The purpose of this analysis is to re-run the DETECT analyses on a set of younger and older participants. If the unidimensional structure of the data in the full dataset is a consequence of mutualism, we would expect this data to intiially be multidimensional and then become unidimensional.

options(max.print=500)
library(wordbankr) # WB data
library(tidyverse) # tidy
library(psych) # some psychometric stuff (tests of dimensionality)
library(knitr) # some formatting, tables, etc
library(sirt) # additional IRT functions
library(vegan)

1 Data Preparation

Inst <- get_instrument_data(language="English (American)", form="WS")
Admin <- get_administration_data(language="English (American)", form="WS", original_ids=TRUE)
N_total = nrow(Admin) # making sure things add up later
N_long = nrow(filter(Admin, longitudinal==TRUE)) # making sure things add up later
Item <- get_item_data(language="English (American)", form = "WS")
Younger <- Admin %>%
  filter(longitudinal==TRUE) %>%
  filter(age < 20)

N_Younger = nrow(Younger) 


Older <- Admin %>%
  filter(longitudinal==TRUE) %>%
  filter(age > 20)

N_Older = nrow(Older)

1.1 Make Younger Dataset

1.1.1 Complexity

Younger_Complex <- Younger %>%
  left_join(.,Inst, by="data_id") %>%
  left_join(., Item, by="num_item_id") %>%
  filter(type == "combine" | # to drop non-combiners
           type == "complexity" # to calculate complexity scores.
         ) %>%
  mutate(
    out = ifelse(value=="complex" | value=="sometimes" | value=="produces", yes=1, 
                 no = ifelse(value=="often", yes=2, no =0))
  ) 

N_complexity_items = nrow(filter(Item, type == "combine" | 
           type == "complexity"))

nrow(Younger_Complex) == N_Younger*N_complexity_items #Not yet updated
## [1] TRUE
Older_Complex <- Older %>%
  left_join(.,Inst, by="data_id") %>%
  left_join(., Item, by="num_item_id") %>%
  filter(type == "combine" | # to drop non-combiners
           type == "complexity" # to calculate complexity scores.
         ) %>%
  mutate(
    out = ifelse(value=="complex" | value=="sometimes" | value=="produces", yes=1, 
                 no = ifelse(value=="often", yes=2, no =0))
  ) 

N_complexity_items = nrow(filter(Item, type == "combine" | 
           type == "complexity"))

nrow(Older_Complex) == N_Older*N_complexity_items #Not yet updated
## [1] TRUE
Younger_Complex$complexity_category <- ifelse(Younger_Complex$complexity_category == "", yes=Younger_Complex$type, no=Younger_Complex$complexity_category)
Older_Complex$complexity_category <- ifelse(Older_Complex$complexity_category == "", yes=Older_Complex$type, no=Older_Complex$complexity_category)
Younger_Complex_short_with_ids_all <- Younger_Complex %>% 
  dplyr::select(data_id, value, out, complexity_category, num_item_id) %>%
  mutate(
    label = str_c(complexity_category, num_item_id)
  ) %>%
  pivot_wider(id_cols=data_id, names_from = "label", values_from="out") %>%
  dplyr::select(starts_with(c("data_id", "combine", "morphology", "syntax")))

Younger_Complex_short_with_ids <- Younger_Complex_short_with_ids_all%>%
  drop_na()

N_Younger_NA = nrow(Younger_Complex_short_with_ids_all) - nrow(Younger_Complex_short_with_ids)

Younger_Complex_short_grammatical <- Younger_Complex_short_with_ids %>%
  filter(combine760 > 0)

N_nog_y <- nrow(filter(Younger_Complex_short_with_ids, combine760 == 0))

nrow(Younger_Complex_short_grammatical) == N_Younger - N_Younger_NA - N_nog_y 
## [1] TRUE
Older_Complex_short_with_ids_all <- Older_Complex %>% 
  dplyr::select(data_id, value, out, complexity_category, num_item_id) %>%
  mutate(
    label = str_c(complexity_category, num_item_id)
  ) %>%
  pivot_wider(id_cols=data_id, names_from = "label", values_from="out") %>%
  dplyr::select(starts_with(c("data_id", "combine", "morphology", "syntax")))

Older_Complex_short_with_ids <- Older_Complex_short_with_ids_all %>%
  drop_na()

N_Older_NA = nrow(Older_Complex_short_with_ids_all) - nrow(Older_Complex_short_with_ids)

Older_Complex_short_grammatical <- Older_Complex_short_with_ids %>%
  filter(combine760 > 0) 

