, Robert Mai [ctb]
| Title: | Flexible Cutoffs for Model Fit Evaluation in Covariance-Based Structural Models |
|---|---|
| Description: | A toolbox to derive flexible cutoffs for fit indices in 'Covariance-based Structural Equation Modeling' based on the paper by 'Niemand & Mai (2018)' <doi:10.1007/s11747-018-0602-9>. Flexible cutoffs are an alternative to fixed cutoffs - rules-of-thumb - regarding an appropriate cutoff for fit indices such as 'CFI' or 'SRMR'. It has been demonstrated that these flexible cutoffs perform better than fixed cutoffs in grey areas where misspecification is not easy to detect. The package provides an alternative to the tool at <https://flexiblecutoffs.org> as it allows to tailor flexible cutoffs to a given dataset and model, which is so far not available in the tool. The package simulates fit indices based on a given dataset and model and then estimates the flexible cutoffs. Some useful functions, e.g., to determine the 'GoF-' or 'BoF-nature' of a fit index, are provided. So far, additional options for a relative use (is a model better than another?) are provided in an exploratory manner. |
| Authors: | Thomas Niemand [aut, cre]
, Robert Mai [ctb]
|
| Maintainer: | Thomas Niemand <[email protected]> |
| License: | GPL (>= 3) |
| Version: | 0.8.0 |
| Built: | 2025-01-29 06:10:38 UTC |
| Source: | https://github.com/thomasniemand/fco |
Data from Babakus & Boller (1992) who investigated the dimensionality of the SERVQUAL scale based on a sample of N = 502. The data is available as a data.frame (simulated via mvrnorm in package MASS based on the correlation matrix provided by the authors) and used in the vignette.
data(bb1992)data(bb1992)
A data.frame of 22 variables (Q1-Q22) with 502 observations
Provided in paper
Babakus, E., & Boller, G. W. (1992). An empirical assessment of the SERVQUAL scale. Journal of Business Research, 24(3), 253–268. https://doi.org/10.1016/0148-2963(92)90022-4
data(bb1992) head(bb1992, 3)data(bb1992) head(bb1992, 3)
Obtain flexible cutoffs for one or two models
flex_co(fits, index, alpha.lev = 0.05, gof = NULL)flex_co(fits, index, alpha.lev = 0.05, gof = NULL)
fits |
A list of simulated fit indices obtained from gen_fit. Based on the structure of fits, the number of models is derived. |
index |
A vector of fit indices or measures provided by function fitmeasures in package lavaan |
alpha.lev |
The predefined uncertainty For example, if the default uncertainty of .05 (5 percent) is accepted a-priori, the 5 percent stats::quantile (of type 8, see ?stats::quantile) of the simulated distribution for correctly specified CFA models with the given model and sample characteristics determines the flexible cutoff. Options are .001, .01, .05, and .10. Higher values are more conservative. |
gof |
An optional vector as to whether the indices are GoF (Goodness-of-Fit index)? If TRUE, a GoF is assumed. If FALSE, a BoF is assumed. Depending on the nature of the underlying fit index, the appropriate lower (GoF) or upper (BoF) width of the respective confidence interval as defined by the stats::quantile is used to derive the flexible cutoff. If not provided or not equal to the number of fit indices, the function guesses the type for known fit indices (e.g., SRMR is a BoF). |
A list of information regarding the selected fit index providing its flexible cutoff for the given parameters.
