CODEWITHSUNDEEP
rmathematical-optimizationr-lavaan
Boxingday115
Boxingday115

Reputation: 1

Robust estimators for lavaan::cfa fails to converge (data strongly violates multivariate normality)

Problem Introduction Hi everyone,

I’m working with a clean dataset of N = 724 participants who completed a personality test based on the HEXACO model. The test is designed to measure 24 sub-components that combine into 6 main personality traits, with around 15-16 questions per sub-component.

I'm performing a Confirmatory Factor Analysis (CFA) to validate the constructs, but I’ve encountered a significant issue: my data strongly deviates from multivariate normality (HZ = 1.000, p < 0.001). This deviation suggests that a standard CFA approach won’t work, so I need an estimator that can handle non-normal data. I’m using lavaan::cfa() in R for the analysis.

From my research, I found that Maximum Likelihood Estimation with Robustness (MLR) is often recommended for such cases. However, since I’m new to this, I’d appreciate any advice on whether MLR is the best option or if there are better alternatives. Additionally, my model has trouble converging, which makes me wonder if I need a different estimator or if there’s another issue with my approach.

Data details The response scale ranges from -5 to 5. Although ordinal data (like Likert scales) is usually treated as non-continuous, I’ve read that when the range is wider (e.g., -5 to 5), treating it as continuous is sometimes appropriate. I’d like to confirm if this is valid for my data.

During data cleaning, I removed participants who displayed extreme response styles (e.g., more than 50% of their answers were at the scale’s extremes or at the midpoint).

In summary, I have two questions:

Thanks in advance for any advice!

Once again, I’m running a CFA using lavaan::cfa() with estimator = "MLR", but the model has convergence issues.

Model Call The model call:

first_order_fit <- cfa(first_order_model, 
                       data = final_model_data, 
                       estimator = "MLR", 
                       verbose = TRUE)

Model Syntax The syntax for the "first_order_model" follows the lavaan style definition:

first_order_model <- '
    a_flexibility =~ Q239 + Q274 + Q262 + Q183
    a_forgiveness =~ Q200 + Q271 + Q264 + Q222
    a_gentleness =~ Q238 + Q244 + Q272 + Q247
    a_patience =~ Q282 + Q253 + Q234 + Q226
    c_diligence =~ Q267 + Q233 + Q195 + Q193
    c_organization =~ Q260 + Q189 + Q275 + Q228
    c_perfectionism =~ Q249 + Q210 + Q263 + Q216 + Q214
    c_prudence =~ Q265 + Q270 + Q254 + Q259
    e_anxiety =~ Q185 + Q202 + Q208 + Q243 + Q261
    e_dependence =~ Q273 + Q236 + Q279 + Q211 + Q204
    e_fearfulness =~ Q217 + Q221 + Q213 + Q205
    e_sentimentality =~ Q229 + Q251 + Q237 + Q209
    h_fairness =~ Q277 + Q192 + Q219 + Q203
    h_greed_avoidance =~ Q188 + Q215 + Q255 + Q231
    h_modesty =~ Q266 + Q206 + Q258 + Q207
    h_sincerity =~ Q199 + Q223 + Q225 + Q240
    o_aesthetic_appreciation =~ Q196 + Q268 + Q281
    o_creativity =~ Q212 + Q191 + Q194 + Q242 + Q256
    o_inquisitivness =~ Q278 + Q246 + Q280 + Q186
    o_unconventionality =~ Q227 + Q235 + Q250 + Q201
    x_livelyness =~ Q220 + Q252 + Q276 + Q230
    x_sociability =~ Q218 + Q224 + Q241 + Q232
    x_social_boldness =~ Q184 + Q197 + Q190 + Q187 + Q245
    x_social_self_esteem =~ Q198 + Q269 + Q248 + Q257
'

Note I did not assign any starting value or fixed any of the covariances.

Convergence Status The relative convergence (4) status indicates that after 4 attempts (2439 iterations), the model reached a solution but it was not stable. In my case, the model keeps processing endlessly:

convergence status (0=ok): 0 nlminb message says: relative convergence (4) number of iterations: 2493 number of function evaluations [objective, gradient]: 3300 2494 lavoptim ... done. lavimplied ... done. lavloglik ... done. lavbaseline ...

Sample Data You can generate similar data using this code:

set.seed(123)

n_participants <- 200
n_questions <- 100

sample_data <- data.frame(
    matrix(
        sample(-5:5, n_participants * n_questions, replace = TRUE), 
        nrow = n_participants, 
        ncol = n_questions
    )
)

colnames(sample_data) <- paste0("Q", 183:282)

Assumption of multivariate normality

To test for multivariate normality, I used: mvn_result <- mvn(data = sample_data, mvnTest = "mardia", multivariatePlot = "qq")

For a formal test: mvn_result_hz <- mvn(data = final_model_data, mvnTest = "hz")

Upvotes: 0

Views: 60

Answers (1)

benimwolfspelz
benimwolfspelz

Reputation: 690

So the principal issue you want to solve is the nonconvergence, right?

A common approach with complex statistical models is to (1.) vary options passed to the optimizier and/or (2.) try other optimiziers (i.e. fitting algorithms).

The default optimizer in lavaan::cfa() is "nlminb" and you can change its default options by adding a list of options to your call to cfa like this:

first_order_fit <- cfa(first_order_model, 
                       data = final_model_data, 
                       estimator = "MLR", 
                       verbose = TRUE,
                       control = list(iter.max = 500,
                                      rel.tol = 1e-9))

See the nlminb help page to find out what options you have and what their defaults are. My first try would be to increase iter.max and maybe slightly increase rel.tol (i.e. make it a slightly less tiny number), as shown above.

If you cannot get convergence (or do get convergence but the estimates are absurd), then you may want to try using another optimizer.

To do this, try the following code:

first_order_fit <- cfa(first_order_model, 
                       data = final_model_data, 
                       estimator = "MLR", 
                       verbose = TRUE,
                       optim.method = "BFGS", # or "L-BFGS-B"
                       )

Again, you can try different options for these optimiziers by adding a control = list(...). Be aware that the options available and their names may differ.

Upvotes: 0

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