N_nog_o <- nrow(filter(Older_Complex_short_with_ids, combine760 == 0))

nrow(Older_Complex_short_grammatical) == N_Older - N_Older_NA - N_nog_o
## [1] TRUE

1.2 Make vocab dataset.

Younger_Vocab <- Younger  %>%
  left_join(.,Inst, by="data_id") %>%
  left_join(., Item, by="num_item_id") %>%
  filter(type == "word"
         ) %>%
  mutate(
    out = ifelse(value=="produces", yes=1, no =0)
    ) 



Older_Vocab <- Older  %>%
  left_join(.,Inst, by="data_id") %>%
  left_join(., Item, by="num_item_id") %>%
  filter(type == "word"
         ) %>%
  mutate(
    out = ifelse(value=="produces", yes=1, no =0)
    ) 

N_vocab = nrow(filter(Item, type == "word")) 

nrow(Younger_Vocab) == (N_Younger)*N_vocab 
## [1] TRUE
nrow(Older_Vocab) == (N_Older)*N_vocab 
## [1] TRUE
Younger_Vocab_short_with_ids_all <- Younger_Vocab %>% 
  filter(lexical_category == "nouns" | lexical_category == "predicates") %>%
  dplyr::select(data_id, value, out, definition) %>%
  pivot_wider(id_cols=data_id, names_from = "definition", values_from="out")

Younger_Vocab_short_with_ids <- Younger_Vocab_short_with_ids_all%>%
  drop_na() # drop participants with missing data


N_Younger_Vocab_NA = nrow(Younger_Vocab_short_with_ids_all) - nrow(Younger_Vocab_short_with_ids)


nrow(Younger_Vocab_short_with_ids) == N_Younger - N_Younger_Vocab_NA
## [1] TRUE
Older_Vocab_short_with_ids_all <- Older_Vocab %>% 
  filter(lexical_category == "nouns" | lexical_category == "predicates") %>%
  dplyr::select(data_id, value, out, definition) %>%
  pivot_wider(id_cols=data_id, names_from = "definition", values_from="out") 

Older_Vocab_short_with_ids <-Older_Vocab_short_with_ids_all %>%
  drop_na() # drop participants with missing data

N_Older_Vocab_NA = nrow(Older_Vocab_short_with_ids_all) - nrow(Older_Vocab_short_with_ids)

nrow(Older_Vocab_short_with_ids) == N_Older - N_Older_Vocab_NA
## [1] TRUE

1.3 Combine

Younger_full <- left_join(
  Younger_Complex_short_grammatical, Younger_Vocab_short_with_ids, by="data_id"
) %>%
  dplyr::select(-c("data_id", "combine760")) %>%
  drop_na()
#216

nrow(Younger_full) == N_Younger - N_Younger_NA - N_nog_y
## [1] TRUE
Older_full <- left_join(
  Older_Complex_short_grammatical, Older_Vocab_short_with_ids, by="data_id"
) %>%
  dplyr::select(-c("data_id", "combine760")) %>%
  drop_na()
#649

nrow(Older_full) == N_Older - N_Older_NA - N_nog_o
## [1] TRUE

2 Initial Tests of Dimensionality

2.1 Younger

# Lots of warings here, but not essential to our anlaysis. Warnings, therefore, supressed. 
Younger_full_tetra <- tetrachoric(Younger_full)
rho <- Younger_full_tetra$rho

