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, 2023) 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. (2023). 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. https://doi.org/10.3758/s13428-023-02224-z

manymome documentation built on Oct. 4, 2024, 5:10 p.m.