Technical Appendix: Workflow of `cond_indirect()`

In manymome: Mediation, Moderation and Moderated-Mediation After Model Fitting

library(DiagrammeR)

Goal

This technical appendix describes how cond_indirect() from the package manymome (Cheung & Cheung, 2024) works internally to extract the parameters and compute a conditional indirect effect.

cond_indirect()

mermaid("
flowchart TD
  classDef default fill:#EEEEFF;
  classDef errornode fill:#FFDDDD;
  classDef startend fill:#DDFFDD;
  classDef mcnode fill:#FFFFDD;
  classDef bootnode fill:#DDFFFF;
  classDef lavnode fill:#FFDDFF;
  classDef lmnode fill:#FFDDDD;

  ZZ([\"Start\"])
  A{{\"Call check_path() to check the path\"}}
  ZZ:::startend --> A
  A -- OK --> B
  B{{\"Confidence interval (CI) requested?\"}}
  B -- Monte Carlo CI --> MCCIA
  B -- Bootstrap CI --> BootA
  B -- CI not requested --> D

  subgraph idmcdo [ ]
  MCCIA{{\"mc_out supplied?\"}}
  MCCIdo[\"Call do_mc() and</br>store results in mc_out\"]
  MCCIA:::mcnode -- No --> MCCIdo:::mcnode
  end
  MCCIA -- Yes --> D
  MCCIdo --> D

  subgraph idbootdo [ ]
  BootA{{\"boot_out supplied?\"}}
  Bootdo[\"Call do_boot() and</br>store results in boot_out\"]
  BootA:::bootnode -- No --> Bootdo:::bootnode
  end
  BootA -- Yes --> D
  Bootdo --> D

  D{{\"fit_type?\"}}

  D -- lavaan --> Elavaanest
  subgraph idlav [ ]
  Elavaanest{{\"est supplied?\"}}
  Elavaangetest[\"Call lavaan::parameterEstimates()</br>to set est\"]
  Elavaanimplied{{\"implied_stats supplied?\"}}
  Elavaangetimplied[\"Call lav_implied_all()</br>to set implied_stats\"]
  Elavaangetdata[\"Call lavaan::lavInspect()</br>to set fit_data\"]
  Elavaanest:::lavnode -- Yes --> Elavaanimplied:::lavnode
  Elavaanest:::lavnode -- No --> Elavaangetest:::lavnode
  Elavaangetest:::lavnode --> Elavaanimplied:::lavnode
  Elavaanimplied:::lavnode -- Yes --> Elavaangetdata:::lavnode
  Elavaanimplied:::lavnode -- No --> Elavaangetimplied:::lavnode
  end
  Elavaangetimplied:::lavnode --> Elavaangetdata:::lavnode

  D -- lm --> Elm
  subgraph idlm [ ]
  Elm[\"Call m2ptable() to convert</br>fit to lm_est, a lavaan-like object\"]
  Elmest{{\"est supplied?\"}}
  Elmgetest[\"Extract est from lm_est\"]
  Elmimplied{{\"implied_stats supplied?\"}}
  Elmgetimplied[\"Extract implied_stats from lm_est\"]
  Elmgetdata[\"Extract data from lm_est</br>to set fit_data\"]
  Elm:::lmnode --> Elmest:::lmnode
  Elmest:::lmnode -- Yes --> Elmimplied:::lmnode
  Elmest:::lmnode -- No --> Elmgetest:::lmnode
  Elmgetest:::lmnode --> Elmimplied:::lmnode
  Elmimplied:::lmnode -- Yes --> Elmgetdata:::lmnode
  Elmimplied:::lmnode -- No --> Elmgetimplied:::lmnode
  end

  Elmgetimplied:::lmnode --> Elmgetdata:::lmnode

  Elmgetdata --> Fprods
  Elavaangetdata --> Fprods
  Fprods{{\"prods supplied?\"}}
  Ggetprods[\"Call indirect_i() with</br>get_prods_only = TRUE</br> to set prods\"]
  Fprods -- No --> Ggetprods
  Fprods -- Yes --> prodsonly
  indirect[\"Call indirect_i() to estimate </br>the (conditional) indirect effect</br>using fit, wvalues, est, and implied_stats\"]

  indirect --> G
  G{{\"Confidence interval (CI) requested?\"}}
  G -- Monte Carlo CI --> HMCCIA
  G -- Bootstrap CI --> HBootA
  G -- CI not requested --> H