Older_full_tetra <- tetrachoric(Older_full)
rho2 <- Older_full_tetra$rho
fa.parallel(rho, fa="fa", fm="minres", cor="poly", n.obs = 216)
## In smc, smcs < 0 were set to .0
## In smc, smcs < 0 were set to .0
## In smc, smcs < 0 were set to .0
## The determinant of the smoothed correlation was zero.
## This means the objective function is not defined.
## Chi square is based upon observed residuals.
## The determinant of the smoothed correlation was zero.
## This means the objective function is not defined for the null model either.
## The Chi square is thus based upon observed correlations.
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.
## Warning in cor.smooth(R): Matrix was not positive definite, smoothing was done
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(R): Matrix was not positive definite, smoothing was done
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done
## The determinant of the smoothed correlation was zero.
## This means the objective function is not defined.
## Chi square is based upon observed residuals.
## The determinant of the smoothed correlation was zero.
## This means the objective function is not defined for the null model either.
## The Chi square is thus based upon observed correlations.
## In factor.scores, the correlation matrix is singular, an approximation is used
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(R): Matrix was not positive definite, smoothing was done
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done
## The determinant of the smoothed correlation was zero.
## This means the objective function is not defined.
## Chi square is based upon observed residuals.
## The determinant of the smoothed correlation was zero.
## This means the objective function is not defined for the null model either.
## The Chi square is thus based upon observed correlations.
## In factor.scores, the correlation matrix is singular, an approximation is used
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(R): Matrix was not positive definite, smoothing was done
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done
## The determinant of the smoothed correlation was zero.
## This means the objective function is not defined.
## Chi square is based upon observed residuals.
## The determinant of the smoothed correlation was zero.
## This means the objective function is not defined for the null model either.
## The Chi square is thus based upon observed correlations.
## In factor.scores, the correlation matrix is singular, an approximation is used
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(R): Matrix was not positive definite, smoothing was done
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done
## The determinant of the smoothed correlation was zero.
## This means the objective function is not defined.
## Chi square is based upon observed residuals.
## The determinant of the smoothed correlation was zero.
## This means the objective function is not defined for the null model either.
## The Chi square is thus based upon observed correlations.
## In factor.scores, the correlation matrix is singular, an approximation is used
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(R): Matrix was not positive definite, smoothing was done
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done
## The determinant of the smoothed correlation was zero.
## This means the objective function is not defined.
## Chi square is based upon observed residuals.
## The determinant of the smoothed correlation was zero.
## This means the objective function is not defined for the null model either.
## The Chi square is thus based upon observed correlations.
## In factor.scores, the correlation matrix is singular, an approximation is used
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(R): Matrix was not positive definite, smoothing was done
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done
## The determinant of the smoothed correlation was zero.
## This means the objective function is not defined.
## Chi square is based upon observed residuals.
## The determinant of the smoothed correlation was zero.
## This means the objective function is not defined for the null model either.
## The Chi square is thus based upon observed correlations.
## In factor.scores, the correlation matrix is singular, an approximation is used
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(R): Matrix was not positive definite, smoothing was done
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done
## The determinant of the smoothed correlation was zero.
## This means the objective function is not defined.
## Chi square is based upon observed residuals.
## The determinant of the smoothed correlation was zero.
## This means the objective function is not defined for the null model either.
## The Chi square is thus based upon observed correlations.
## In factor.scores, the correlation matrix is singular, an approximation is used
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(R): Matrix was not positive definite, smoothing was done
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done
## The determinant of the smoothed correlation was zero.
## This means the objective function is not defined.
## Chi square is based upon observed residuals.
## The determinant of the smoothed correlation was zero.
## This means the objective function is not defined for the null model either.
## The Chi square is thus based upon observed correlations.
## In factor.scores, the correlation matrix is singular, an approximation is used
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(R): Matrix was not positive definite, smoothing was done
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done
## The determinant of the smoothed correlation was zero.
## This means the objective function is not defined.
## Chi square is based upon observed residuals.
## The determinant of the smoothed correlation was zero.
## This means the objective function is not defined for the null model either.
## The Chi square is thus based upon observed correlations.
## In factor.scores, the correlation matrix is singular, an approximation is used
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(R): Matrix was not positive definite, smoothing was done
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done