#Note: Demonstration only! Please use higher numbers of replications for your applications (>= 500). #A single model to obtain fit indices for mod <- " F1 =~ Q5 + Q7 + Q8 F2 =~ Q2 + Q4 F3 =~ Q10 + Q11 + Q12 + Q13 + Q18 + Q19 + Q20 + Q21 + Q22 F4 =~ Q1 + Q17 F5 =~ Q6 + Q14 + Q15 + Q16 " fits.single <- gen_fit(mod1 = mod, x = bb1992, rep = 10, standardized = FALSE) flex_co(fits = fits.single, index = c("CFI", "SRMR")) #Two models, an unconstrained and a constrained model to compare fit indices mod.con <- " F1 =~ Q5 + Q7 + Q8 F2 =~ Q2 + Q4 F3 =~ Q10 + Q11 + Q12 + Q13 + Q18 + Q19 + Q20 + Q21 + Q22 F4 =~ Q1 + Q17 F5 =~ Q6 + Q14 + Q15 + Q16 F1 ~~ 0 * F2 " fits.con <- gen_fit( mod1 = mod, mod2 = mod.con, x = bb1992, rep = 10 ) flex_co(fits = fits.con, index = c("CFI", "SRMR"), alpha.lev = .05) #Two models for discriminant validity testing, this resembles constraining with a cutoff of .9 fits.dv.con <- gen_fit( mod1 = mod, x = bb1992, rep = 10, dv = TRUE, dv.factors = c("F4", "F5"), dv.cutoff = .9 ) flex_co(fits = fits.dv.con, index = "CFI", alpha.lev = .05) mod.dv.con <- " F1 =~ Q5 + Q7 + Q8 F2 =~ Q2 + Q4 F3 =~ Q10 + Q11 + Q12 + Q13 + Q18 + Q19 + Q20 + Q21 + Q22 F4 =~ Q1 + Q17 F5 =~ Q6 + Q14 + Q15 + Q16 F4 ~~ .9 * F5 " lavaan::fitmeasures( lavaan::cfa( model = mod.dv.con, data = bb1992, auto.fix.first = FALSE, std.lv = TRUE ), fit.measures = "cfi" ) #Two models for discriminant validity testing, this resembles merging. fits.dv.merge <- gen_fit( mod1 = mod, x = bb1992, rep = 10, dv = TRUE, dv.factors = c("F4", "F5"), merge.mod = TRUE) flex_co(fits = fits.dv.merge, index = "CFI", alpha.lev = .05) mod.dv.merge <- " F1 =~ Q5 + Q7 + Q8 F2 =~ Q2 + Q4 F3 =~ Q10 + Q11 + Q12 + Q13 + Q18 + Q19 + Q20 + Q21 + Q22 F4 =~ Q1 + Q17 + Q6 + Q14 + Q15 + Q16 " lavaan::fitmeasures( lavaan::cfa( model = mod.dv.merge, data = bb1992 ), fit.measures = "cfi" )#Note: Demonstration only! Please use higher numbers of replications for your applications (>= 500). #A single model to obtain fit indices for mod <- " F1 =~ Q5 + Q7 + Q8 F2 =~ Q2 + Q4 F3 =~ Q10 + Q11 + Q12 + Q13 + Q18 + Q19 + Q20 + Q21 + Q22 F4 =~ Q1 + Q17 F5 =~ Q6 + Q14 + Q15 + Q16 " fits.single <- gen_fit(mod1 = mod, x = bb1992, rep = 10, standardized = FALSE) flex_co(fits = fits.single, index = c("CFI", "SRMR")) #Two models, an unconstrained and a constrained model to compare fit indices mod.con <- " F1 =~ Q5 + Q7 + Q8 F2 =~ Q2 + Q4 F3 =~ Q10 + Q11 + Q12 + Q13 + Q18 + Q19 + Q20 + Q21 + Q22 F4 =~ Q1 + Q17 F5 =~ Q6 + Q14 + Q15 + Q16 F1 ~~ 0 * F2 " fits.con <- gen_fit( mod1 = mod, mod2 = mod.con, x = bb1992, rep = 10 ) flex_co(fits = fits.con, index = c("CFI", "SRMR"), alpha.lev = .05) #Two models for discriminant validity testing, this resembles constraining with a cutoff of .9 fits.dv.con <- gen_fit( mod1 = mod, x = bb1992, rep = 10, dv = TRUE, dv.factors = c("F4", "F5"), dv.cutoff = .9 ) flex_co(fits = fits.dv.con, index = "CFI", alpha.lev = .05) mod.dv.con <- " F1 =~ Q5 + Q7 + Q8 F2 =~ Q2 + Q4 F3 =~ Q10 + Q11 + Q12 + Q13 + Q18 + Q19 + Q20 + Q21 + Q22 F4 =~ Q1 + Q17 F5 =~ Q6 + Q14 + Q15 + Q16 F4 ~~ .9 * F5 " lavaan::fitmeasures( lavaan::cfa( model = mod.dv.con, data = bb1992, auto.fix.first = FALSE, std.lv = TRUE ), fit.measures = "cfi" ) #Two models for discriminant validity testing, this resembles merging. fits.dv.merge <- gen_fit( mod1 = mod, x = bb1992, rep = 10, dv = TRUE, dv.factors = c("F4", "F5"), merge.mod = TRUE) flex_co(fits = fits.dv.merge, index = "CFI", alpha.lev = .05) mod.dv.merge <- " F1 =~ Q5 + Q7 + Q8 F2 =~ Q2 + Q4 F3 =~ Q10 + Q11 + Q12 + Q13 + Q18 + Q19 + Q20 + Q21 + Q22 F4 =~ Q1 + Q17 + Q6 + Q14 + Q15 + Q16 " lavaan::fitmeasures( lavaan::cfa( model = mod.dv.merge, data = bb1992 ), fit.measures = "cfi" )
Obtain fit statistics from one or two models
