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Get started with fit indices

Source: vignettes/get-started-fit-indices.Rmd
get-started-fit-indices.Rmd

Goal

By the end of this guide, you will be able to:

  1. Fit a CFA model with lavaan.
  2. Extract fit indices with model_fit().
  3. Compare alternative estimators with compare_model_fit().
  4. Fit an ordinal-item version with WLSMV and ordered = TRUE.

Prerequisites

  • R >= 4.1.0
  • Packages: psymetrics, lavaan

Setup

Step 1: Fit a baseline CFA model 

model <- '
  visual  =~ x1 + x2 + x3
  textual =~ x4 + x5 + x6
  speed   =~ x7 + x8 + x9
'

fit_mlr <- cfa(
  model,
  data = HolzingerSwineford1939,
  estimator = "MLR"
)

Step 2: Extract fit indices 

model_fit(fit_mlr)
#> NOBS | ESTIMATOR | NPAR | Chi2(24) | p (Chi2) |  CFI  |  TLI  | RMSEA
#> ---------------------------------------------------------------------
#> 301  |    MLR    |  21  |  87.13   |  < .001  | 0.925 | 0.888 | 0.093
#> 
#> NOBS |   RMSEA  CI    | SRMR 
#> -----------------------------
#> 301  | [0.073, 0.115] | 0.065

Request only selected metrics when needed:

model_fit(fit_mlr, metrics = c("cfi", "tli", "rmsea"))
#> NOBS | ESTIMATOR | NPAR |  CFI  |  TLI  | RMSEA
#> -----------------------------------------------
#> 301  |    MLR    |  21  | 0.925 | 0.888 | 0.093

Step 3: Compare two fitted models 

fit_ulsm <- cfa(
  model,
  data = HolzingerSwineford1939,
  estimator = "ULSM"
)
compare_model_fit(MLR = fit_mlr, ULSM = fit_ulsm)
#> MODEL | NOBS | ESTIMATOR | NPAR | Chi2(24) | p (Chi2) |  CFI  |  TLI  | RMSEA
#> -----------------------------------------------------------------------------
#> MLR   | 301  |    MLR    |  21  |  87.13   |  < .001  | 0.925 | 0.888 | 0.093
#> ULSM  | 301  |   ULSM    |  21  |  90.60   |  < .001  | 0.931 | 0.897 | 0.096
#> 
#> MODEL |   RMSEA  CI    | SRMR 
#> ------------------------------
#> MLR   | [0.073, 0.115] | 0.065
#> ULSM  | [0.073, 0.120] | 0.059

Step 4: Ordinal example with WLSMV (ordered = TRUE)

This example converts the nine Holzinger-Swineford items (x1 to x9) into four ordered categories, then fits the same CFA model with WLSMV.

item_names <- paste0("x", 1:9)
ordered_data <- HolzingerSwineford1939

ordered_data[item_names] <- lapply(
  ordered_data[item_names],
  function(x) ordered(cut(x, breaks = 4, include.lowest = TRUE))
)

fit_wlsmv <- cfa(
  model,
  data = ordered_data,
  estimator = "WLSMV",
  ordered = TRUE
)

model_fit(fit_wlsmv)
#> NOBS | ESTIMATOR | NPAR | Chi2(24) | p (Chi2) |  CFI  |  TLI  | RMSEA
#> ---------------------------------------------------------------------
#> 301  |   WLSMV   |  39  |  63.89   |  < .001  | 0.969 | 0.954 | 0.074
#> 
#> NOBS |   RMSEA  CI    | SRMR 
#> -----------------------------
#> 301  | [0.053, 0.097] | 0.066
compare_model_fit(MLR = fit_mlr, WLSMV = fit_wlsmv)
#> MODEL | NOBS | ESTIMATOR | NPAR | Chi2(24) | p (Chi2) |  CFI  |  TLI  | RMSEA
#> -----------------------------------------------------------------------------
#> MLR   | 301  |    MLR    |  21  |  87.13   |  < .001  | 0.925 | 0.888 | 0.093
#> WLSMV | 301  |   WLSMV   |  39  |  63.89   |  < .001  | 0.969 | 0.954 | 0.074
#> 
#> MODEL |   RMSEA  CI    | SRMR 
#> ------------------------------
#> MLR   | [0.073, 0.115] | 0.065
#> WLSMV | [0.053, 0.097] | 0.066

Common pitfalls

  • When using robust estimators, metric names may map to scaled/robust variants.
  • Keep model names explicit (MLR, ULSM, etc.) for clearer comparison tables.
  • This ordinal recoding is only a didactic example; use substantively justified category definitions in real analyses.

Next steps