## The determinant of the smoothed correlation was zero.
## This means the objective function is not defined.
## Chi square is based upon observed residuals.
## The determinant of the smoothed correlation was zero.
## This means the objective function is not defined for the null model either.
## The Chi square is thus based upon observed correlations.
## In factor.scores, the correlation matrix is singular, an approximation is used
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(R): Matrix was not positive definite, smoothing was done
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done
## The determinant of the smoothed correlation was zero.
## This means the objective function is not defined.
## Chi square is based upon observed residuals.
## The determinant of the smoothed correlation was zero.
## This means the objective function is not defined for the null model either.
## The Chi square is thus based upon observed correlations.
## In factor.scores, the correlation matrix is singular, an approximation is used
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(R): Matrix was not positive definite, smoothing was done
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done
## The determinant of the smoothed correlation was zero.
## This means the objective function is not defined.
## Chi square is based upon observed residuals.
## The determinant of the smoothed correlation was zero.
## This means the objective function is not defined for the null model either.
## The Chi square is thus based upon observed correlations.
## In factor.scores, the correlation matrix is singular, an approximation is used
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(R): Matrix was not positive definite, smoothing was done
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done
## The determinant of the smoothed correlation was zero.
## This means the objective function is not defined.
## Chi square is based upon observed residuals.
## The determinant of the smoothed correlation was zero.
## This means the objective function is not defined for the null model either.
## The Chi square is thus based upon observed correlations.
## In factor.scores, the correlation matrix is singular, an approximation is used
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(R): Matrix was not positive definite, smoothing was done
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done
## The determinant of the smoothed correlation was zero.
## This means the objective function is not defined.
## Chi square is based upon observed residuals.
## The determinant of the smoothed correlation was zero.
## This means the objective function is not defined for the null model either.
## The Chi square is thus based upon observed correlations.
## In factor.scores, the correlation matrix is singular, an approximation is used
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(R): Matrix was not positive definite, smoothing was done
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done
## The determinant of the smoothed correlation was zero.
## This means the objective function is not defined.
## Chi square is based upon observed residuals.
## The determinant of the smoothed correlation was zero.
## This means the objective function is not defined for the null model either.
## The Chi square is thus based upon observed correlations.
## In factor.scores, the correlation matrix is singular, an approximation is used
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(R): Matrix was not positive definite, smoothing was done
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done
## The determinant of the smoothed correlation was zero.
## This means the objective function is not defined.
## Chi square is based upon observed residuals.
## The determinant of the smoothed correlation was zero.
## This means the objective function is not defined for the null model either.
## The Chi square is thus based upon observed correlations.
## In factor.scores, the correlation matrix is singular, an approximation is used
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(R): Matrix was not positive definite, smoothing was done
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done
## The determinant of the smoothed correlation was zero.
## This means the objective function is not defined.
## Chi square is based upon observed residuals.
## The determinant of the smoothed correlation was zero.
## This means the objective function is not defined for the null model either.
## The Chi square is thus based upon observed correlations.
## In factor.scores, the correlation matrix is singular, an approximation is used
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(R): Matrix was not positive definite, smoothing was done
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done
## The determinant of the smoothed correlation was zero.
## This means the objective function is not defined.
## Chi square is based upon observed residuals.
## The determinant of the smoothed correlation was zero.
## This means the objective function is not defined for the null model either.
## The Chi square is thus based upon observed correlations.
## In factor.scores, the correlation matrix is singular, an approximation is used
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(R): Matrix was not positive definite, smoothing was done
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done
## The determinant of the smoothed correlation was zero.
## This means the objective function is not defined.
## Chi square is based upon observed residuals.
## The determinant of the smoothed correlation was zero.
## This means the objective function is not defined for the null model either.
## The Chi square is thus based upon observed correlations.
## In factor.scores, the correlation matrix is singular, an approximation is used
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(R): Matrix was not positive definite, smoothing was done
## In smc, smcs < 0 were set to .0
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done
## The determinant of the smoothed correlation was zero.
## This means the objective function is not defined.
## Chi square is based upon observed residuals.
## The determinant of the smoothed correlation was zero.
## This means the objective function is not defined for the null model either.
## The Chi square is thus based upon observed correlations.
## In factor.scores, the correlation matrix is singular, an approximation is used
## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done