gen_fit( mod1 = NULL, mod2 = NULL, x = NULL, n = NULL, rep = 500, type = "NM", dv = FALSE, dv.factors = NULL, merge.mod = FALSE, dv.cutoff = 0.9, standardized = TRUE, assume.mvn = TRUE, multi.core = TRUE, cores = 2, seed = 1111, pop.mod1 = NULL, pop.mod2 = NULL )gen_fit( mod1 = NULL, mod2 = NULL, x = NULL, n = NULL, rep = 500, type = "NM", dv = FALSE, dv.factors = NULL, merge.mod = FALSE, dv.cutoff = 0.9, standardized = TRUE, assume.mvn = TRUE, multi.core = TRUE, cores = 2, seed = 1111, pop.mod1 = NULL, pop.mod2 = NULL )
mod1 |
A lavaan model to specify the CFA. |
mod2 |
Another lavaan model for a model comparison. If missing and merge.mod = TRUE, a merged model from function merge_factors is estimated based on mod1. |
x |
A dataset for the model of nrow observations (minimum: 50) and ncol indicators (minimum: 4) |
n |
A sample size specified instead of a dataset (minimum: 50, maximum: 50000). Requires a population model via pop.mod1. |
rep |
Number of replications to be simulated (default: 500, minimum: 10, maximum: 5000) |
type |
Type of underlying population model. Based on the model(s) provided, a population model is derived to simulate the fit indices by function pop_mod. The type determines the factor loadings and covariances assumed for this population model. NM (the default when only one model is provided): Uses the factor loadings and covariances from Niemand & Mai's (2018) simulation study. HB: Uses the factor loadings and covariances from Hu & Bentler's (1999) simulation study. EM: Empirical (the default when two models are provided or merge.mod is TRUE), uses the given factor loadings and covariances. |
dv |
Should the fit statistics be calculated for discriminant validity testing? If no (the default), this is not assumed. If yes, consider the arguments of merge.mod, dv.factors and cutoff. So far, two options of discriminant validity testing are supported. Constraining: A factor correlation between two factors can be constrained as selected by the dv.factors argument. In this case, dv.cutoff applies and merge.mod is not required. Merging: Two factors can be merged into one, again controlled by the dv.factors argument. In this case, merge.mod applies and dv.cutoff is not required (as cutoff = 1 is implied). |
dv.factors |
Names of the factors to be considered. Must be equal to 2. If missing (the default), the first and second factor of the model are selected. |
merge.mod |
This is used for merging. If FALSE (the default), fit measures for mod1 are estimated for a single model as long as no mod2 is provided. If TRUE, a merged model from function merge_factors is estimated based on mod1. In this case, no mod2 is required. |
dv.cutoff |
This is used for constraining. It determines the critical correlation assumed to be a cutoff for discriminant validity testing. For example, based on Rönkkö & Cho (2020), a cutoff of .9 indicates a severe issue in discriminant validity between the selected factors. Cutoffs between .8 and 1 are recommended. The function returns a warning, if the cutoff is below .8. |
standardized |
Are factor loadings assumed to be standardized and covariances to be correlations (default: TRUE)? |
assume.mvn |
Should multivariate normality (mvn) be assumed? If TRUE (the default), kurtosis and skewness are set to 1 for simulated data. If FALSE, kurtosis and skewness are estimated from dataset x via semTools::mardiaKurtosis and semTools::mardiaSkew. |
multi.core |
Should multiple cores be used to simulate fit indices? If TRUE (the default), mclapply (on Linux or Mac machines) or parLapply (on Windows machines) from parallel package with the number of specified cores is used. If FALSE, a single core is used. |
cores |
How many cores should be used for multiple cores? The default is 2. Consider the available number of cores of your system. |
seed |
The seed to be set to obtain reproducible cutoffs (default: 1111). Defines a vector of length rep with the seed being the first value. |
pop.mod1 |
For flexibility reasons, an optional lavaan population model can be provided. This is required together with n if x is missing. |
pop.mod2 |
Another optional lavaan population model. |
A list of simulated fit statistics (fco) and all previously defined parameters.
