Using wsMed: A step-by-step tutorial

Introduction

wsMed() fits multiple mediation and moderated mediation models for two-condition within-subject designs. A complete call identifies the paired mediator and outcome variables, selects the mediation structure, specifies the estimation options, and, when needed, adds moderators or covariates.

This tutorial shows how to construct a wsMed() call one step at a time. Each section begins with the same basic call and changes only the arguments needed for the next part of the analysis.

Quick start

The following example fits a parallel mediation model with two mediators. It uses example_data, which is included in the package.

data("example_data", package = "wsMed")

result <- wsMed(
  data = example_data,
  M_C1 = c("A1", "B1"),
  M_C2 = c("A2", "B2"),
  Y_C1 = "C1",
  Y_C2 = "C2",
  form = "P",
  Na = "DE",
  ci_method = "mc",
  R = 5000,
  seed = 123
)

print(result)

The arguments in this call answer four basic questions:

• Which data set should be analyzed?
• Which columns contain the mediator and outcome measurements under the two conditions?
• What is the mediation structure?
• How should missing data and confidence intervals be handled?

The following sections explain how to answer each question.

Step 1: Specify the repeated-measures variables

The data must be in wide format. Each row represents one participant, and each repeated measure has a separate column for each condition.

The mediator names are supplied through M_C1 and M_C2. Their positions must match. For example:

M_C1 = c("A1", "B1")
M_C2 = c("A2", "B2")

This tells wsMed() that A1 and A2 are the two measurements of the first mediator, whereas B1 and B2 are the two measurements of the second mediator. The outcome pair is supplied through Y_C1 and Y_C2:

Y_C1 = "C1"
Y_C2 = "C2"

The variable mapping in the quick-start example is therefore:

Construct	Condition 1	Condition 2	Internal label
A	A1	A2	M1
B	B1	B2	M2
C	C1	C2	Y

The internal mediator labels are determined by position. If three mediators are supplied as follows:

M_C1 = c("A1", "B1", "C1")
M_C2 = c("A2", "B2", "C2")

then A, B, and C are labeled M1, M2, and M3, respectively. This numbering is especially important when specifying a user-defined model in Step 2.

wsMed() automatically prepares the difference and level components used in the model. Users should supply the original condition-specific columns, not manually computed difference or average scores.

Step 2: Choose the mediation structure

The mediation structure is selected with form. Users can choose one of four predefined structures or define the mediator paths themselves.

Predefined models

The predefined options are:

form	Structure	How the mediators are connected
"P"	Parallel	All mediators operate in parallel.
"CN"	Chained/serial	The mediators form one serial chain.
"CP"	Chained–parallel	The first mediator predicts multiple later mediators.
"PC"	Parallel–chained	Multiple mediators predict one final mediator.

For a predefined model, the mediator order in M_C1 and M_C2 determines their positions in the structure. To fit a different predefined structure, replace the value of form in the basic call:

form = "P"
form = "CN"
form = "CP"
form = "PC"

For example, the following call fits a three-mediator chained model:

result_chained <- wsMed(
  data = example_data,
  M_C1 = c("A1", "B1", "C1"),
  M_C2 = c("A2", "B2", "C2"),
  Y_C1 = "D1",
  Y_C2 = "D2",
  form = "CN",
  Na = "DE",
  ci_method = "mc",
  R = 5000,
  seed = 123
)

Here, the mediator order defines the chain from A (M1) to B (M2) and then to C (M3).

User-defined models

Use form = "UD" when the intended paths cannot be represented by one of the four predefined structures. The mediator labels still come from the order of M_C1 and M_C2, but the paths are supplied through paths.

Suppose A, B, and C are the three mediators and the intended structure contains:

• a path from A (M1) to C (M3);
• a path from C (M3) to the outcome; and
• a path from B (M2) to the outcome.

The path vector is:

custom_paths <- c(
  "M1 -> M3",
  "M3 -> Y",
  "M2 -> Y"
)

Pass this vector to wsMed() together with form = "UD":

result_custom <- wsMed(
  data = example_data,
  M_C1 = c("A1", "B1", "C1"),
  M_C2 = c("A2", "B2", "C2"),
  Y_C1 = "D1",
  Y_C2 = "D2",
  form = "UD",
  paths = custom_paths,
  Na = "DE",
  ci_method = "mc",
  R = 5000,
  seed = 123
)

Only mediator-to-mediator and mediator-to-outcome paths are included in paths. Do not add paths beginning with X: wsMed() automatically adds the condition-to-mediator paths and the direct path from the condition to the outcome.

The specified mediator structure must be acyclic. Detailed path rules, parameter labels, generated equations, and indirect-effect definitions are described in the GenerateModelCustom() vignette.

Step 3: Choose the estimation options

After selecting the mediation structure, choose how to handle missing data, construct confidence intervals, and, if required, standardize the effects.

Missing data and confidence intervals

The Na argument selects the missing-data method, and ci_method selects the confidence-interval method.

Na	Missing-data method	Available ci_method
"DE"	Listwise deletion	"mc", "bootstrap", or "both"
"FIML"	Full-information maximum likelihood	"mc", "bootstrap", or "both"
"MI"	Multiple imputation	"mc"

For a complete data analysis using Monte Carlo confidence intervals, use:

Na = "DE"
ci_method = "mc"
R = 5000
seed = 123

R controls the number of Monte Carlo draws, and seed makes the results reproducible.

To use bootstrap confidence intervals instead, use:

Na = "DE"
ci_method = "bootstrap"
bootstrap = 2000
boot_ci_type = "perc"
iseed = 123

The supported values of boot_ci_type are "perc", "bc", and "bca.simple". Setting ci_method = "both" requests Monte Carlo and bootstrap intervals in the same analysis.

The following code creates a copy of example_data with missing values for the FIML and multiple-imputation examples:

set.seed(123)
example_data_missing <- example_data
analysis_variables <- c("A1", "A2", "B1", "B2", "C1", "C2")

for (variable in analysis_variables) {
  missing_rows <- sample(
    seq_len(nrow(example_data_missing)),
    size = ceiling(0.10 * nrow(example_data_missing))
  )
  example_data_missing[missing_rows, variable] <- NA_real_
}

For data with missing values, FIML can be requested by changing Na:

result_fiml <- wsMed(
  data = example_data_missing,
  M_C1 = c("A1", "B1"),
  M_C2 = c("A2", "B2"),
  Y_C1 = "C1",
  Y_C2 = "C2",
  form = "P",
  Na = "FIML",
  ci_method = "mc",
  R = 5000,
  seed = 123
)

For FIML with Monte Carlo intervals, MCmethod can be set to "mc" or "bootSD".