  HMCCIA[\"Use mapply on indirect_i</br>to generate Monte Carlo estimates\"]
  HMMCCIB[\"Form CI and store in mc_ci\"]
  subgraph idmcci [ ]
  HMCCIA:::mcnode --> HMMCCIB:::mcnode
  end
  HMMCCIB --> H

  HBootA[\"Use mapply on indirect_i</br>to generate bootstrap estimates\"]
  HBootB[\"Form CI and store in boot_ci\"]
  subgraph idbootci [ ]
  HBootA:::bootnode --> HBootB:::bootnode
  end
  HBootB --> H:::startend

  H([\"Return the results\"])

  AFailed([\"Error: No path from x to y\"])
  A -- Failed --> AFailed:::errornode
  prodsonly{{\"get_prods_only TRUE?\"}}
  prodsonlyYes([\"Quit and return prods\"])
  Ggetprods --> prodsonly
  prodsonly -- Yes --> prodsonlyYes:::startend
  prodsonly -- No --> indirect
", height = 2000, width = 800)

cond_indirect_effects()

mermaid("
flowchart TD
  classDef default fill:#EEEEFF;
  classDef errornode fill:#FFDDDD;
  classDef startend fill:#DDFFDD;
  classDef mcnode fill:#FFFFDD;
  classDef bootnode fill:#DDFFFF;

  ZZ([\"Start\"])
  wlevels{{\"wlevels supplied?\"}}

  ZZ:::startend --> wlevels

  wlevels -- Yes --> B

  B{{\"Confidence interval (CI) requested?\"}}
  B -- Monte Carlo CI --> MCCIA:::mcnode
  B -- Bootstrap CI --> BootA:::bootnode
  B -- CI not requested --> getprods

  MCCIA{{\"mc_out supplied?\"}}
  MCCIdo[\"Call do_mc() and</br>store results in mc_out\"]
  subgraph idmcdo [ ]
  MCCIA:::mcnode -- No --> MCCIdo:::mcnode
  end
  MCCIA -- Yes --> getprods
  MCCIdo --> getprods

  BootA{{\"boot_out supplied?\"}}
  Bootdo[\"Call do_boot() and</br>store results in boot_out\"]
  subgraph idbootdo [ ]
  BootA:::bootnode -- No --> Bootdo:::bootnode
  end
  BootA -- Yes --> getprods
  Bootdo --> getprods

  getprods[\"Call cond_indirect() to get prods,</br>product term(s) along the path, if any\"]

  getprods --> condi
  condi[\"Call cond_indirect() for each row of wlevels</br>to compute the conditional indirect effects\"]

  condi --> df
  df{{\"output_type == \'data.frame\'?\"}}
  df -- Yes --> dfYes:::startend
  df -- No --> dfNo:::startend
  dfYes([\"Pack the results in a data frame and</br>retrun a cond_indirect_effects-class object\"])
  dfNo([\"Return a list of the outputs of cond_indirect()\"])

  wlevelsNo([\"Error: wlevels is required.\"])
  wlevels -- No --> wlevelsNo

  class wlevelsNo errornode;

", height = 1000, width = 800)

indirect_i()

Main workflow

mermaid("
flowchart TD
  classDef default fill:#EEEEFF;
  classDef errornode fill:#FFDDDD;
  classDef startend fill:#DDFFDD;
  classDef subnode fill:#FFFFDD;

  ZZ([\"Start\"])
  ZZ:::startend --> ZA

  ZA[\"If est is NULL,</br> get est from fit\"]
  A{{\"Call check_path() to check the path\"}}
  ZA --> A
  B{{\"Call get_b() to get </br>coefficient(s) from x to y (bs)\"}}

  AFailed([\"Error: No path from x to y\"])
  A -- OK --> B
  A -->|Failed| AFailed:::errornode

  BFailed([\"Error: Path between</br>a latent variable and</br>an observed variable.\"])
  C{{\"prods supplied?\"}}
  B -- Failed --> BFailed:::errornode
  B -- OK --> C