Hu, L., & Bentler, P. M. (1999). Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives. Structural Equation Modeling, 6(1), 1–55. https://doi.org/10.1080/10705519909540118
Niemand, T., & Mai, R. (2018). Flexible cutoff values for fit indices in the evaluation of structural equation models. Journal of the Academy of Marketing Science, 46(6), 1148—1172. https://doi.org/10.1007/s11747-018-0602-9
Rönkkö, M., & Cho, E. (2020). An updated guideline for assessing discriminant validity. Organizational Research Methods. https://doi.org/10.1177/1094428120968614
#Note: Demonstration only! Please use higher numbers of replications for your applications (>= 500). #A single model to obtain fit indices for mod <- " F1 =~ Q5 + Q7 + Q8 F2 =~ Q2 + Q4 F3 =~ Q10 + Q11 + Q12 + Q13 + Q18 + Q19 + Q20 + Q21 + Q22 F4 =~ Q1 + Q17 F5 =~ Q6 + Q14 + Q15 + Q16 " fits.single <- gen_fit(mod1 = mod, x = bb1992, rep = 10, standardized = FALSE) #Two models, an unconstrained and a constrained model to compare fit indices mod.con <- " F1 =~ Q5 + Q7 + Q8 F2 =~ Q2 + Q4 F3 =~ Q10 + Q11 + Q12 + Q13 + Q18 + Q19 + Q20 + Q21 + Q22 F4 =~ Q1 + Q17 F5 =~ Q6 + Q14 + Q15 + Q16 F1 ~~ 0 * F2 " fits.con <- gen_fit( mod1 = mod, mod2 = mod.con, x = bb1992, rep = 10 ) #Two models for discriminant validity testing, this resembles constraining with a cutoff of .9 fits.dv.con <- gen_fit( mod1 = mod, x = bb1992, rep = 10, dv = TRUE, dv.factors = c("F4", "F5"), dv.cutoff = .9 ) #Two models for discriminant validity testing, this resembles merging. fits.dv.merge <- gen_fit( mod1 = mod, x = bb1992, rep = 10, dv = TRUE, dv.factors = c("F4", "F5"), merge.mod = TRUE )#Note: Demonstration only! Please use higher numbers of replications for your applications (>= 500). #A single model to obtain fit indices for mod <- " F1 =~ Q5 + Q7 + Q8 F2 =~ Q2 + Q4 F3 =~ Q10 + Q11 + Q12 + Q13 + Q18 + Q19 + Q20 + Q21 + Q22 F4 =~ Q1 + Q17 F5 =~ Q6 + Q14 + Q15 + Q16 " fits.single <- gen_fit(mod1 = mod, x = bb1992, rep = 10, standardized = FALSE) #Two models, an unconstrained and a constrained model to compare fit indices mod.con <- " F1 =~ Q5 + Q7 + Q8 F2 =~ Q2 + Q4 F3 =~ Q10 + Q11 + Q12 + Q13 + Q18 + Q19 + Q20 + Q21 + Q22 F4 =~ Q1 + Q17 F5 =~ Q6 + Q14 + Q15 + Q16 F1 ~~ 0 * F2 " fits.con <- gen_fit( mod1 = mod, mod2 = mod.con, x = bb1992, rep = 10 ) #Two models for discriminant validity testing, this resembles constraining with a cutoff of .9 fits.dv.con <- gen_fit( mod1 = mod, x = bb1992, rep = 10, dv = TRUE, dv.factors = c("F4", "F5"), dv.cutoff = .9 ) #Two models for discriminant validity testing, this resembles merging. fits.dv.merge <- gen_fit( mod1 = mod, x = bb1992, rep = 10, dv = TRUE, dv.factors = c("F4", "F5"), merge.mod = TRUE )
Helper function that guesses GoF or BoF from a given index name
index_guess(index)index_guess(index)
index |
A fit index or measure provided by function fitmeasures in package lavaan |
Returns GoF (Goodness-of-Fit index) or BoF (Badness of Fit index).