Multiple imputation is requested with Na = "MI". Its controls are supplied through mi_args:

result_mi <- wsMed(
  data = example_data_missing,
  M_C1 = c("A1", "B1"),
  M_C2 = c("A2", "B2"),
  Y_C1 = "C1",
  Y_C2 = "C2",
  form = "P",
  Na = "MI",
  ci_method = "mc",
  mi_args = list(
    m = 20,
    method_num = "pmm"
  ),
  R = 5000,
  seed = 123
)

Here, m is the number of imputed data sets and method_num is the imputation method passed to the multiple-imputation procedure.

Standardized effects

Set standardized = TRUE when standardized path coefficients and effects are needed:

result_standardized <- wsMed(
  data = example_data,
  M_C1 = c("A1", "B1"),
  M_C2 = c("A2", "B2"),
  Y_C1 = "C1",
  Y_C2 = "C2",
  form = "P",
  Na = "DE",
  ci_method = "mc",
  R = 5000,
  standardized = TRUE,
  seed = 123
)

Step 4: Add optional model components

Moderators and covariates are added to the same wsMed() call. They do not require a separate analysis workflow.

Moderators

A moderated mediation analysis requires three arguments:

• W identifies the moderator variable;
• W_type specifies whether it is "continuous" or "categorical"; and
• MP identifies the paths moderated by W.

For example:

result_moderated <- wsMed(
  data = example_data,
  M_C1 = c("A1", "B1"),
  M_C2 = c("A2", "B2"),
  Y_C1 = "C1",
  Y_C2 = "C2",
  form = "CN",
  W = "D3",
  W_type = "continuous",
  MP = c("a1", "b_1_2", "b2", "cp"),
  Na = "DE",
  ci_method = "mc",
  R = 5000,
  seed = 123
)

In this chained model, a1 is the condition-to-M1 path, b_1_2 is the M1-to-M2 difference-component path, b2 is the M2-to-outcome difference-component path, and cp is the direct effect. Every label in MP must correspond to a path that exists in the selected model.

The same arguments can be used with form = "UD". For example, the user-defined model in Step 2 contains the labels b_1_3, b2, and b3, but it does not contain b1 because "M1 -> Y" was not specified.

For a categorical moderator, change the relevant arguments:

W = "Group"
W_type = "categorical"

After fitting a moderated model, plot_moderation_curve() can be used to display conditional effects:

plot_moderation_curve(
  result_moderated,
  "indirect_effect_1_2"
)

plot_moderation_curve(
  result_moderated,
  "b_1_2"
)

The conditional indirect effect used by plot_moderation_curve() is named indirect_effect_1_2; the corresponding indirect effect in the generated SEM syntax is named indirect_1_2.

Covariates

Within-subject covariates are supplied as matched pairs through C_C1 and C_C2. Between-subject covariates are supplied through C, with their type identified by C_type.

result_covariates <- wsMed(
  data = example_data,
  M_C1 = c("A1", "B1"),
  M_C2 = c("A2", "B2"),
  Y_C1 = "C1",
  Y_C2 = "C2",
  form = "P",
  C_C1 = "D1",
  C_C2 = "D2",
  C = "D3",
  C_type = "continuous",
  Na = "DE",
  ci_method = "mc",
  R = 5000,
  seed = 123
)

In this example, D1 and D2 form one within-subject covariate, and D3 is a continuous between-subject covariate. The prepared covariate terms are included in the mediator and outcome regressions.

Step 5: Inspect the results

Print the fitted object to obtain the main analysis summary:

print(result)

Depending on the selected options, the printed output includes:

• the variables included in the analysis;
• model-fit information;
• regression paths;
• specific indirect effects;
• the total indirect effect;
• the direct and total effects;
• confidence intervals;
• standardized effects; and
• conditional effects for moderated models.

Use printGM() to display the generated model equations:

printGM(result)

Frequently used components of the fitted object can also be accessed directly:

result$sem_model       # generated lavaan syntax
result$mc$fit          # fitted lavaan object
result$moderation      # moderation results, when requested
result$paths           # path vector when form = "UD"

The exact contents depend on the selected missing-data and confidence-interval methods.

Step 6: Interpret the printed results

This section uses two examples to explain the object returned by wsMed(). Example 1 describes the output shared by analyses without an external moderator. Example 2 then focuses on the additional output produced when a continuous moderator is included.

The explanations follow the order of the sections printed by print(). They describe what each section contains and how to locate the relevant results; they are not substantive interpretations of the example data.

Example 1: A model without an external moderator

The first example fits a parallel mediation model using multiple imputation and Monte Carlo confidence intervals. Standardized results are also requested so that all principal output sections are illustrated.

result4_mi <- wsMed(
  data = example_data_missing,
  M_C1 = c("A1", "B1"),
  M_C2 = c("A2", "B2"),
  Y_C1 = "C1",
  Y_C2 = "C2",
  form = "P",
  Na = "MI",
  ci_method = "mc",
  mi_args = list(
    m = 20,
    method_num = "pmm"
  ),
  R = 5000,
  standardized = TRUE,
  seed = 123
)