## Parallel analysis suggests that the number of factors =  23  and the number of components =  NA
fa.parallel(rho2, fa="fa", fm="minres", cor="poly", n.obs = 653)
## In smc, smcs < 0 were set to .0
## In smc, smcs < 0 were set to .0
## In smc, smcs < 0 were set to .0
## The determinant of the smoothed correlation was zero.
## This means the objective function is not defined.
## Chi square is based upon observed residuals.
## The determinant of the smoothed correlation was zero.
## This means the objective function is not defined for the null model either.
## The Chi square is thus based upon observed correlations.
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.

## Parallel analysis suggests that the number of factors =  26  and the number of components =  NA
vss(rho, fa="fa", fm="minres", cor="poly", n.obs = 216)
## In smc, smcs < 0 were set to .0
## In smc, smcs < 0 were set to .0
## In smc, smcs < 0 were set to .0
## The determinant of the smoothed correlation was zero.
## This means the objective function is not defined.
## Chi square is based upon observed residuals.
## The determinant of the smoothed correlation was zero.
## This means the objective function is not defined for the null model either.
## The Chi square is thus based upon observed correlations.
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.
## In smc, smcs < 0 were set to .0
## In smc, smcs < 0 were set to .0
## In smc, smcs < 0 were set to .0
## The determinant of the smoothed correlation was zero.
## This means the objective function is not defined.
## Chi square is based upon observed residuals.
## The determinant of the smoothed correlation was zero.
## This means the objective function is not defined for the null model either.
## The Chi square is thus based upon observed correlations.
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.
## In smc, smcs < 0 were set to .0
## In smc, smcs < 0 were set to .0
## In smc, smcs < 0 were set to .0
## The determinant of the smoothed correlation was zero.
## This means the objective function is not defined.
## Chi square is based upon observed residuals.
## The determinant of the smoothed correlation was zero.
## This means the objective function is not defined for the null model either.
## The Chi square is thus based upon observed correlations.
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.
## In smc, smcs < 0 were set to .0
## In smc, smcs < 0 were set to .0
## In smc, smcs < 0 were set to .0
## The determinant of the smoothed correlation was zero.
## This means the objective function is not defined.
## Chi square is based upon observed residuals.
## The determinant of the smoothed correlation was zero.
## This means the objective function is not defined for the null model either.
## The Chi square is thus based upon observed correlations.
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.
## In smc, smcs < 0 were set to .0
## In smc, smcs < 0 were set to .0
## In smc, smcs < 0 were set to .0
## The determinant of the smoothed correlation was zero.
## This means the objective function is not defined.
## Chi square is based upon observed residuals.
## The determinant of the smoothed correlation was zero.
## This means the objective function is not defined for the null model either.
## The Chi square is thus based upon observed correlations.
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.
## In smc, smcs < 0 were set to .0
## In smc, smcs < 0 were set to .0
## In smc, smcs < 0 were set to .0
## The determinant of the smoothed correlation was zero.
## This means the objective function is not defined.
## Chi square is based upon observed residuals.
## The determinant of the smoothed correlation was zero.
## This means the objective function is not defined for the null model either.
## The Chi square is thus based upon observed correlations.
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.
## In smc, smcs < 0 were set to .0
## In smc, smcs < 0 were set to .0
## In smc, smcs < 0 were set to .0
## The determinant of the smoothed correlation was zero.
## This means the objective function is not defined.
## Chi square is based upon observed residuals.
## The determinant of the smoothed correlation was zero.
## This means the objective function is not defined for the null model either.
## The Chi square is thus based upon observed correlations.
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.
## In smc, smcs < 0 were set to .0
## In smc, smcs < 0 were set to .0
## In smc, smcs < 0 were set to .0
## The determinant of the smoothed correlation was zero.
## This means the objective function is not defined.
## Chi square is based upon observed residuals.
## The determinant of the smoothed correlation was zero.
## This means the objective function is not defined for the null model either.
## The Chi square is thus based upon observed correlations.
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.

