1.1 Real words

The set of real words is taken from the Massive Auditory Lexical Decision (MALD) Database (Tucker et al., 2018). It is a subset of the complete MALD database, containing 8285 words of which 2120 words contain one of 36 different affixes. This dataframe is called realwords.

1.2 Pseudowords

Pseudowords are taken from the production study by Schmitz et al. (2020). In total, 48 pseudowords are contained within this data set, with half of them representing monomorphemic words (e.g. singular bloufs) and half of them representing plural wordforms (e.g. plural bloufs). As a number of pseudowords show more than one consistent pronunciation, these are contained more than twice, e.g. prups. This dataframe is called pseudowords.

1.3 All Words

The combined word set contains both data on real and on nonce words as introduced in 1.1 and 1.2. In total, 8333 words and 36 different affixes are part of this data set. This dataframe is called allwords.

3.1 Real Words

The cue matrix for real words \(real.C\) is computed based on the set of real words and \(Word+Affix\), i.e. words and affixes are considered.

real.C = make_cue_matrix(data = realwords, formula = ~ Word + Affix, grams = 3, wordform = "DISC")

3.2 Pseudowords

The cue matrix for pseudowords \(pseudo.C\) is computed based on the set of pseudoword and \(Word+Affix\), i.e. words and affixes are considered.

pseudo.C = make_cue_matrix(data = pseudowords, formula = ~ Word + Affix, grams = 3, wordform = "DISC")

3.3 All Words

The cue matrix for real and nonce words \(all.C\) is computed based on the combined set of all real and nonce words and \(Word+Affix\), i.e. words and affixes are considered.

all.C = make_cue_matrix(data = allwords, formula = ~ Word + Affix, grams = 3, wordform = "DISC")

4.1 Real Words

The semantic matrix for real words \(real.S\) is computed based on the set of real words, the real word \(A\) matrix, and \(Word+Affix\), i.e. words and affixes are considered.

real.S = make_S_matrix(data = realwords, formula = ~ Word + Affix, inputA = A.matrix, grams = 3, wordform = "DISC")

dim(real.S)
# 8362 5487

4.2 Pseudowords

We can create an estimated semantic matrix for pseudowords \(pseudo.S\) (Chuang et al., 2020) based on the semantics of real words solving the following equation

\[pseudo.S = pseudo.C * F\]

with \(pseudo.S\) being the estimated semantic matrix for pseudowords, \(pseudo.C\) being the cue matrix of pseudowords, and \(F\) being the transformation matrix for mapping real word cues onto real word semantics.

To obtain this real word transformation matrix \(F\) we first need to learn comprehension of real words.

real.comprehension = learn_comprehension(cue_obj = real.C, S = real.S)

Then, we can extract \(F\) from real.comprehension.

F = real.comprehension$F

dim(F) 
# 7610 5487

The following toy example illustrates the use of the \(F\) transformation matrix in mapping \(C\) onto \(S\), i.e. solving

\[real.C * F = predicted.real.S\]

Consider the following toy example illustrating the procedure. The lexicon of this toy example includes the words cat, bus, and eel. Thus, its cue matrix \(C\) looks as follows:

For the same toy lexicon, suppose that the semantic vectors for these three words are the row vectors of the following semantic matrix \(S\):

Then, we are interested in a transformation matrix \(F\), such that

\[C*F=S\] The transformation matrix \(F\) is straightforward to obtain. Let \(C'\) denote the Moore-Penrose generalized inverse of \(C\). Then,

\[F=C'S\]

Thus, for the toy lexicon example,

with \(CF\) being exactly equal to \(S\) in this simple toy example.

Additionally, for matrix multiplication, the number of columns in the first matrix must be equal to the number of rows in the second matrix (e.g. Nykamp, 2020). While this is easily achieved, one must also consider the order of columns. This is easily illustrated by the following example:

\[ \left(\begin{array}{cc} A & B\\ C & D \end{array}\right) \left(\begin{array}{cc} \alpha & \beta \\ \gamma & \delta \end{array}\right) = \left(\begin{array}{cc} A\alpha+B\gamma & A\beta+B\delta \\ C\alpha+D\gamma & C\beta+D\delta \end{array}\right) \] Let the first matrix be a simplified version of \(pseudo.C\) and the second matrix a simplified version of \(F\). The resulting matrix then is a simplified version of \(pseudo.S\). However, if the order of columns (i.e. triphones) in \(real.C\), from which \(F\) is derived, is different to the order of columns (i.e. triphones) in \(pseudo.C\), multiplication is possible, yet different (wrong) columns and rows are multiplied, as shown in the following example:

\[ \left(\begin{array}{cc} B & A \\ D & C \end{array}\right) \left(\begin{array}{cc} \alpha & \beta \\ \gamma & \delta \end{array}\right) = \left(\begin{array}{cc} B\alpha+A\gamma & B\beta+A\delta \\ D\alpha+C\gamma & D\beta+C\delta \end{array}\right) \]

Thus, we must make sure to use a pseudoword cue matrix \(pseudo.C\) with the same order of columns as the real word cue matrix \(real.C\). This, in turn, also expands the pseudoword cue matrix \(pseudo.C\), i.e. to contain all column names of the real word cue matrix \(real.C\) it must have an identical number of columns.