print(result4_mi)
#> 
#> 
#> *************** VARIABLES ***************
#> Outcome (Y):
#>    Condition 1: C1 
#>    Condition 2: C2 
#> Mediators (M):
#>   M1:
#>     Condition 1: A1
#>     Condition 2: A2
#>   M2:
#>     Condition 1: B1
#>     Condition 2: B2
#> Sample size (rows kept): 100 
#> 
#> 
#> *************** MODEL FIT ***************
#> 
#> 
#> |Measure   |  Value|
#> |:---------|------:|
#> |Chi-Sq    | 13.724|
#> |df        |  5.000|
#> |p         |  0.017|
#> |CFI       |  0.160|
#> |TLI       | -0.512|
#> |RMSEA     |  0.132|
#> |RMSEA Low |  0.051|
#> |RMSEA Up  |  0.218|
#> |SRMR      |  0.083|
#> 
#> 
#> ************* TOTAL / DIRECT / TOTAL-IND (MC) *************
#> 
#> 
#> |Label          | Estimate|    SE| 2.5%CI.Lo| 97.5%CI.Up|
#> |:--------------|--------:|-----:|---------:|----------:|
#> |Total effect   |    0.026| 0.018|    -0.009|      0.060|
#> |Direct effect  |    0.022| 0.017|    -0.012|      0.056|
#> |Total indirect |    0.004| 0.005|    -0.005|      0.015|
#> 
#> Indirect effects:
#> 
#> 
#> |Label | Estimate|    SE| 2.5%CI.Lo| 97.5%CI.Up|
#> |:-----|--------:|-----:|---------:|----------:|
#> |ind_1 |    0.004| 0.004|    -0.003|      0.014|
#> |ind_2 |   -0.000| 0.002|    -0.005|      0.004|
#> 
#> Indirect-effect key:
#> 
#> 
#> |Ind   |Path                 |
#> |:-----|:--------------------|
#> |ind_1 |X -> M1diff -> Ydiff |
#> |ind_2 |X -> M2diff -> Ydiff |
#> 
#> 
#> *************** MODERATION EFFECTS (d-paths, MC) ***************
#> 
#> 
#> |Coefficient | Estimate|    SE| 2.5%CI.Lo| 97.5%CI.Up|
#> |:-----------|--------:|-----:|---------:|----------:|
#> |d1          |    0.031| 0.105|    -0.172|      0.239|
#> |d2          |   -0.096| 0.089|    -0.271|      0.081|
#> 
#> 
#> *************** MODERATION KEY (d-paths) ***************
#> 
#> 
#> |Coefficient |Path           |Moderated       |
#> |:-----------|:--------------|:---------------|
#> |d1          |M1avg -> Ydiff |M1diff -> Ydiff |
#> |d2          |M2avg -> Ydiff |M2diff -> Ydiff |
#> 
#> 
#> *************** CONTRAST INDIRECT EFFECTS (No Moderator) ***************
#> 
#> 
#> |Contrast                  | Estimate|    SE| 2.5%CI.Lo| 97.5%CI.Up|
#> |:-------------------------|--------:|-----:|---------:|----------:|
#> |indirect_2  -  indirect_1 |   -0.004| 0.005|    -0.015|      0.004|
#> 
#> 
#> *************** C1-C2 COEFFICIENTS (No Moderator) ***************
#> 
#> 
#> |Coeff | Estimate|    SE| 2.5%CI.Lo| 97.5%CI.Up|
#> |:-----|--------:|-----:|---------:|----------:|
#> |X1_b1 |   -0.147| 0.105|    -0.347|      0.062|
#> |X0_b1 |   -0.179| 0.109|    -0.396|      0.033|
#> |X1_b2 |   -0.090| 0.105|    -0.297|      0.114|
#> |X0_b2 |    0.004| 0.102|    -0.191|      0.207|
#> 
#> 
#> *************** REGRESSION PATHS (MC) ***************
#> 
#> 
#> |Path           |Label | Estimate|    SE| 2.5%CI.Lo| 97.5%CI.Up|
#> |:--------------|:-----|--------:|-----:|---------:|----------:|
#> |Ydiff ~ M1diff |b1    |   -0.162| 0.094|    -0.344|      0.022|
#> |Ydiff ~ M1avg  |d1    |    0.031| 0.105|    -0.172|      0.239|
#> |Ydiff ~ M2diff |b2    |   -0.043| 0.094|    -0.224|      0.144|
#> |Ydiff ~ M2avg  |d2    |   -0.096| 0.089|    -0.271|      0.081|
#> 
#> 
#> *************** INTERCEPTS (MC) ***************
#> 
#> 
#> |Intercept |Label | Estimate|    SE| 2.5%CI.Lo| 97.5%CI.Up|
#> |:---------|:-----|--------:|-----:|---------:|----------:|
#> |Ydiff~1   |cp    |    0.022| 0.017|    -0.012|      0.056|
#> |M1diff~1  |a1    |   -0.025| 0.020|    -0.063|      0.014|
#> |M2diff~1  |a2    |    0.006| 0.020|    -0.033|      0.045|
#> |M1avg~1   |      |   -0.000| 0.000|    -0.000|     -0.000|
#> |M2avg~1   |      |   -0.000| 0.000|    -0.000|     -0.000|
#> 
#> 
#> *************** VARIANCES (MC) ***************
#> 
#> 
#> |Variance       |Label | Estimate|    SE| 2.5%CI.Lo| 97.5%CI.Up|
#> |:--------------|:-----|--------:|-----:|---------:|----------:|
#> |Ydiff~~Ydiff   |      |    0.024| 0.004|     0.017|      0.032|
#> |M1diff~~M1diff |      |    0.033| 0.006|     0.021|      0.045|
#> |M2diff~~M2diff |      |    0.033| 0.005|     0.023|      0.044|
#> |M1avg~~M1avg   |      |    0.033| 0.000|     0.033|      0.033|
#> |M2avg~~M2avg   |      |    0.040| 0.000|     0.040|      0.040|
#> 
#> 
#> *************** STANDARDIZED (MC) ***************
#> 
#> 
#> |Parameter      | Estimate|    SE|        R|   2.5%| 97.5%|
#> |:--------------|--------:|-----:|--------:|------:|-----:|
#> |cp             |    0.136| 0.108| 5000.000| -0.073| 0.346|
#> |b1             |   -0.185| 0.103| 5000.000| -0.379| 0.023|
#> |d1             |    0.035| 0.115| 5000.000| -0.188| 0.256|
#> |b2             |   -0.049| 0.105| 5000.000| -0.250| 0.159|
#> |d2             |   -0.125| 0.111| 5000.000| -0.330| 0.103|
#> |a1             |   -0.138| 0.113| 5000.000| -0.367| 0.078|
#> |a2             |    0.032| 0.112| 5000.000| -0.182| 0.253|
#> |Ydiff~~Ydiff   |    0.949| 0.052| 5000.000|  0.783| 0.984|
#> |M1diff~~M1diff |    1.000| 0.000| 5000.000|  1.000| 1.000|
#> |M2diff~~M2diff |    1.000| 0.000| 5000.000|  1.000| 1.000|
#> |M1avg~~M1avg   |    1.000| 0.000| 5000.000|  1.000| 1.000|
#> |M1avg~~M2avg   |    0.254| 0.000| 5000.000|  0.254| 0.254|
#> |M2avg~~M2avg   |    1.000| 0.000| 5000.000|  1.000| 1.000|
#> |M1avg~1        |    0.000| 0.000| 5000.000|  0.000| 0.000|
#> |M2avg~1        |    0.000| 0.000| 5000.000|  0.000| 0.000|
#> |indirect_1     |    0.026| 0.026| 5000.000| -0.016| 0.085|
#> |indirect_2     |   -0.002| 0.013| 5000.000| -0.030| 0.027|
#> |total_indirect |    0.024| 0.029| 5000.000| -0.028| 0.089|
#> |total_effect   |    0.160| 0.110| 5000.000| -0.055| 0.383|