  C -- Yes --> CYes
  C -- No --> CNo:::subnode

  subgraph idgetprod [ ]
  CNo[[\"Call get_prod() to</br>get all product terms</br>along the path(s), if any.\"]]
  CYes[\"Update prods by est\"]
  end

  D{{\"get_prods_only TRUE?\"}}
  CYes --> D
  CNo --> D
  DYes([\"Quit and return prods\"])
  D -- Yes --> DYes:::startend

  E{{\"wvalues NULL?\"}}
  D -- No --> E
  subgraph idcond [ ]
  ENOTNULL[\"Compute the change(s) in effect(s) (b_cond)</br>due to wvalues along the path\"]
  ENOTNULL2[\"Update bs\"]
  F[\"Set b_cond to NAs\"]
  E -- Not NULL --> ENOTNULL
  ENOTNULL --> ENOTNULL2
  E -- NULL --> F
  G[\"Create the string representation (b_cond_str)</br>of the computation of effect\"]
  F --> G
  ENOTNULL2 --> G
  H[\"Compute the (raw) indirect effect (b_all)\"]
  G --> H
  end

  I{{\"standardized_x or standardized_y TRUE?\"}}
  J([\"Pack and return the results as</br>an indirect-class object\"])
  H --> I

  ITRUE[\"Call lav_implied_all(fit() to</br> compute the implied statistics\"]
  IA[\"Compute the scaling factor(s) for x and/or y\"]
  IB[\"Scale the indirect effect\"]
  I -- Either or both TRUE --> ITRUE

  subgraph idstd [ ]
  ITRUE --> IA
  IA --> IB
  end

  I -- Both FALSE --> J
  IB --> J:::startend
", height = 1900, width = 800)

For Call get_prod(), see the workflow of Creating prods.

prods not supplied

Creating prods

mermaid("
flowchart TD
  classDef default fill:#EEEEFF;
  classDef errornode fill:#FFDDDD;
  classDef startend fill:#DDFFDD;
  classDef subnode fill:#FFFFDD;

  ZZ([\"Start\"])
  ZZ:::startend --> ZA

  ZA[\"From \'Call get_prod()\' in the main workflow\"]
  ZA --> A
  A{{\"chk_lv all TRUE?</br>(All variables in the path are latent)\"}}
  B{{\"Is data supplied?\"}}
  A -- No --> B
  C{{\"Is fit supplied?\"}}
  B -- No --> C
  CYes[\"Extract data from fit\"]
  C -- Yes --> CYes
  C -- No --> Dfit
  CYes --> Dfit
  B -- Yes --> Dfit
  Dfit{{\"Is fit supplied?\"}}
  DfitYes[\"Use mapply() on get_prod</br> to find</br>the product term(s), if any,</br>using fit and data\"]
  Dfit -- Yes --> DfitYes
  DfitNo[\"Use mapply() on get_prod</br> to find</br>the product term(s), if any,</br>using est and data\"]
  Dfit -- No --> DfitNo
  DfitYes --> AEnd
  DfitNo --> AEnd

  AYes[\"Use mapply() on all paths</br>to find</br>the product term(s), if any,</br>using operator\"]
  AEnd([\"Set prods and</br>return to \'Call get_prod()\' in the main workflow\"])
  A -- Yes --> AYes
  AYes --> AEnd:::startend
", height = 950, width = 800)

Notes

Latent variables

If all variables along a path are latent variables, product term(s) must be identified by their names because raw scores are not available.

Default uses "_x_". For example, f1_x_f2 is the product term between f1 and f2.

Extracting Point Estimates and Variance-Covariance Matrix

When the point estimates or variance-covariance matrix of the point estimates are needed, they will be extracted internally using functions developed for the fit object, which can be a lavaan-class object, a list of the outputs from stats::lm(), or a lavaan.mi-class object generated by fitting a model to several datasets using multiple imputation.

Reference

Cheung, S. F., & Cheung, S.-H. (2024). manymome: An R package for computing the indirect effects, conditional effects, and conditional indirect effects, standardized or unstandardized, and their bootstrap confidence intervals, in many (though not all) models. Behavior Research Methods, 56(5), 4862--4882. https://doi.org/10.3758/s13428-023-02224-z

manymome documentation built on June 21, 2025, 9:07 a.m.