burnout	~	social_support	cprime	-0.148	0.064	-2.335	0.02	-0.275	-0.026
burnout	~	weekly_hours		0.837	0.108	7.759	0.00	0.627	1.048
work_life_balance	~	social_support	a	0.381	0.056	6.822	0.00	0.271	0.489
burnout		burnout		86.059	6.791	12.672	0.00	71.906	98.786
work_life_balance		work_life_balance		79.847	7.111	11.229	0.00	66.146	93.582
social_support		social_support		93.853	0.000	NA	NA	93.853	93.853
social_support		weekly_hours		4.496	0.000	NA	NA	4.496	4.496
weekly_hours		weekly_hours		36.043	0.000	NA	NA	36.043	36.043
indirect	:=	a*b	indirect	-0.220	0.041	-5.334	0.00	-0.307	-0.143
total	:=	indirect+cprime	total	-0.368	0.072	-5.149	0.00	-0.504	-0.227

The \(a\)-path shows that each additional point of perceived social support is associated with a 0.381-point increase in work-life balance, and the \(b\)-path shows that, holding social support and weekly hours constant, each additional point of work-life balance is associated with a -0.578-point change in burnout. The bootstrapped indirect effect is -0.22, 95% CI [-0.307, -0.143]: because this interval does not contain zero, work-life balance carries a statistically credible share of the relationship between social support and burnout.

Whether mediation is full or partial turns on the direct path \(c'\), not on the indirect effect alone. Inspecting \(c'\)’s own \(p\)-value in the summary above is a starting point, but a formal test compares this model to a nested model in which \(c'\) is fixed to zero, and asks whether that restriction costs a significant amount of fit.

model2_constrained <- '
  burnout ~ b*work_life_balance + 0*social_support + weekly_hours
  work_life_balance ~ a*social_support

  indirect := a*b
'
fit2_constrained <- sem(model2_constrained, data = d, se = "bootstrap", bootstrap = 5000)
lrt2 <- anova(fit2, fit2_constrained)
lrt2

## 
## Chi-Squared Difference Test
## 
##                  Df  AIC  BIC Chisq Chisq diff RMSEA Df diff Pr(>Chisq)  
## fit2              1 3640 3661  0.88                                      
## fit2_constrained  2 3643 3660  5.91       5.04 0.127       1      0.025 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

The anova() table above lays out the actual computation being compared: the chi-square and degrees of freedom of the full model (with \(c'\) free), the chi-square and degrees of freedom of the constrained model (with \(c'\) fixed to zero), and, on the difference row, \(\Delta\chi^2\) (the constrained model’s chi-square minus the full model’s) with its \(p\)-value. If that \(p\)-value is below .05, fixing \(c'\) to zero worsens the model fit or costs a significant amount of fit, so the direct path is needed and mediation by work-life balance is partial rather than full. If it is not significant, the direct path can be dropped without worsening fit, consistent with full mediation.

lavaanPlot(model = fit2, coefs = TRUE, stand = TRUE, stars = "regress",
           node_options = list(shape = "box", fontname = "Helvetica"),
           edge_options = list(color = "grey40"))

3.6 Stage 3 – does adding job control as a second mediator change the picture? (two-parallel-mediator model)

model3 <- '
  burnout ~ b1*work_life_balance + b2*job_control + cprime*social_support + weekly_hours
  work_life_balance ~ a1*social_support
  job_control ~ a2*social_support

  indirect_wlb := a1*b1
  indirect_jc := a2*b2
  total_indirect := indirect_wlb + indirect_jc
  total := total_indirect + cprime
  ind_diff := indirect_wlb - indirect_jc
'
fit3 <- sem(model3, data = d, se = "bootstrap", bootstrap = 5000)
summary(fit3, standardized = TRUE, fit.measures = TRUE)