The output sections and their main purposes are:

Printed section	What it answers
VARIABLES	Which observed variables and how many cases were used?
MODEL FIT	How well does the complete SEM reproduce the observed covariance structure?
TOTAL / DIRECT / TOTAL-IND	What are the overall, direct, and combined indirect effects?
Indirect effects and Indirect-effect key	What is the estimate for each mediation route, and which route does each label represent?
MODERATION EFFECTS (d-paths) and its key	What are the level-component coefficients associated with the mediator paths?
CONTRAST INDIRECT EFFECTS	How do the specific indirect effects differ from one another?
C1-C2 COEFFICIENTS	What are the reconstructed coefficients for the two conditions?
REGRESSION PATHS	What are the estimates for the individual regression paths?
INTERCEPTS	What are the estimated difference-score intercepts, including the a and cp paths?
VARIANCES	What are the estimated residual variances?
STANDARDIZED	What are the standardized estimates and confidence intervals?

The suffix in a heading identifies the requested confidence-interval engine. For example, (MC) denotes Monte Carlo results. When bootstrap intervals are requested, the corresponding bootstrap output is printed; with ci_method = "both", both sets of results can be returned.

Variables and analysis sample

The VARIABLES section restates the condition-specific outcome and mediator columns. It also maps each mediator pair to its internal label (M1, M2, and so on) and reports the number of rows retained for the analysis.

This section should be checked before interpreting any estimates. In particular, verify that:

• the Condition 1 and Condition 2 columns have not been reversed;
• the order of the mediator pairs matches the intended model; and
• the retained sample size is consistent with the selected missing-data method.

Model fit

The MODEL FIT section reports the model chi-squared statistic, degrees of freedom, its $p$ value, CFI, TLI, RMSEA with its confidence interval, and SRMR. These indices evaluate the model as a whole; they do not test an individual direct or indirect effect.

Fit indices should be interpreted in light of the fitted model. For a just-identified or saturated model, global fit is perfect by construction and does not provide evidence that the individual paths are substantively appropriate.

Total, direct, and indirect effects

The TOTAL / DIRECT / TOTAL-IND section gives a compact decomposition:

$$\text{total effect} = \text{direct effect} + \text{total indirect effect}.$$

The rows have the following meanings:

• Total effect is the overall condition effect on the outcome difference.
• Direct effect is the remaining condition effect after accounting for the mediators; its model label is cp.
• Total indirect is the sum of all specific indirect effects identified by the selected mediation structure.

The Indirect effects table then reports each specific route separately. The accompanying Indirect-effect key should be used to translate a printed label into a path. For example, a key may map ind_1 to X -> M1diff -> Ydiff. For serial or user-defined models, a label can refer to a route through more than one mediator.

Each row reports an estimate, its standard error, and confidence limits. For an indirect effect, inference should be based on the confidence interval for the complete product rather than on whether every component path is individually significant. An interval that excludes zero provides evidence that the corresponding effect differs from zero at the stated confidence level.

Level-component paths and condition-specific coefficients

The printed heading MODERATION EFFECTS (d-paths) can appear even when no external moderator was supplied through W. In this section, the d coefficients are the effects of mediator level components, such as M1avg, in the outcome or mediator-difference equation. They are part of the within-subject parameterization and should not be confused with moderation by a user-supplied variable.

The associated key maps each d label to its regression path. For a direct mediator-to-outcome path, the difference-component and level-component terms appear together, for example:

Ydiff ~ b1 * M1diff + d1 * M1avg

The C1-C2 COEFFICIENTS section expresses this pair as coefficients for the two conditions. It is useful when the research question concerns whether the corresponding mediator-to-outcome relation is the same under both conditions. The b coefficient summarizes the common component, whereas the d coefficient captures the difference between the two condition-specific coefficients.

Contrasts between indirect effects

When the model contains more than one specific indirect effect, CONTRAST INDIRECT EFFECTS reports pairwise differences between them. A contrast should be read according to the order shown in its label. For example:

indirect_2 - indirect_1

compares the second specific indirect effect with the first. Its confidence interval evaluates the difference between the two effects, not whether either effect separately differs from zero.

Regression paths, intercepts, and variances

REGRESSION PATHS lists the individual regression coefficients in the generated SEM. The Path column shows the regression in lavaan notation, whereas Label gives the name used elsewhere in the output and in MP. Common labels include:

• b1, b2, and so on for mediator difference-component paths to the outcome;
• d1, d2, and so on for the corresponding level-component paths; and
• labels such as b_1_2 and d_1_2 for paths from one mediator to another.

INTERCEPTS contains the a paths and the direct effect because, after the paired measurements are transformed, the condition effects are represented as intercepts of the difference-score equations. Thus, a1 is found on the M1diff ~ 1 row, and cp is found on the Ydiff ~ 1 row.

VARIANCES reports the estimated residual variances for the endogenous difference components and any other modeled variables. These rows describe unexplained variability; they are not additional mediation effects.

Standardized results

The STANDARDIZED section is printed when standardized = TRUE. It contains standardized versions of the path coefficients and derived effects, including the specific indirect, total indirect, and total effects when available.

Standardized and unstandardized results answer different reporting needs. Unstandardized estimates retain the scale of the original variables, whereas standardized estimates facilitate comparisons across variables or effects. A report should state explicitly which version is presented and should not combine an unstandardized estimate with a standardized confidence interval.

Inspecting and extracting Example 1

Use printGM() to connect the printed labels to the generated model:

printGM(result4_mi)

The returned object can also be inspected programmatically:

names(result4_mi)

result4_mi$input_vars    # variables supplied to wsMed()
result4_mi$sem_model     # generated lavaan syntax
result4_mi$mc$fit        # fitted lavaan model
result4_mi$mc$result     # Monte Carlo results
result4_mi$mc$std_mc     # standardized Monte Carlo results

print(result4_mi) is intended for reading the analysis summary, whereas the stored components are intended for inspection or downstream programming.