Using two functions of the LDLConvFunctions package, this is easily done. First, find which column in the real word cue matrix \(real.C\) corresponds to which column in the pseudoword cue matrix \(pseudo.C\):

found_triphones <- find_triphones(pseudo_C_matrix = pseudo.C, real_C_matrix = real.C)

Then, use this information to create a new pseudoword cue matrix \(new.pseudo.C\) which a) has the same number of columns as the real word cue matrix, and b) the same order of columns (i.e. triphones) as the real word cue matrix:

new.pseudo.C <- reorder_pseudo_C_matrix(pseudo_C_matrix = pseudo.C, real_C_matrix = real.C, found_triphones = found_triphones)

Finally, we can solve the aforementioned equation \(pseudo.S = pseudo.C * F\).

pseudo.S = new.pseudo.C %*% F

# change rownames to pseudoword rownames (instead of numbers)
rownames(engs.Smat) <- engs.data$DISC

In this semantic matrix, 48 pseudowords (i.e. 78 pronunciations) and their semantic vectors are contained. However, all of our pseudoword pairs are homophones, thus, they show identical semantic vectors even though half of them contain a suffix, e.g. the semantic vectors for bloufs (non-morphemic S) and bloufs (plural S) are identical.

We “fix” this issue by adding the “PL” semantic vector values to the semantic vectors of plural pseudowords.

Thus, we first need to extract the “PL” semantic vector contained in the general \(A\) matrix.

PL.vec <- A.matrix[rownames(A.matrix)=="PL"]

Taking a closer look at the pseudoword semantic matrix \(pseudo.S\), we find that every second row corresponds to a plural pseudoword, i.e. this is where we add the “PL” vector.

pseduo.pl = pseudo.S[seq(2, nrow(pseudo.S), 2), ]

Taking this plural subset, we add the “PL” semantic vector to all rows.

pseudo.pl.added <- pseduo.pl + rep(PL.vec, each = nrow(pseduo.pl))

We then recombine the original monomorphemic semantic matrix and the modified plural semantic matrix, and recreate the original row order.

pseudo.nm = pseudo.S[seq(1, nrow(pseudo.S), 2), ]

pseudo.S <- rbind(pseudo.nm, pseudo.pl.added)

sort.rows <- row.names(previous.pseudo.S)
pseudo.S <- pseudo.S[order(match(rownames(pseudo.S), sort.rows)), , drop = FALSE]

Now, homophonous pseudowords have differing semantic vectors.

Similary, we now add the semantic vectors of “alien” and “creature” to all pseudoword semantic vectors to accommodate for the original experimental setup.

# extract the 'alien' semantic vector
alien.vec <- mald.Amat[rownames(mald.Amat)=="alien"]

# extract the 'creature' semantic vector
creature.vec <- mald.Amat[rownames(mald.Amat)=="creature"]

## add the 'alien' + 'creature' semantic vectors to all rows of the pseudoword S matrix
pseudo.S <- pseudo.S + rep(alien.vec, each = nrow(pseudo.S))
pseudo.S <- pseudo.S + rep(creature.vec, each = nrow(pseudo.S))

4.3 All Words

Finally, we can create one combined semantic matrix \(all.S\) for real and nonce words.

all.S <- rbind(real.S, pseudo.S)

7.1 WpmWithLdl measures

Extracting and saving comprehension and production measures as introduced by the WpmWithLdl package (Baayen et al., 2018) is straightforward.

all.comprehension.measures = comprehension_measures(comp_acc = all.comprehension.accuracy, Shat = all.comprehension$Shat, S = all.S, A = A.matrix, affixFunctions = allwords$Affix)

all.production.measures = production_measures(prod_acc = all.production.accuracy, S = all.S, prod = all.production)

7.2 Further Measures

Another set of variables consists of the measures introduced by Chuang et al. (2020). To extract these measures, one can use the LDLConvFunctions package.

# load package
library(LDLConvFunctions)

# compute measures
ALCframe <- ALC(pseudo_S_matrix = pseudo.S, real_S_matrix = real.S, pseudo_word_data = pseudowords)

ALDCframe <- ALDC(prod_acc = all.production.accuracy, data = allwords)

EDNNframe <- EDNN(comprehension = all.comprehension, data = allwords)

NNCframe <- NNC(pseudo_S_matrix = pseudo.S, real_S_matrix = real.S, pseudo_word_data = pseudowords, real_word_data = realwords)

7.3 Cluster Analysis

As suggested by an anonymous reviewer, we include a cluster analysis of our variables of interest. We find that the clustering represents quite well the components retained from the Principal Component Analyses given in the accompanying R File.

# load data
data <- read.csv("data/final_S_LDL_data_210609.csv", stringsAsFactors = T)

# define variables, i.e. LDL variables
variables <- data[, c(36:37, 39, 41:43, 45:46, 49:50, 52)]

# compute clustering
clustering <- corclust(variables)

No factor variables!

# plot clustering
plot(clustering)