## lavaan 0.6-21 ended normally after 1 iteration
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                         9
## 
##   Number of observations                           250
## 
## Model Test User Model:
##                                                       
##   Test statistic                                 3.036
##   Degrees of freedom                                 3
##   P-value (Chi-square)                           0.386
## 
## Model Test Baseline Model:
## 
##   Test statistic                               233.100
##   Degrees of freedom                                 9
##   P-value                                        0.000
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    1.000
##   Tucker-Lewis Index (TLI)                       1.000
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)              -2714.316
##   Loglikelihood unrestricted model (H1)      -2712.798
##                                                       
##   Akaike (AIC)                                5446.632
##   Bayesian (BIC)                              5478.325
##   Sample-size adjusted Bayesian (SABIC)       5449.794
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.007
##   90 Percent confidence interval - lower         0.000
##   90 Percent confidence interval - upper         0.107
##   P-value H_0: RMSEA <= 0.050                    0.625
##   P-value H_0: RMSEA >= 0.080                    0.162
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.033
## 
## Parameter Estimates:
## 
##   Standard errors                            Bootstrap
##   Number of requested bootstrap draws             5000
##   Number of successful bootstrap draws            5000
## 
## Regressions:
##                       Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   burnout ~                                                                
##     wrk_lf_   (b1)      -0.567    0.066   -8.638    0.000   -0.567   -0.455
##     jb_cntr   (b2)      -0.254    0.069   -3.691    0.000   -0.254   -0.207
##     scl_spp (cprm)      -0.059    0.064   -0.923    0.356   -0.059   -0.047
##     wkly_hr              0.805    0.106    7.592    0.000    0.805    0.401
##   work_life_balance ~                                                      
##     scl_spp   (a1)       0.381    0.054    7.012    0.000    0.381    0.382
##   job_control ~                                                            
##     scl_spp   (a2)       0.362    0.061    5.931    0.000    0.362    0.357
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .burnout          80.684    6.680   12.078    0.000   80.684    0.556
##    .work_life_blnc   79.847    7.077   11.282    0.000   79.847    0.854
##    .job_control      83.951    7.147   11.747    0.000   83.951    0.872
## 
## Defined Parameters:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     indirect_wlb     -0.216    0.040   -5.346    0.000   -0.216   -0.174
##     indirect_jc      -0.092    0.028   -3.247    0.001   -0.092   -0.074
##     total_indirect   -0.308    0.049   -6.225    0.000   -0.308   -0.248
##     total            -0.367    0.070   -5.209    0.000   -0.367   -0.295
##     ind_diff         -0.124    0.049   -2.518    0.012   -0.124   -0.100

pe3 <- parameterEstimates(fit3, ci = TRUE, boot.ci.type = "perc")
pe3 %>% kable(digits = 3)

lhs	op	rhs	label	est	se	z	pvalue	ci.lower	ci.upper
burnout	~	work_life_balance	b1	-0.567	0.066	-8.638	0.000	-0.696	-0.437
burnout	~	job_control	b2	-0.254	0.069	-3.691	0.000	-0.388	-0.114
burnout	~	social_support	cprime	-0.059	0.064	-0.923	0.356	-0.186	0.063
burnout	~	weekly_hours		0.805	0.106	7.592	0.000	0.602	1.021
work_life_balance	~	social_support	a1	0.381	0.054	7.012	0.000	0.272	0.487
job_control	~	social_support	a2	0.362	0.061	5.931	0.000	0.240	0.481
burnout		burnout		80.684	6.680	12.078	0.000	66.186	92.480
work_life_balance		work_life_balance		79.847	7.077	11.282	0.000	65.858	93.964
job_control		job_control		83.951	7.147	11.747	0.000	69.672	97.473
social_support		social_support		93.853	0.000	NA	NA	93.853	93.853
social_support		weekly_hours		4.496	0.000	NA	NA	4.496	4.496
weekly_hours		weekly_hours		36.043	0.000	NA	NA	36.043	36.043
indirect_wlb	:=	a1*b1	indirect_wlb	-0.216	0.040	-5.346	0.000	-0.301	-0.144
indirect_jc	:=	a2*b2	indirect_jc	-0.092	0.028	-3.247	0.001	-0.151	-0.039
total_indirect	:=	indirect_wlb+indirect_jc	total_indirect	-0.308	0.049	-6.225	0.000	-0.408	-0.214
total	:=	total_indirect+cprime	total	-0.367	0.070	-5.209	0.000	-0.502	-0.229
ind_diff	:=	indirect_wlb-indirect_jc	ind_diff	-0.124	0.049	-2.518	0.012	-0.225	-0.031

Both specific indirect effects are in the expected direction. Via work-life balance, the indirect effect is -0.216, 95% CI [-0.301, -0.144]. Via job control, the indirect effect is -0.092, 95% CI [-0.151, -0.039]. Neither interval contains zero, so both mediators carry a statistically credible share of the total effect.

Are the two indirect effects significantly different from each other? Their difference, ind_diff := indirect_wlb - indirect_jc, is -0.124, 95% CI [-0.225, -0.031]. The interval does not contain zero, so the two indirect effects are significantly different: the indirect effect through work-life balance is significantly larger (more negative) than the indirect effect through job control.