Example 2: A model with a continuous moderator

The second example fits a chained–parallel model and adds D3 as a continuous moderator. The paths listed in MP are allowed to vary with the moderator.

result5 <- wsMed(
  data = example_data_missing,
  M_C1 = c("A1", "B1", "C1"),
  M_C2 = c("A2", "B2", "C2"),
  Y_C1 = "D1",
  Y_C2 = "D2",
  form = "CP",
  W = "D3",
  W_type = "continuous",
  MP = c("a1", "b2", "d1", "cp", "b_1_2", "d_1_2"),
  Na = "DE",
  ci_method = "mc",
  R = 5000,
  seed = 123
)

print(result5)
#> 
#> 
#> *************** VARIABLES ***************
#> Outcome (Y):
#>    Condition 1: D1 
#>    Condition 2: D2 
#> Mediators (M):
#>   M1:
#>     Condition 1: A1
#>     Condition 2: A2
#>   M2:
#>     Condition 1: B1
#>     Condition 2: B2
#>   M3:
#>     Condition 1: C1
#>     Condition 2: C2
#> Moderators (W):
#>    W1 : D3 
#> Sample size (rows kept): 100 
#> 
#> 
#> *************** MODEL FIT ***************
#> 
#> 
#> |Measure   |  Value|
#> |:---------|------:|
#> |Chi-Sq    | 14.576|
#> |df        | 16.000|
#> |p         |  0.556|
#> |CFI       |  1.000|
#> |TLI       | -2.294|
#> |RMSEA     |  0.000|
#> |RMSEA Low |  0.000|
#> |RMSEA Up  |  0.111|
#> |SRMR      |  0.048|
#> 
#> 
#> ************* TOTAL / DIRECT / TOTAL-IND (MC) *************
#> 
#> 
#> |Label          | Estimate|    SE| 2.5%CI.Lo| 97.5%CI.Up|
#> |:--------------|--------:|-----:|---------:|----------:|
#> |Total effect   |   -0.032| 0.024|    -0.076|      0.016|
#> |Direct effect  |   -0.029| 0.023|    -0.074|      0.016|
#> |Total indirect |   -0.003| 0.008|    -0.019|      0.013|
#> 
#> Indirect effects:
#> 
#> 
#> |Label   | Estimate|    SE| 2.5%CI.Lo| 97.5%CI.Up|
#> |:-------|--------:|-----:|---------:|----------:|
#> |ind_1   |    0.002| 0.005|    -0.007|      0.014|
#> |ind_2   |    0.000| 0.004|    -0.008|      0.008|
#> |ind_1_2 |   -0.000| 0.002|    -0.003|      0.004|
#> |ind_3   |   -0.004| 0.006|    -0.018|      0.005|
#> |ind_1_3 |   -0.001| 0.001|    -0.004|      0.001|
#> 
#> Indirect-effect key:
#> 
#> 
#> |Ind     |Path                           |
#> |:-------|:------------------------------|
#> |ind_1   |X -> M1diff -> Ydiff           |
#> |ind_2   |X -> M2diff -> Ydiff           |
#> |ind_1_2 |X -> M1diff -> M2diff -> Ydiff |
#> |ind_3   |X -> M3diff -> Ydiff           |
#> |ind_1_3 |X -> M1diff -> M3diff -> Ydiff |
#> 
#> 
#> *************** MODERATION EFFECTS (d-paths, MC) ***************
#> 
#> 
#> |Coefficient | Estimate|    SE| 2.5%CI.Lo| 97.5%CI.Up|
#> |:-----------|--------:|-----:|---------:|----------:|
#> |d1          |   -0.040| 0.124|    -0.290|      0.202|
#> |d2          |   -0.000| 0.129|    -0.249|      0.256|
#> |d3          |   -0.160| 0.142|    -0.434|      0.122|
#> |d_1_2       |   -0.044| 0.107|    -0.251|      0.167|
#> |d_1_3       |    0.088| 0.115|    -0.134|      0.312|
#> 
#> 
#> *************** MODERATION KEY (d-paths) ***************
#> 
#> 
#> |Coefficient |Path            |Moderated        |
#> |:-----------|:---------------|:----------------|
#> |d1          |M1avg -> Ydiff  |M1diff -> Ydiff  |
#> |d2          |M2avg -> Ydiff  |M2diff -> Ydiff  |
#> |d3          |M3avg -> Ydiff  |M3diff -> Ydiff  |
#> |d_1_2       |M1avg -> M2diff |M1diff -> M2diff |
#> |d_1_3       |M1avg -> M3diff |M1diff -> M3diff |
#> 
#> 
#> *************** MODERATION RESULTS (Continuous Moderator) ***************
#> 
#> --- Moderated Coefficients ---
#> 
#> 
#> |Path      |BaseCoef |W_dummy | Estimate|    SE| 2.5%CI.Lo| 97.5%CI.Up|Sig |
#> |:---------|:--------|:-------|--------:|-----:|---------:|----------:|:---|
#> |cpw_W1    |cp       |D3      |   -0.172| 0.101|    -0.369|      0.022|    |
#> |dw1_W1    |d1       |D3      |   -0.103| 0.666|    -1.402|      1.204|    |
#> |bw2_W1    |b2       |D3      |   -0.520| 0.667|    -1.856|      0.781|    |
#> |aw1_W1    |a1       |D3      |    0.057| 0.098|    -0.134|      0.258|    |
#> |bw_1_2_W1 |b_1_2    |D3      |   -0.296| 0.545|    -1.373|      0.721|    |
#> |dw_1_2_W1 |d_1_2    |D3      |    0.592| 0.601|    -0.596|      1.755|    |
#> 
#> --- Conditional Indirect Effects ---
#> 
#> 
#> |Path                |Mediators | Level| W_value| Estimate|    SE| 2.5.%CI.Lo| 97.5.%CI.Up|Sig |
#> |:-------------------|:---------|-----:|-------:|--------:|-----:|----------:|-----------:|:---|
#> |indirect_effect_1   |1         | -1 SD|   0.223|    0.003| 0.007|     -0.010|       0.021|    |
#> |indirect_effect_1   |1         |  0 SD|   0.452|    0.002| 0.005|     -0.007|       0.014|    |
#> |indirect_effect_1   |1         | +1 SD|   0.681|    0.001| 0.005|     -0.009|       0.014|    |
#> |indirect_effect_1_2 |1 2       | -1 SD|   0.223|   -0.002| 0.005|     -0.013|       0.006|    |
#> |indirect_effect_1_2 |1 2       |  0 SD|   0.452|    0.000| 0.002|     -0.003|       0.004|    |