index_guess("cfi") index_guess("tli") index_guess("rmsea") index_guess("srmr")index_guess("cfi") index_guess("tli") index_guess("rmsea") index_guess("srmr")
Helper function to obtain population model for simulation based on data and model
pop_mod(mod, x, type = "NM", standardized = TRUE, afl = 0.7, aco = 0.3)pop_mod(mod, x, type = "NM", standardized = TRUE, afl = 0.7, aco = 0.3)
mod |
A lavaan model (only CFA supported so far) |
x |
A dataset for the model of nrow observations (minimum: 50) and ncol indicators (minimum: 4) |
type |
Type of population model. NM (the default): Uses the factor loadings and covariances from Niemand & Mai's (2018) simulation study. HB: Uses the factor loadings and covariances from Hu & Bentler's (1999) simulation study. EM: Empirical, uses the given factor loadings and covariances. EM is not recommended for confirmative use as it leads to the least generalizable cutoffs. |
standardized |
Are factor loadings assumed to be standardized and covariances to be correlations (default: TRUE)? |
afl |
Average factor loading of indicators per factor, only relevant for type = "NM" (default: .7). |
aco |
Average correlation between factors, only relevant for type = "NM" (default: .3). |
List of population model type, standardized, average factor loading and average correlation. All values are round to three decimals.
mod <- " F1 =~ Q5 + Q7 + Q8 F2 =~ Q2 + Q4 F3 =~ Q10 + Q11 + Q12 + Q13 + Q18 + Q19 + Q20 + Q21 + Q22 F4 =~ Q1 + Q17 F5 =~ Q6 + Q14 + Q15 + Q16 " pop_mod(mod, x = bb1992, type = "NM")$pop.mod pop_mod(mod, x = bb1992, type = "HB")$pop.mod pop_mod(mod, x = bb1992, type = "EM")$pop.mod pop_mod(mod, x = bb1992, type = "NM", afl = .9)$pop.mod pop_mod(mod, x = bb1992, type = "NM", aco = .5)$pop.mod pop_mod(mod, x = bb1992, type = "EM", standardized = FALSE)$pop.modmod <- " F1 =~ Q5 + Q7 + Q8 F2 =~ Q2 + Q4 F3 =~ Q10 + Q11 + Q12 + Q13 + Q18 + Q19 + Q20 + Q21 + Q22 F4 =~ Q1 + Q17 F5 =~ Q6 + Q14 + Q15 + Q16 " pop_mod(mod, x = bb1992, type = "NM")$pop.mod pop_mod(mod, x = bb1992, type = "HB")$pop.mod pop_mod(mod, x = bb1992, type = "EM")$pop.mod pop_mod(mod, x = bb1992, type = "NM", afl = .9)$pop.mod pop_mod(mod, x = bb1992, type = "NM", aco = .5)$pop.mod pop_mod(mod, x = bb1992, type = "EM", standardized = FALSE)$pop.mod
This function recommends pre-defined selected fit indices in case the user does not know which fit index should be used for model evaluation. Results may differ based on three settings, the sample size of the data, the research purpose of the investigated model and the focus of the model. For obvious reasons, this function only works for single models and does not accept any other model type.
recommend( fits, purpose = "novel", focus = "cfa", override = FALSE, index = NULL, digits = 3 )recommend( fits, purpose = "novel", focus = "cfa", override = FALSE, index = NULL, digits = 3 )
fits |
A list of simulated fit indices obtained from gen_fit. Based on the structure of fits, the number of models is derived. |
purpose |
The research purpose of the model investigated. Is the underlying model novel (default) or established (= established). This parameter is relevant to find the proper recommended fit indices. |
focus |
The focus of estimation for the model. Is the focus on CFA (default) or analyzing the structural model of a theoretical model (= structural)? This parameter is relevant to find the proper recommended fit indices. |
override |
Should the recommendations by Mai et al. (2021) overridden (default: FALSE)? This may be useful to explore models outside of the scope of the paper. In this case, the recommended fit indices are not determined by the function, and hence need to be provided. In this case, the function requires the argument index. |
index |
An optional vector of fit indices or measures provided by function fitmeasures in package lavaan. This argument is required when override is TRUE. It is ignored otherwise. |
digits |
An optional integer to round fit values and cutoffs (min: 1, max: 5). |
A list of information regarding the recommended fit indices based on Mai et al. (2021) or when overridden, based on the provided indices.