The direct effect \(c'\) in this model is -0.059. Compare its \(p\)-value, and the chi-square difference test below, against Stage 2’s conclusion.

model3_constrained <- '
  burnout ~ b1*work_life_balance + b2*job_control + 0*social_support + weekly_hours
  work_life_balance ~ a1*social_support
  job_control ~ a2*social_support

  indirect_wlb := a1*b1
  indirect_jc := a2*b2
'
fit3_constrained <- sem(model3_constrained, data = d, se = "bootstrap", bootstrap = 5000)
lrt3 <- anova(fit3, fit3_constrained)
lrt3

## 
## Chi-Squared Difference Test
## 
##                  Df  AIC  BIC Chisq Chisq diff RMSEA Df diff Pr(>Chisq)
## fit3              3 5447 5478  3.04                                    
## fit3_constrained  4 5445 5474  3.80      0.767     0       1       0.38

As in Stage 2, this table compares the fit of the full model against a model with \(c'\) fixed to zero, on one degree of freedom. Here the test is not significant (\(\Delta\chi^2(1)\) = 0.77, \(p\) = 0.38): fixing \(c'\) to zero does not worsen fit, so with both mediators in the model the mediation is full. This move from a significant test (Stage 2) to a non-significant one (here) is a substantively important finding in its own right: it means the single-mediator model in Stage 2 looked like partial mediation only because a second, genuine mediating route (through job control) had not yet been modeled and was instead leaking into the apparent direct effect. Once both mediators are in the model, social support’s relationship with burnout is explained entirely by these two routes, which is full mediation by the pair of mediators taken together, even though each one alone would tell only part of the story.

lavaanPlot(model = fit3, coefs = TRUE, stand = TRUE, stars = "regress",
           node_options = list(shape = "box", fontname = "Helvetica"),
           edge_options = list(color = "grey40"))

3.7 Building the summary table of effects

effects2 <- pe2 %>%
  filter(label %in% c("cprime", "a", "b", "indirect", "total")) %>%
  transmute(Model = "Stage 2: single mediator (work-life balance)",
            Effect = recode(label,
                             a = "a-path (support -> work-life balance)",
                             b = "b-path (work-life balance -> burnout)",
                             cprime = "Direct effect (c')",
                             indirect = "Indirect (via work-life balance)",
                             total = "Total effect"),
            Estimate = est, `CI lower` = ci.lower, `CI upper` = ci.upper)

effects3 <- pe3 %>%
  filter(label %in% c("cprime", "a1", "a2", "b1", "b2",
                       "indirect_wlb", "indirect_jc", "total_indirect", "total", "ind_diff")) %>%
  transmute(Model = "Stage 3: two parallel mediators",
            Effect = recode(label,
                             a1 = "a1-path (support -> work-life balance)",
                             a2 = "a2-path (support -> job control)",
                             b1 = "b1-path (work-life balance -> burnout)",
                             b2 = "b2-path (job control -> burnout)",
                             cprime = "Direct effect (c')",
                             indirect_wlb = "Indirect (via work-life balance)",
                             indirect_jc = "Indirect (via job control)",
                             total_indirect = "Total indirect",
                             total = "Total effect",
                             ind_diff = "Difference between the two indirect effects (WLB - job control)"),
            Estimate = est, `CI lower` = ci.lower, `CI upper` = ci.upper)

bind_rows(effects2, effects3) %>% kable(digits = 3)

Model	Effect	Estimate	CI lower	CI upper
Stage 2: single mediator (work-life balance)	b-path (work-life balance -> burnout)	-0.578	-0.709	-0.451
Stage 2: single mediator (work-life balance)	Direct effect (c’)	-0.148	-0.275	-0.026
Stage 2: single mediator (work-life balance)	a-path (support -> work-life balance)	0.381	0.271	0.489
Stage 2: single mediator (work-life balance)	Indirect (via work-life balance)	-0.220	-0.307	-0.143
Stage 2: single mediator (work-life balance)	Total effect	-0.368	-0.504	-0.227
Stage 3: two parallel mediators	b1-path (work-life balance -> burnout)	-0.567	-0.696	-0.437
Stage 3: two parallel mediators	b2-path (job control -> burnout)	-0.254	-0.388	-0.114
Stage 3: two parallel mediators	Direct effect (c’)	-0.059	-0.186	0.063
Stage 3: two parallel mediators	a1-path (support -> work-life balance)	0.381	0.272	0.487
Stage 3: two parallel mediators	a2-path (support -> job control)	0.362	0.240	0.481
Stage 3: two parallel mediators	Indirect (via work-life balance)	-0.216	-0.301	-0.144
Stage 3: two parallel mediators	Indirect (via job control)	-0.092	-0.151	-0.039
Stage 3: two parallel mediators	Total indirect	-0.308	-0.408	-0.214
Stage 3: two parallel mediators	Total effect	-0.367	-0.502	-0.229
Stage 3: two parallel mediators	Difference between the two indirect effects (WLB - job control)	-0.124	-0.225	-0.031