#> |indirect_effect_1_2 |1 2       | +1 SD|   0.681|    0.000| 0.002|     -0.004|       0.006|    |
#> |indirect_effect_1_3 |1 3       | -1 SD|   0.223|   -0.001| 0.002|     -0.006|       0.001|    |
#> |indirect_effect_1_3 |1 3       |  0 SD|   0.452|   -0.001| 0.001|     -0.004|       0.001|    |
#> |indirect_effect_1_3 |1 3       | +1 SD|   0.681|   -0.000| 0.001|     -0.004|       0.002|    |
#> |indirect_effect_2   |2         | -1 SD|   0.223|    0.002| 0.006|     -0.009|       0.016|    |
#> |indirect_effect_2   |2         |  0 SD|   0.452|    0.000| 0.004|     -0.008|       0.008|    |
#> |indirect_effect_2   |2         | +1 SD|   0.681|   -0.002| 0.006|     -0.016|       0.009|    |
#> 
#> --- Indirect Effect Contrasts ---
#> 
#> 
#> |Path                |            Contrast| Estimate|    SE| 2.5%CI.Lo| 97.5%CI.Up|Sig |
#> |:-------------------|-------------------:|--------:|-----:|---------:|----------:|:---|
#> |indirect_effect_1   | (0 SD)   -  (-1 SD)|    0.001| 0.004|    -0.006|      0.011|    |
#> |indirect_effect_1   | (+1 SD)  -  (-1 SD)|    0.002| 0.008|    -0.012|      0.023|    |
#> |indirect_effect_1   | (+1 SD)  -   (0 SD)|    0.001| 0.004|    -0.006|      0.011|    |
#> |indirect_effect_1_2 | (0 SD)   -  (-1 SD)|   -0.002| 0.004|    -0.012|      0.004|    |
#> |indirect_effect_1_2 | (+1 SD)  -  (-1 SD)|   -0.002| 0.005|    -0.015|      0.007|    |
#> |indirect_effect_1_2 | (+1 SD)  -   (0 SD)|   -0.000| 0.002|    -0.005|      0.004|    |
#> |indirect_effect_1_3 | (0 SD)   -  (-1 SD)|   -0.000| 0.001|    -0.003|      0.001|    |
#> |indirect_effect_1_3 | (+1 SD)  -  (-1 SD)|   -0.001| 0.002|    -0.006|      0.003|    |
#> |indirect_effect_1_3 | (+1 SD)  -   (0 SD)|   -0.000| 0.001|    -0.003|      0.001|    |
#> |indirect_effect_2   | (0 SD)   -  (-1 SD)|    0.002| 0.005|    -0.006|      0.013|    |
#> |indirect_effect_2   | (+1 SD)  -  (-1 SD)|    0.003| 0.009|    -0.013|      0.027|    |
#> |indirect_effect_2   | (+1 SD)  -   (0 SD)|    0.002| 0.005|    -0.006|      0.013|    |
#> 
#> --- Moderated Path Coefficients ---
#> 
#> 
#> |Path  | Level| W_value| Estimate|    SE| 2.5.%CI.Lo| 97.5.%CI.Up|Sig |
#> |:-----|-----:|-------:|--------:|-----:|----------:|-----------:|:---|
#> |a1    | -1 SD|   0.223|   -0.039| 0.033|     -0.104|       0.022|    |
#> |a1    |  0 SD|   0.452|   -0.026| 0.023|     -0.070|       0.018|    |
#> |a1    | +1 SD|   0.681|   -0.013| 0.032|     -0.076|       0.047|    |
#> |b2    | -1 SD|   0.223|    0.119| 0.205|     -0.281|       0.518|    |
#> |b2    |  0 SD|   0.452|    0.000| 0.138|     -0.271|       0.275|    |
#> |b2    | +1 SD|   0.681|   -0.119| 0.207|     -0.523|       0.288|    |
#> |d1    | -1 SD|   0.223|   -0.020| 0.205|     -0.440|       0.372|    |
#> |d1    |  0 SD|   0.452|   -0.044| 0.124|     -0.290|       0.202|    |
#> |d1    | +1 SD|   0.681|   -0.067| 0.188|     -0.437|       0.298|    |
#> |cp    | -1 SD|   0.223|   -0.022| 0.018|     -0.057|       0.012|    |
#> |cp    |  0 SD|   0.452|   -0.029| 0.023|     -0.074|       0.016|    |
#> |cp    | +1 SD|   0.681|   -0.036| 0.029|     -0.091|       0.019|    |
#> |b_1_2 | -1 SD|   0.223|    0.372| 0.169|      0.046|       0.701|*   |
#> |b_1_2 |  0 SD|   0.452|    0.304| 0.116|      0.076|       0.531|*   |
#> |b_1_2 | +1 SD|   0.681|    0.236| 0.172|     -0.093|       0.569|    |
#> |d_1_2 | -1 SD|   0.223|   -0.180| 0.172|     -0.515|       0.155|    |
#> |d_1_2 |  0 SD|   0.452|   -0.044| 0.107|     -0.251|       0.167|    |
#> |d_1_2 | +1 SD|   0.681|    0.091| 0.177|     -0.252|       0.446|    |
#> 
#> --- Path Coefficient Contrasts ---
#> 
#> 
#> |Path  |            Contrast| Estimate|    SE| 2.5%CI.Lo| 97.5%CI.Up|Sig |
#> |:-----|-------------------:|--------:|-----:|---------:|----------:|:---|
#> |a1    | (0 SD)   -  (-1 SD)|   -0.013| 0.023|    -0.059|      0.031|    |
#> |a1    | (+1 SD)  -  (-1 SD)|   -0.026| 0.045|    -0.118|      0.061|    |
#> |a1    | (+1 SD)  -   (0 SD)|   -0.013| 0.023|    -0.059|      0.031|    |
#> |b_1_2 | (0 SD)   -  (-1 SD)|    0.068| 0.125|    -0.165|      0.315|    |
#> |b_1_2 | (+1 SD)  -  (-1 SD)|    0.136| 0.250|    -0.331|      0.630|    |
#> |b_1_2 | (+1 SD)  -   (0 SD)|    0.068| 0.125|    -0.165|      0.315|    |
#> |b2    | (0 SD)   -  (-1 SD)|    0.119| 0.153|    -0.179|      0.425|    |
#> |b2    | (+1 SD)  -  (-1 SD)|    0.238| 0.306|    -0.358|      0.851|    |
#> |b2    | (+1 SD)  -   (0 SD)|    0.119| 0.153|    -0.179|      0.425|    |
#> |cp    | (0 SD)   -  (-1 SD)|    0.007| 0.005|    -0.004|      0.017|    |
#> |cp    | (+1 SD)  -  (-1 SD)|    0.013| 0.011|    -0.007|      0.034|    |
#> |cp    | (+1 SD)  -   (0 SD)|    0.007| 0.005|    -0.004|      0.017|    |
#> |d_1_2 | (0 SD)   -  (-1 SD)|   -0.136| 0.138|    -0.402|      0.137|    |
#> |d_1_2 | (+1 SD)  -  (-1 SD)|   -0.271| 0.275|    -0.805|      0.273|    |
