Aggregate similar constructs/ FA with binary variables - r

Question

I would like to aggregate, in order to reduce the number of constructs, its following data frame containing only binary variables that correspond to "yes/no", its following data frame (first 10 row). The original data frame contains 169 rows.
outcome <-
structure(list(Q9_Automazione.processi = c(0, 0, 0, 0, 0, 0,
1, 1, 1, 0), Q9_Velocita.Prod = c(1, 0, 0, 1, 0, 0, 1, 1, 1,
0), Q9_Flessibilita.Prod = c(0, 0, 0, 1, 0, 0, 1, 1, 0, 1), Q9_Controllo.processi = c(0,
0, 0, 1, 0, 0, 1, 1, 0, 0), Q9_Effic.Magazzino = c(0, 0, 0, 1,
0, 0, 0, 0, 0, 0), Q9_Riduz.Costi = c(0, 1, 0, 0, 0, 0, 0, 0,
0, 1), Q9_Miglior.Sicurezza = c(0, 0, 0, 0, 0, 0, 1, 0, 1, 1),
Q9_Connett.Interna = c(0, 0, 0, 0, 0, 0, 0, 1, 1, 0), Q9_Connett.Esterna = c(0,
0, 0, 0, 0, 0, 0, 0, 0, 0), Q9_Virtualizzazione = c(0, 0,
0, 0, 0, 0, 0, 0, 0, 0), Q9_Innov.Prod = c(0, 0, 0, 0, 0,
1, 0, 0, 0, 1), Q9_Person.Prod = c(0, 1, 0, 1, 0, 1, 0, 0,
0, 1), Q9_Nuovi.Mercati = c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0),
Q9_Nuovi.BM = c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0), Q9_Perform.Energ = c(0,
0, 0, 0, 0, 0, 0, 0, 0, 0), Q9_Perform.SostAmb = c(0, 0,
0, 0, 0, 0, 0, 0, 0, 0)), row.names = c(NA, 10L), class = "data.frame")
I have tried performing factor analysis via the tethracoric method on the obtained correlation matrix ( the obtained value from the KMO function turns out to be inadequate) both directly on the dataframe and then using tethracoric correletions in fafunction (using cor = "tet" I get a negative Tucker Lewis Index).
I have been reading up on this but cannot find a methodology that is adequate and of which I am certain of the correctness of the analysis.
So basically what I would like to achieve is to aggregate similar constructs, e.g., assess whether column 5 has value 1 (i.e., "yes") almost always when column 11 has value 1 and then aggregate.
Here the code that I try to used
library(psych)
tet <- tetrachoric(outcome)
corrplot(tet$rho, "ellipse", tl.cex = 0.75, tl.col = "black")
par(mfrow = c(1,2))
corr_matrix %>%
ggcorrplot(show.diag = F,
type="lower",
lab=TRUE,
lab_size=2)
KMO(corr_matrix)
cortest.bartlett(corr_matrix)
fa.parallel(corr_matrix, fm = "ml")
factor <- fa(corr_matrix, nfactors = 3, rotate = "oblimin", fm = "ml")
print(factor, cut = 0.3, digits = 3)
# -------- Pearson --------
cor(outcome, method = 'pearson', use = "pairwise.complete.obs") %>%
ggcorrplot(show.diag = F,
type="lower",
lab=TRUE,
lab_size=2)
KMO(outcome)
cortest.bartlett(outcome)
fa.parallel(outcome)
factor1 <- fa(outcome, nfactors = 3, rotate = "oblimin", cor = "tet", fm = "ml")
print(factor1, cut = 0.3, digits = 3)