3.8 Interpreting the findings

Perceived social support relates to burnout on its own (Stage 1). Once work-life balance is entered as a single mediator (Stage 2), a substantial share of that relationship runs through work-life balance, and a formal chi-square difference test shows the remaining direct path is still needed, consistent with partial mediation. Once job control is entered as a second, parallel mediator (Stage 3), the picture becomes more complete: both mediators carry a statistically credible share of the effect, and the direct path that remained significant in Stage 2 is no longer needed once both routes are represented, consistent with full mediation once both work-life balance and job control are modeled together. A single-mediator model, however carefully estimated, could have left a genuine explanatory route folded into what looked like an unexplained direct effect.

3.9 Reporting the results

Perceived workplace social support was associated with lower job burnout (total effect \(c\), Stage 1). This relationship was partially carried by perceived work-life balance: the bootstrapped indirect effect through work-life balance was statistically distinguishable from zero, and the remaining direct effect of social support on burnout was still required by a formal chi-square difference test (Stage 2). Extending the model to include perceived job control as a second, parallel mediator (Stage 3) showed that job control also carried a statistically credible share of the effect, and that the direct path from social support to burnout was no longer required once both mediators were represented together, consistent with full mediation once both proposed mechanisms are modeled jointly rather than one at a time. Because employees were not randomly assigned to levels of perceived social support, these results describe a statistically well-supported pattern of association and are consistent with, but do not on their own establish, a causal chain running from social support through work-life balance and job control to burnout.

4 Solutions

Expected answers to the Questions above. The reasoning for each is in the Guided Walkthrough section; this section states the answers directly, reusing the models already fitted there.

Part A

250 employees. See the descriptives table under Inspecting the data above for the mean and standard deviation of each variable.
See the two scatterplots above. Both work-life balance and job control rise roughly linearly with perceived social support.

Part B

-0.328 (see summary(fit_total) above for \(SE\), \(t\), \(df\), and \(p\)). In a mediation framework this is the total effect, \(c\): the overall relationship between social support and burnout before any mediator is introduced.
Higher perceived social support is associated with lower burnout overall, but this coefficient does not yet say through what mechanism, or whether a direct relationship would remain once a candidate mediator is accounted for.

Part C

See the model2 object and fit2 above for the labeled lavaan syntax and the fitted model.
\(a\) = 0.381: each additional point of social support is associated with a work-life balance increase of that size. \(b\) = -0.578: holding social support and weekly hours constant, each additional point of work-life balance is associated with a burnout change of that size.
Indirect effect = -0.22, 95% CI [-0.307, -0.143]. The interval does not contain zero.
Partial mediation. The direct effect shrinks from \(c\) = -0.328 (Question 3) to \(c'\) = -0.148, but it does not disappear: fixing \(c'\) to zero significantly worsens fit, \(\Delta\chi^2(1)\) = 5.04, \(p\) = 0.025 (see the anova(fit2, fit2_constrained) output above for both models’ chi-square and \(df\) and the difference row). The direct path is therefore still needed, so work-life balance alone only partially mediates the relationship between social support and burnout.

Part D

See the model3 object and fit3 above for the labeled lavaan syntax and the fitted model, including both specific indirect effects, their sum, and the total effect.
Indirect via work-life balance = -0.216, 95% CI [-0.301, -0.144]. Indirect via job control = -0.092, 95% CI [-0.151, -0.039].
Difference = -0.124, 95% CI [-0.225, -0.031]. The interval excludes zero, so yes: the two indirect effects are significantly different, and the indirect effect through work-life balance is the larger of the two.
No, \(c'\) is no longer significant, and the mediation is now full. In the two-mediator model, \(c'\) = -0.059 (\(p\) = 0.36), and fixing it to zero does not worsen fit, \(\Delta\chi^2(1)\) = 0.77, \(p\) = 0.38 (see the anova(fit3, fit3_constrained) output above). The conclusion therefore changes from partial mediation (Question 8) to full mediation: work-life balance and job control together account for the relationship between social support and burnout. It changes because job control is a genuine second mediating route; in the single-mediator model its share of the effect had nowhere to go but the direct path, which made \(c'\) look larger than it is.