#> |d_1_2 | (+1 SD)  -   (0 SD)|   -0.136| 0.138|    -0.402|      0.137|    |
#> |d1    | (0 SD)   -  (-1 SD)|    0.024| 0.153|    -0.276|      0.321|    |
#> |d1    | (+1 SD)  -  (-1 SD)|    0.047| 0.305|    -0.552|      0.643|    |
#> |d1    | (+1 SD)  -   (0 SD)|    0.024| 0.153|    -0.276|      0.321|    |
#> 
#> --- Conditional Total Effect and Total Indirect Effect ---
#> 
#> 
#> |Effect         | Level| W_value| Estimate|    SE| 2.5.%CI.Lo| 97.5.%CI.Up|Sig |
#> |:--------------|-----:|-------:|--------:|-----:|----------:|-----------:|:---|
#> |total_indirect | -1 SD|   0.223|    0.002| 0.009|     -0.016|       0.022|    |
#> |total_indirect |  0 SD|   0.452|    0.002| 0.006|     -0.010|       0.015|    |
#> |total_indirect | +1 SD|   0.681|   -0.000| 0.008|     -0.017|       0.016|    |
#> |total_effect   | -1 SD|   0.223|    0.012| 0.034|     -0.053|       0.077|    |
#> |total_effect   |  0 SD|   0.452|   -0.028| 0.024|     -0.074|       0.018|    |
#> |total_effect   | +1 SD|   0.681|   -0.069| 0.033|     -0.132|      -0.005|*   |
#> 
#> 
#> *************** REGRESSION PATHS (MC) ***************
#> 
#> 
#> |Path                   |Label     | Estimate|    SE| 2.5%CI.Lo| 97.5%CI.Up|
#> |:----------------------|:---------|--------:|-----:|---------:|----------:|
#> |Ydiff ~ M1diff         |b1        |   -0.085| 0.133|    -0.346|      0.175|
#> |Ydiff ~ M1avg          |d1        |   -0.040| 0.124|    -0.290|      0.202|
#> |Ydiff ~ M2diff         |b2        |    0.002| 0.138|    -0.271|      0.275|
#> |Ydiff ~ M2avg          |d2        |   -0.000| 0.129|    -0.249|      0.256|
#> |Ydiff ~ M3diff         |b3        |   -0.182| 0.130|    -0.438|      0.076|
#> |Ydiff ~ M3avg          |d3        |   -0.160| 0.142|    -0.434|      0.122|
#> |Ydiff ~ W1             |cpw_W1    |   -0.173| 0.101|    -0.369|      0.022|
#> |Ydiff ~ int_M1avg_W1   |dw1_W1    |   -0.114| 0.666|    -1.402|      1.204|
#> |Ydiff ~ int_M2diff_W1  |bw2_W1    |   -0.514| 0.667|    -1.856|      0.781|
#> |M1diff ~ W1            |aw1_W1    |    0.056| 0.098|    -0.134|      0.258|
#> |M2diff ~ M1diff        |b_1_2     |    0.306| 0.116|     0.076|      0.531|
#> |M2diff ~ M1avg         |d_1_2     |   -0.044| 0.107|    -0.251|      0.167|
#> |M2diff ~ W1            |          |    0.007| 0.097|    -0.182|      0.193|
#> |M2diff ~ int_M1diff_W1 |bw_1_2_W1 |   -0.300| 0.545|    -1.373|      0.721|
#> |M2diff ~ int_M1avg_W1  |dw_1_2_W1 |    0.593| 0.601|    -0.596|      1.755|
#> |M3diff ~ M1diff        |b_1_3     |   -0.147| 0.121|    -0.385|      0.094|
#> |M3diff ~ M1avg         |d_1_3     |    0.088| 0.115|    -0.134|      0.312|
#> |M3diff ~ W1            |          |   -0.081| 0.096|    -0.268|      0.102|
#> 
#> 
#> *************** INTERCEPTS (MC) ***************
#> 
#> 
#> |Intercept       |Label | Estimate|    SE| 2.5%CI.Lo| 97.5%CI.Up|
#> |:---------------|:-----|--------:|-----:|---------:|----------:|
#> |Ydiff~1         |cp    |   -0.029| 0.023|    -0.074|      0.016|
#> |M1diff~1        |a1    |   -0.026| 0.023|    -0.070|      0.018|
#> |M2diff~1        |a2    |    0.014| 0.022|    -0.028|      0.056|
#> |M3diff~1        |a3    |    0.023| 0.022|    -0.021|      0.066|
#> |M1avg~1         |      |   -0.014| 0.026|    -0.067|      0.035|
#> |M2avg~1         |      |    0.001| 0.025|    -0.049|      0.050|
#> |M3avg~1         |      |   -0.012| 0.023|    -0.060|      0.033|
#> |W1~1            |      |    0.004| 0.031|    -0.056|      0.064|
#> |int_M1avg_W1~1  |      |    0.009| 0.005|    -0.000|      0.017|
#> |int_M2diff_W1~1 |      |    0.002| 0.004|    -0.007|      0.011|
#> |int_M1diff_W1~1 |      |    0.003| 0.005|    -0.008|      0.013|
#> 
#> 
#> *************** VARIANCES (MC) ***************
#> 
#> 
#> |Variance                     |Label | Estimate|    SE| 2.5%CI.Lo| 97.5%CI.Up|
#> |:----------------------------|:-----|--------:|-----:|---------:|----------:|
#> |Ydiff~~Ydiff                 |      |    0.027| 0.005|     0.018|      0.037|
#> |M1diff~~M1diff               |      |    0.031| 0.006|     0.020|      0.042|
#> |M2diff~~M2diff               |      |    0.025| 0.005|     0.016|      0.034|
#> |M3diff~~M3diff               |      |    0.027| 0.005|     0.017|      0.037|
#> |M1avg~~M1avg                 |      |    0.038| 0.007|     0.024|      0.053|
#> |M2avg~~M2avg                 |      |    0.038| 0.007|     0.024|      0.051|
#> |M3avg~~M3avg                 |      |    0.031| 0.006|     0.020|      0.043|
#> |W1~~W1                       |      |    0.054| 0.010|     0.034|      0.074|
#> |int_M1avg_W1~~int_M1avg_W1   |      |    0.001| 0.000|     0.001|      0.002|
#> |int_M2diff_W1~~int_M2diff_W1 |      |    0.001| 0.000|     0.001|      0.002|
#> |int_M1diff_W1~~int_M1diff_W1 |      |    0.002| 0.000|     0.001|      0.002|