## 
## Very Simple Structure
## Call: vss(x = rho, fm = "minres", n.obs = 216, cor = "poly", fa = "fa")
## VSS complexity 1 achieves a maximimum of 0.92  with  1  factors
## VSS complexity 2 achieves a maximimum of 0.95  with  2  factors
## 
## The Velicer MAP achieves a minimum of 0.01  with  8  factors 
## BIC achieves a minimum of  -614499.7  with  8  factors
## Sample Size adjusted BIC achieves a minimum of  -230214.9  with  8  factors
## 
## Statistics by number of factors 
##   vss1 vss2   map    dof  chisq prob sqresid  fit RMSEA     BIC   SABIC complex
## 1 0.92 0.00 0.018 124749 101364    1    2180 0.92     0 -569197 -173888     1.0
## 2 0.53 0.95 0.014 124249  68607    1    1497 0.95     0 -599266 -205542     1.6
## 3 0.37 0.82 0.013 123750  59941    1    1327 0.95     0 -605249 -213106     2.0
## 4 0.38 0.75 0.013 123252  53232    1    1196 0.96     0 -609282 -218717     2.3
## 5 0.33 0.67 0.013 122755  48269    1    1101 0.96     0 -611573 -222583     2.6
## 6 0.33 0.65 0.013 122259  44307    1    1026 0.96     0 -612869 -225450     2.8
## 7 0.34 0.66 0.013 121764  40643    1     956 0.97     0 -613873 -228022     2.9
## 8 0.33 0.64 0.013 121270  37360    1     893 0.97     0 -614500 -230215     3.1
##   eChisq  SRMR eCRMS    eBIC
## 1 419629 0.088 0.088 -250931
## 2 278862 0.072 0.072 -389011
## 3 245506 0.067 0.068 -419685
## 4 219946 0.064 0.064 -442568
## 5 201690 0.061 0.062 -458152
## 6 187505 0.059 0.060 -469671
## 7 174116 0.057 0.058 -480400
## 8 162141 0.055 0.056 -489719
vss(rho, fa="fa", fm="minres", cor="poly", n.obs = 653)
## In smc, smcs < 0 were set to .0
## In smc, smcs < 0 were set to .0
## In smc, smcs < 0 were set to .0
## The determinant of the smoothed correlation was zero.
## This means the objective function is not defined.
## Chi square is based upon observed residuals.
## The determinant of the smoothed correlation was zero.
## This means the objective function is not defined for the null model either.
## The Chi square is thus based upon observed correlations.
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.
## In smc, smcs < 0 were set to .0
## In smc, smcs < 0 were set to .0
## In smc, smcs < 0 were set to .0
## The determinant of the smoothed correlation was zero.
## This means the objective function is not defined.
## Chi square is based upon observed residuals.
## The determinant of the smoothed correlation was zero.
## This means the objective function is not defined for the null model either.
## The Chi square is thus based upon observed correlations.
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.
## In smc, smcs < 0 were set to .0
## In smc, smcs < 0 were set to .0
## In smc, smcs < 0 were set to .0
## The determinant of the smoothed correlation was zero.
## This means the objective function is not defined.
## Chi square is based upon observed residuals.
## The determinant of the smoothed correlation was zero.
## This means the objective function is not defined for the null model either.
## The Chi square is thus based upon observed correlations.
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.
## In smc, smcs < 0 were set to .0
## In smc, smcs < 0 were set to .0
## In smc, smcs < 0 were set to .0
## The determinant of the smoothed correlation was zero.
## This means the objective function is not defined.
## Chi square is based upon observed residuals.
## The determinant of the smoothed correlation was zero.
## This means the objective function is not defined for the null model either.
## The Chi square is thus based upon observed correlations.
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.
## In smc, smcs < 0 were set to .0
## In smc, smcs < 0 were set to .0
## In smc, smcs < 0 were set to .0
## The determinant of the smoothed correlation was zero.
## This means the objective function is not defined.
## Chi square is based upon observed residuals.
## The determinant of the smoothed correlation was zero.
## This means the objective function is not defined for the null model either.
## The Chi square is thus based upon observed correlations.
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.
## In smc, smcs < 0 were set to .0
## In smc, smcs < 0 were set to .0
## In smc, smcs < 0 were set to .0
## The determinant of the smoothed correlation was zero.
## This means the objective function is not defined.
## Chi square is based upon observed residuals.
## The determinant of the smoothed correlation was zero.
## This means the objective function is not defined for the null model either.
## The Chi square is thus based upon observed correlations.
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.
## In smc, smcs < 0 were set to .0
## In smc, smcs < 0 were set to .0
## In smc, smcs < 0 were set to .0
## The determinant of the smoothed correlation was zero.
## This means the objective function is not defined.
## Chi square is based upon observed residuals.
## The determinant of the smoothed correlation was zero.
## This means the objective function is not defined for the null model either.
## The Chi square is thus based upon observed correlations.
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.
## In smc, smcs < 0 were set to .0
## In smc, smcs < 0 were set to .0
## In smc, smcs < 0 were set to .0
## The determinant of the smoothed correlation was zero.
## This means the objective function is not defined.
## Chi square is based upon observed residuals.
## The determinant of the smoothed correlation was zero.
## This means the objective function is not defined for the null model either.
## The Chi square is thus based upon observed correlations.
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.

## 
## Very Simple Structure
## Call: vss(x = rho, fm = "minres", n.obs = 653, cor = "poly", fa = "fa")
## VSS complexity 1 achieves a maximimum of 0.92  with  1  factors
## VSS complexity 2 achieves a maximimum of 0.95  with  2  factors
## 
## The Velicer MAP achieves a minimum of 0.01  with  8  factors 
## BIC achieves a minimum of  -358387.2  with  8  factors
## Sample Size adjusted BIC achieves a minimum of  26644.54  with  8  factors
## 
## Statistics by number of factors 
##   vss1 vss2   map    dof   chisq prob sqresid  fit RMSEA     BIC  SABIC complex
## 1 0.92 0.00 0.018 124749 1053965    0    2180 0.92 0.107  245395 641472     1.0
## 2 0.53 0.95 0.014 124249  722739    0    1497 0.95 0.086  -82590 311900     1.6
## 3 0.37 0.82 0.013 123750  639889    0    1327 0.95 0.080 -162206 230700     2.0
## 4 0.38 0.75 0.013 123252  575979    0    1196 0.96 0.075 -222888 168436     2.3
## 5 0.33 0.67 0.013 122755  529489    0    1101 0.96 0.071 -266157 123589     2.6
## 6 0.33 0.65 0.013 122259  492853    0    1026 0.96 0.068 -299579  88593     2.8
## 7 0.34 0.66 0.013 121764  458545    0     956 0.97 0.065 -330678  55922     2.9
## 8 0.33 0.64 0.013 121270  427634    0     893 0.97 0.062 -358387  26645     3.1
##    eChisq  SRMR eCRMS    eBIC
## 1 1268602 0.088 0.088  460031
## 2  843041 0.072 0.072   37712
## 3  742201 0.067 0.068  -59894
## 4  664930 0.064 0.064 -133938
## 5  609739 0.061 0.062 -185907
## 6  566855 0.059 0.060 -225576
## 7  526378 0.057 0.058 -262845
## 8  490177 0.055 0.056 -295844