Part E

See the Building the summary table of effects section above.
See the lavaanPlot diagram of fit3 above (and the lavaanPlot diagram of fit2 for the single-mediator model).
Example paragraph:

Perceived workplace social support was associated with lower job burnout among the 250 employees in this sample. Part of that association was explained by perceived work-life balance, and, in a fuller model, part was also explained by perceived job control; together, these two factors accounted for the entire statistically detectable relationship between social support and burnout, with no reliably remaining direct path once both were modeled. This suggests that interventions aimed at improving employees’ sense of work-life balance and their sense of control over their own job are two concrete, and apparently complementary, routes through which greater workplace social support could translate into lower burnout. Because employees were not randomly assigned to levels of social support, work-life balance, or job control, these findings describe a well-supported statistical pattern rather than a demonstrated causal effect, and unmeasured factors, such as a supervisor’s general management style, could plausibly influence several of these variables at once.

Common errors and points to watch for

Judging full versus partial mediation from \(c'\)’s own \(p\)-value alone, rather than from a formal nested-model chi-square difference test.
Reporting only the larger of two specific indirect effects as “the” mediator, without testing whether the difference between them is significant.
Treating a covariate (weekly_hours) as though it were a third mediator, when it was never modeled as a consequence of social_support.
Forgetting that adding a second mediator changes the meaning of \(c'\): it is no longer “the effect not explained by work-life balance” but “the effect not explained by either mediator,” which is why the full-versus-partial-mediation conclusion can change between Stage 2 and Stage 3.

sessionInfo()

## R version 4.4.2 (2024-10-31)
## Platform: aarch64-apple-darwin20
## Running under: macOS 27.0.1
## 
## Matrix products: default
## BLAS:   /Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/lib/libRblas.0.dylib 
## LAPACK: /Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/lib/libRlapack.dylib;  LAPACK version 3.12.0
## 
## locale:
## [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
## 
## time zone: Europe/Oslo
## tzcode source: internal
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
##  [1] kableExtra_1.4.0 knitr_1.51       lavaanPlot_0.8.1 lavaan_0.6-21    lubridate_1.9.5  forcats_1.0.1   
##  [7] stringr_1.6.0    dplyr_1.2.0      purrr_1.2.1      readr_2.2.0      tidyr_1.3.2      tibble_3.3.1    
## [13] ggplot2_4.0.2    tidyverse_2.0.0  pacman_0.5.1    
## 
## loaded via a namespace (and not attached):
##  [1] DiagrammeR_1.0.11  sass_0.4.10        generics_0.1.4     xml2_1.5.2         lattice_0.22-9     stringi_1.8.7     
##  [7] hms_1.1.4          digest_0.6.39      magrittr_2.0.4     evaluate_1.0.5     grid_4.4.2         timechange_0.4.0  
## [13] RColorBrewer_1.1-3 fastmap_1.2.0      Matrix_1.7-5       jsonlite_2.0.0     mgcv_1.9-4         viridisLite_0.4.3 
## [19] scales_1.4.0       pbivnorm_0.6.0     textshaping_1.0.5  jquerylib_0.1.4    mnormt_2.1.2       cli_3.6.5         
## [25] rlang_1.1.7        visNetwork_2.1.4   splines_4.4.2      withr_3.0.2        cachem_1.1.0       yaml_2.3.12       
## [31] otel_0.2.0         parallel_4.4.2     tools_4.4.2        tzdb_0.5.0         vctrs_0.7.2        R6_2.6.1          
## [37] stats4_4.4.2       lifecycle_1.0.5    htmlwidgets_1.6.4  pkgconfig_2.0.3    pillar_1.11.1      bslib_0.10.0      
## [43] gtable_0.3.6       glue_1.8.0         systemfonts_1.3.2  xfun_0.57          tidyselect_1.2.1   rstudioapi_0.18.0 
## [49] farver_2.1.2       nlme_3.1-168       htmltools_0.5.9    labeling_0.4.3     svglite_2.2.2      rmarkdown_2.30    
## [55] compiler_4.4.2     S7_0.2.1           quadprog_1.5-8

Lab Practical, Topic 3: Path Analysis and Mediation

Scenario and Dataset, Questions, Guided Walkthrough, and Solutions

Frederick Anyan – PSY3100

Teaching Assistant: Hanna Pay Eriksen

13 October 2026