Most printed sections have the same interpretation as in Example 1. The important additions are:

Additional output	What it contains
Moderator in VARIABLES	The observed variable mapped to the internal moderator label, such as W1.
Moderated Coefficients	Interaction terms for the paths named in MP.
Conditional Indirect Effects	Indirect effects evaluated at selected moderator values.
Indirect Effect Contrasts	Differences between conditional indirect effects at those values.
Moderated Path Coefficients	The selected path coefficients evaluated at each moderator value.
Path Coefficient Contrasts	Differences between conditional path coefficients.
Conditional Total Effect and Total Indirect Effect	Overall and combined indirect effects evaluated at each moderator value.

Moderated coefficients

The Moderated Coefficients table reports the interaction term associated with each path in MP. The BaseCoef column links the interaction to the original path. For example, a row whose base coefficient is a1 indicates whether the condition-to-M1 path changes with D3.

The interaction estimate describes the expected change in the base path for a one-unit increase in the moderator. Its confidence interval evaluates whether that change differs from zero. This table should be consulted before interpreting the pattern of conditional path coefficients.

Because the continuous moderator is centered during data preparation, the ordinary path estimates in the main output refer to the value represented by centered $W=0$, typically the sample mean of the original moderator. The conditional tables make the values used for interpretation explicit.

Conditional effects

For a continuous moderator, conditional results are commonly reported at three reference levels:

• one standard deviation below the mean (-1 SD);
• the mean (0 SD); and
• one standard deviation above the mean (+1 SD).

The W_value column gives the corresponding value on the moderator’s original scale. The Estimate, SE, and confidence-limit columns describe the effect at that value of $W$.

Conditional Indirect Effects reports how each mediation route changes across these values. Labels used here have the prefix indirect_effect_. For example:

indirect_effect_1_2

refers to the conditional indirect route through M1 and M2. This name is used by the moderation output and plotting functions. The corresponding defined parameter in the generated SEM uses:

indirect_1_2

The Indirect Effect Contrasts table directly compares the conditional indirect effect between moderator levels. These contrasts answer whether the indirect effect changes between the selected values; they are distinct from testing the indirect effect against zero at any one value.

Moderated Path Coefficients and Path Coefficient Contrasts provide the same two views for the individual paths listed in MP. The first table shows each conditional coefficient, and the second tests differences between the selected moderator levels.

Finally, Conditional Total Effect and Total Indirect Effect combines the relevant paths at each moderator value. When a specific indirect effect is of primary interest, its row in Conditional Indirect Effects should still be reported separately rather than relying only on the conditional total indirect effect.

Significance markers and confidence intervals

The Sig column provides a compact marker when the reported confidence interval excludes zero. The confidence limits should remain the primary basis for interpretation because they show both the direction and precision of the estimate.

A blank marker does not show that two moderator levels are equivalent. To evaluate a difference between levels, use the relevant contrast table rather than comparing the two significance markers.

Visualizing conditional effects

plot_moderation_curve() displays a conditional indirect effect, an individual path coefficient, or a total effect across the observed range of a continuous moderator:

plot_moderation_curve(
  result5,
  "indirect_effect_1_2"
)

plot_moderation_curve(
  result5,
  "b_1_2"
)

plot_moderation_curve(
  result5,
  "total_effect"
)

The first call uses a conditional-effect label from the moderation output. The second uses an individual model-path label. The third displays the conditional total effect. The curve shows the estimated effect over $W$, the confidence band shows its uncertainty, and the zero reference line indicates where the interval changes from including to excluding zero.

Available curve labels can be checked before plotting:

names(result5$moderation)

unique(result5$moderation$theta_curve$Path)
unique(result5$moderation$path_curve$Path)

When ci_method = "both", the Monte Carlo and bootstrap moderation results are stored separately. Select the desired branch before accessing its curve data:

result_both$moderation$mc$theta_curve
result_both$moderation$boot$theta_curve

What to report

The exact reporting format depends on the research question, but a reproducible summary should identify:

1. the selected model form and the order of the mediators;
2. the missing-data method and confidence-interval method;
3. the number of Monte Carlo draws or bootstrap samples;
4. model-fit information when it is informative for the fitted model;
5. the direct, specific indirect, total indirect, and total effects, with confidence intervals;
6. whether the reported estimates are standardized or unstandardized; and
7. for moderated models, the moderator, the paths in MP, their interaction estimates, and the relevant conditional effects or contrasts.

For every indirect-effect label, use the printed key or printGM() to verify the exact mediator route before reporting it.

Further model details

This tutorial focuses on constructing and running wsMed() calls. The model-generation vignettes provide the corresponding equations, parameter-label conventions, and indirect-effect definitions:

• GenerateModelP() for parallel models;
• GenerateModelCN() for chained models;
• GenerateModelCP() for chained–parallel models;
• GenerateModelPC() for parallel–chained models; and
• GenerateModelCustom() for user-defined models.

These vignettes are most useful when users need to inspect how a selected structure is translated into lavaan syntax or determine the label of a path supplied through MP.

Summary

A wsMed() analysis can be completed in six steps:

1. Supply matched mediator and outcome variables for the two conditions.
2. Select a predefined model with form, or use form = "UD" together with paths.
3. Choose Na, ci_method, and whether standardized effects are required.
4. Add moderators or covariates when they are part of the analysis.
5. Print the fitted object and inspect the generated model.
6. Read the shared output first, then interpret any additional conditional results for a moderated model.

The same basic call is therefore used across simple, user-defined, missing-data, moderated, and covariate-adjusted analyses. Only the arguments needed for the intended analysis have to be added or changed. The returned object can be read through print(), connected to the generated model with printGM(), and accessed directly for further analysis or reporting.