Mai, R., Niemand, T., & Kraus, S. (2021). A Tailor-Fit Model Evaluation Strategy for Better Decisions about Structural Equation Models, Technological Forecasting & Social Change, 173(December) 121142. https://doi.org/10.1016/j.techfore.2021.121142
#Note: Demonstration only! Please use higher numbers of replications for your applications (>= 500). mod <- " F1 =~ Q5 + Q7 + Q8 F2 =~ Q2 + Q4 F3 =~ Q10 + Q11 + Q12 + Q13 + Q18 + Q19 + Q20 + Q21 + Q22 F4 =~ Q1 + Q17 F5 =~ Q6 + Q14 + Q15 + Q16 " fits.single <- gen_fit(mod1 = mod, x = bb1992, rep = 10, standardized = FALSE) recommend(fits.single) recommend(fits.single, purpose = "established") recommend(fits.single, override = TRUE, index = c("CFI", "SRMR"))#Note: Demonstration only! Please use higher numbers of replications for your applications (>= 500). mod <- " F1 =~ Q5 + Q7 + Q8 F2 =~ Q2 + Q4 F3 =~ Q10 + Q11 + Q12 + Q13 + Q18 + Q19 + Q20 + Q21 + Q22 F4 =~ Q1 + Q17 F5 =~ Q6 + Q14 + Q15 + Q16 " fits.single <- gen_fit(mod1 = mod, x = bb1992, rep = 10, standardized = FALSE) recommend(fits.single) recommend(fits.single, purpose = "established") recommend(fits.single, override = TRUE, index = c("CFI", "SRMR"))
This function recommends on potential issues for discriminant validity testing, based on differences between fit values and differences between flexible cutoffs. Two approaches of testing are supported: merging and constraining.
recommend_dv(fits, index = "CFI", digits = 3)recommend_dv(fits, index = "CFI", digits = 3)
fits |
A list of simulated fit indices obtained from gen_fit. Based on the structure of fits, the number of models is derived. |
index |
A vector of fit indices or measures provided by function fitmeasures in package lavaan. The default is set to CFI. |
digits |
An optional integer to round fit values and cutoffs (min: 1, max: 5). |
A list of information regarding discriminant validity testing.
#Note: Demonstration only! Please use higher numbers of replications for your applications (>= 500). mod <- " F1 =~ Q5 + Q7 + Q8 F2 =~ Q2 + Q4 F3 =~ Q10 + Q11 + Q12 + Q13 + Q18 + Q19 + Q20 + Q21 + Q22 F4 =~ Q1 + Q17 F5 =~ Q6 + Q14 + Q15 + Q16 " #Two models for discriminant validity testing, this resembles constraining with a cutoff of .9 fits.dv.con <- gen_fit( mod1 = mod, x = bb1992, rep = 10, dv = TRUE, dv.factors = c("F4", "F5"), dv.cutoff = .9 ) recommend_dv(fits.dv.con) #Two models for discriminant validity testing, this resembles merging. fits.dv.merge <- gen_fit( mod1 = mod, x = bb1992, rep = 10, dv = TRUE, dv.factors = c("F4", "F5"), merge.mod = TRUE ) recommend_dv(fits.dv.merge)#Note: Demonstration only! Please use higher numbers of replications for your applications (>= 500). mod <- " F1 =~ Q5 + Q7 + Q8 F2 =~ Q2 + Q4 F3 =~ Q10 + Q11 + Q12 + Q13 + Q18 + Q19 + Q20 + Q21 + Q22 F4 =~ Q1 + Q17 F5 =~ Q6 + Q14 + Q15 + Q16 " #Two models for discriminant validity testing, this resembles constraining with a cutoff of .9 fits.dv.con <- gen_fit( mod1 = mod, x = bb1992, rep = 10, dv = TRUE, dv.factors = c("F4", "F5"), dv.cutoff = .9 ) recommend_dv(fits.dv.con) #Two models for discriminant validity testing, this resembles merging. fits.dv.merge <- gen_fit( mod1 = mod, x = bb1992, rep = 10, dv = TRUE, dv.factors = c("F4", "F5"), merge.mod = TRUE ) recommend_dv(fits.dv.merge)