3 DETECT

Try MIRT model - shouldn’t run because of low number of observations. Is there a way to use existing model to predict factor scores for new dataset?

#m1 <- mirt(full, 1, "2PL")
#saveRDS(m1, "combined_irt_output/re_test/m1.rds")
#m1 <-  readRDS("combined_irt_output/re_test/m1.rds")

Use sum score - no IRT

fscores_younger <- rowSums(Younger_full)

Prepare dataframe

Younger_full2 <- data.frame(Younger_full)

Confirmatory DETECT

dtct <- c(rep(1, 37), rep(2, 478)) # grammar vs vocab
dtct2 <- c(rep(1,37), rep(2, 286), rep(1,192)) # grammar & predicates vs nouns
conf <- conf.detect(Younger_full2, fscores_younger, dtct)
## -----------------------------------------------------------
## Confirmatory DETECT Analysis 
## Conditioning on 1 Score
## Bandwidth Scale: 1.1 
## Pairwise Estimation of Conditional Covariances
## ...........................................................
## Nonparametric ICC estimation 
##  5% 10% 15% 20% 25% 30% 35% 40% 45% 50% 
## 55% 60% 65% 70% 75% 80% 85% 90% 95% 
## ...........................................................
## Nonparametric Estimation of conditional covariances 
##  5% 10% 15% 20% 25% 30% 35% 40% 45% 50% 
## 55% 60% 65% 70% 75% 80% 85% 90% 95% 
## -----------------------------------------------------------
##           unweighted weighted
## DETECT         0.020    0.020
## ASSI           0.024    0.024
## RATIO          0.056    0.056
## MADCOV100      0.365    0.365
## MCOV100        0.016    0.016
conf <- conf.detect(Younger_full2, fscores_younger, dtct2)
## -----------------------------------------------------------
## Confirmatory DETECT Analysis 
## Conditioning on 1 Score
## Bandwidth Scale: 1.1 
## Pairwise Estimation of Conditional Covariances
## ...........................................................
## Nonparametric ICC estimation 
##  5% 10% 15% 20% 25% 30% 35% 40% 45% 50% 
## 55% 60% 65% 70% 75% 80% 85% 90% 95% 
## ...........................................................
## Nonparametric Estimation of conditional covariances 
##  5% 10% 15% 20% 25% 30% 35% 40% 45% 50% 
## 55% 60% 65% 70% 75% 80% 85% 90% 95% 
## -----------------------------------------------------------
##           unweighted weighted
## DETECT         0.044    0.044
## ASSI           0.061    0.061
## RATIO          0.121    0.121
## MADCOV100      0.365    0.365
## MCOV100        0.016    0.016

Does not seem like the 2-dimensional structure implied by the distinction between lexical items and grammatical items is justified.

Exploratory detect to look for any other form of multidimensionality.

d1 <- expl.detect(Younger_full2, fscores_younger, nclusters=2)
## Pairwise Estimation of Conditional Covariances
## ...........................................................
## Nonparametric ICC estimation 
##  5% 10% 15% 20% 25% 30% 35% 40% 45% 50% 
## 55% 60% 65% 70% 75% 80% 85% 90% 95% 
## ...........................................................
## Nonparametric Estimation of conditional covariances 
##  5% 10% 15% 20% 25% 30% 35% 40% 45% 50% 
## 55% 60% 65% 70% 75% 80% 85% 90% 95% 
## Pairwise Estimation of Conditional Covariances
## ...........................................................
## Nonparametric ICC estimation 
##  5% 10% 15% 20% 25% 30% 35% 40% 45% 50% 
## 55% 60% 65% 70% 75% 80% 85% 90% 95% 
## ...........................................................
## Nonparametric Estimation of conditional covariances 
##  5% 10% 15% 20% 25% 30% 35% 40% 45% 50% 
## 55% 60% 65% 70% 75% 80% 85% 90% 95% 
## 
## 
## DETECT (unweighted)
## 
## Optimal Cluster Size is  2  (Maximum of DETECT Index)
## 
##   N.Cluster N.items N.est N.val size.cluster DETECT.est ASSI.est RATIO.est
## 1         2     515   108   108      404-111      0.064     0.03      0.15
##   MADCOV100.est MCOV100.est DETECT.val ASSI.val RATIO.val MADCOV100.val
## 1         0.423        0.03      0.023   -0.019     0.046         0.489
##   MCOV100.val
## 1        0.02

#options(max.print=2000)
#d1

3.1 Older

Use sum score

fscores_older <- rowSums(Older_full)

Exploratory Detect

Older_full2 <- data.frame(Older_full)

Confirmatory DETECT

conf <- conf.detect(Older_full2, fscores_older, dtct)
## -----------------------------------------------------------
## Confirmatory DETECT Analysis 
## Conditioning on 1 Score
## Bandwidth Scale: 1.1 
## Pairwise Estimation of Conditional Covariances
## ...........................................................
## Nonparametric ICC estimation 
##  5% 10% 15% 20% 25% 30% 35% 40% 45% 50% 
## 55% 60% 65% 70% 75% 80% 85% 90% 95% 
## ...........................................................
## Nonparametric Estimation of conditional covariances 
##  5% 10% 15% 20% 25% 30% 35% 40% 45% 50% 
## 55% 60% 65% 70% 75% 80% 85% 90% 95% 
## -----------------------------------------------------------
##           unweighted weighted
## DETECT         0.084    0.084
## ASSI           0.063    0.063
## RATIO          0.194    0.194
## MADCOV100      0.432    0.432
## MCOV100        0.031    0.031
conf <- conf.detect(Older_full2, fscores_older, dtct2)
## -----------------------------------------------------------
## Confirmatory DETECT Analysis 
## Conditioning on 1 Score
## Bandwidth Scale: 1.1 
## Pairwise Estimation of Conditional Covariances
## ...........................................................
## Nonparametric ICC estimation 
##  5% 10% 15% 20% 25% 30% 35% 40% 45% 50% 
## 55% 60% 65% 70% 75% 80% 85% 90% 95% 
## ...........................................................
## Nonparametric Estimation of conditional covariances 
##  5% 10% 15% 20% 25% 30% 35% 40% 45% 50% 
## 55% 60% 65% 70% 75% 80% 85% 90% 95% 
## -----------------------------------------------------------
##           unweighted weighted
## DETECT         0.182    0.182
## ASSI           0.247    0.247
## RATIO          0.420    0.420
## MADCOV100      0.432    0.432
## MCOV100        0.031    0.031
d1 <- expl.detect(Older_full2, fscores_older, nclusters=2)
## Pairwise Estimation of Conditional Covariances
## ...........................................................
## Nonparametric ICC estimation 
##  5% 10% 15% 20% 25% 30% 35% 40% 45% 50% 
## 55% 60% 65% 70% 75% 80% 85% 90% 95% 
## ...........................................................
## Nonparametric Estimation of conditional covariances 
##  5% 10% 15% 20% 25% 30% 35% 40% 45% 50% 
## 55% 60% 65% 70% 75% 80% 85% 90% 95% 
## Pairwise Estimation of Conditional Covariances
## ...........................................................
## Nonparametric ICC estimation 
##  5% 10% 15% 20% 25% 30% 35% 40% 45% 50% 
## 55% 60% 65% 70% 75% 80% 85% 90% 95% 
## ...........................................................
## Nonparametric Estimation of conditional covariances 
##  5% 10% 15% 20% 25% 30% 35% 40% 45% 50% 
## 55% 60% 65% 70% 75% 80% 85% 90% 95% 
## 
## 
## DETECT (unweighted)
## 
## Optimal Cluster Size is  2  (Maximum of DETECT Index)
## 
##   N.Cluster N.items N.est N.val size.cluster DETECT.est ASSI.est RATIO.est
## 1         2     515   324   325       35-480       0.09    0.068     0.164
##   MADCOV100.est MCOV100.est DETECT.val ASSI.val RATIO.val MADCOV100.val
## 1         0.549       0.044      0.091    0.072     0.168         0.541
##   MCOV100.val
## 1       0.049