Supplementary materials: Is metaphony (and sound change) sensitive to grammatical category? The case of verbs in the dialects of the Lausberg area
Pia Greca & Jonathan Harrington
library(tidyverse)
library(magrittr)
library(gridExtra)
library(wrassp)
library(emuR)
library(lme4)
library(lmerTest)
library(emmeans)
library(optimx)0. Preliminaries
Open dataframe with all formant values (raw, time and speaker-normalised) from mid stem vowels
D_basic=read.table("D.txt")
# add "Gram" as for the DCT dataframe:
D_basic=D_basic %>%
mutate(Gram = ifelse(Word %in%
c("anelli", "anello", "bella",
"bello", "cappelli", "cappello",
"capretta", "capretti",
"capretto", "cervelli", "cervello",
"coltelli", "coltello", "dente",
"denti" , "donna" ,
"donne", "ferri",
"ferro" , "letti", "letto" ,
"mela", "mele" , "mese",
"mesi", "pecora" , "pecore",
"pesca", "pesche" , "pettine",
"pettini", "pezza", "pezzo",
"piede", "piedi", "pietra",
"pietre", "prete", "preti",
"sedia", "sedie", "stella" ,
"stelle", "venti", "vento",
"vecchia", "vecchio", "verme", "vermi",
"buona", "buone", "buoni",
"buono", "corna", "corno",
"cotta", "cotto", "cuore", "cuori" ,
"foglia", "foglie","fuochi", "fuoco",
"grossa", "grosso", "lunga", "lungo", "lunghi",
"morta", "morti", "morto", "nipote",
"nipoti", "nuova", "nuovo",
"occhi", "occhio", "ossa", "osso",
"ponte", "ponti", "porci", "porco",
"rosa", "rose", "ruota", "ruote" ,
"sole", "sposa","sposo",
"topi", "topo", "uomini", "uomo",
"uova", "uovo", "zoppa", "zoppo",
"chiodo", "chiodi", "fiore", "fiori", "gioco", "giochi"),
"NAdj", "V"))
# add "MET"
D_basic = D_basic %>%
mutate(MET = ifelse(Suffix_vowel %in%
c("i", "u"), T, F))
# order levels of "Region"
D_basic$Region = factor(D_basic$Region, levels = c("MM", "ZZ", "MZ"))Open dataframe with DCT-scores for each stem vowel token:
Some information about our database.
How many speakers?
## [1] "CA01F" "CC01F" "CC01M" "CC02F" "CC02M" "CC03F" "CC03M" "CC04F" "CC05F"
## [10] "CC06F" "CC07F" "CC08F" "CV01F" "CV02F" "CV03F" "LA01F" "LI01M" "LI02M"
## [19] "LI03M" "LI04M" "LI05M" "LI06M" "MG01M" "MG02M" "MM02F" "MM03F" "MM03M"
## [28] "MM04F" "MM04M" "MM05F" "MM05M" "MM06F" "MM06M" "MM07F" "MM07M" "MM08F"
## [37] "MM08M" "MM09F" "MM09M" "MM10F" "MM11F" "MM11M" "MM12F" "MM12M" "MM13F"
## [46] "MM13M" "MM14F" "MM14M" "MM15F" "MM15M" "MM16F" "MM16M" "OM01F" "OM01M"
## [55] "OM02F" "OM02M" "OM03F" "RI01M" "RI02M" "SC01F" "SC01M" "SC02F" "SC02M"
## [64] "SC03F" "SC03M" "SC04M" "SC05M" "SC06M" "SC07M" "SD01F" "SH01M" "SL01F"
## [73] "SL01M" "SL02F" "SL02M" "SL03F" "TR01F" "TR01M" "TR02F" "TR02M" "TR03F"
## [82] "TR03M" "TR04F" "TR05F" "TR06F" "VB01F" "VB01M" "VB02F" "VB02M" "VB03F"
## [91] "VB04F" "VB05F" "VB06F" "VI01F" "VI01M" "VI02F" "VI02M" "VI03F" "VI03M"In particular:
- Mormanno (MM): 28 speakers
- Cerchiara (MZ): 11 speakers
- Scalea (ZZ): 10 speakers
- Trebisacce (MZ): 9 speakers
- Verbicaro (ZZ): 8 speakers
- Orsomarso (MZ): 5 speakers
- Villapiana (MZ): 6 speakers
- San Lorenzo Bellizzi (MZ): 5 speakers
- Castrovillari (MZ): 3 speakers
- Montegiordano (MZ): 2 speakers
- Rocca Imperiale(MZ): 2 speakers
- Laino (ZZ): 6 speakers
- Lauria (MZ): 1 speaker
- S. Domenica Talao (ZZ): 1 speaker
- Canna (MZ): 1 speaker
- Schiavonea (ZZ): 1 speaker
N.B.: “Region” here is based on the expected metaphonic patterns and does not strictly refer to geography. In particular:
MZ now includes also Orsomarso (a monophthongal isle in the ZZ), Lauria (which is Mittelzone but on the western, Basilicata side), and Castrovillari (Südzone, monophthongising metaphony).
ZZ also includes Schiavonea, which is on the East coast but belongs to the Südzone (see division in zones by Lausberg, 1939).
1. DCT analysis of F1 in all suffix vowel contexts, verbs vs Nouns/adjectives
F1 values of /e/ and /o/- stems were analysed altogether since for both vowel types F1 lowering or raising corresponds to raising or lowering of the vowel respectively.
What to expect:
k0 is proportional the signal’s mean: we expect higher values (thus pointing to vowel lowering) for /a/-suffixed forms, and lower k0 values (pointing to vowel raising) for the other suffixes. Also, based on previous analyses (see Introduction in the paper and Greca et al. 2024), we expect these differences being mostly marked in MZ, least in MM, and in-between the two in ZZ.
k1 is proportional the signal’s linear slope: based on Greca et al. 2024, we expect k1 to be significant only for ZZ. In particular, decreasing k1 values point to more opening diphthonigsation, which is the type of diphthongisation we would expect in metaphonic contexts (suffixes /i, u/).
1.1. Overview: plots
Plot of aggregated formants (F1) separately by region, grammatical class, metaphonic vs non-metaphonic forms. We do this to have a look at how stem vowel F1 generally look like depending on metaphonic context (TRUE = suffixes /i, u/; FALSE = suffixes /a, e/).
v.mean.F1 = D_basic %>%
# 2 vowels
filter(Stem_vowel %in% c("e", "o") ) %>%
# for each label, speaker and normalised time point
group_by(speaker, Gram, times_norm, MET, Stem_vowel, Region) %>%
# calculate mean F2
summarise(F1n = mean(F1n)) %>%
ungroup()
cols = c("darkorange", "purple")
v.mean.F1 %>%
ggplot +
# plot F1 as a function of normalised time
# colour-coded by MET
aes(y = F1n, x = times_norm, col=MET, group=MET) +
facet_grid(Gram~Region)+
geom_smooth()+
theme_light() +
ylab("Normalised F1 (standard deviations)")+
xlab("Normalised time")+
scale_x_continuous("Normalised time", breaks = c(0, 0.25, 0.5, 0.75)) +
theme(strip.text.x = element_text(color = "black"), strip.text.y = element_text(color = "black"),
text = element_text(size = 12), legend.position = "top")+
scale_color_manual(values = cols, name = "Metaphony")
Alternatively, we can also plot the stem vowels separately (suggested by Reviewer 2):
a=v.mean.F1 %>% filter(Stem_vowel == "e") %>%
ggplot +
# plot F1 as a function of normalised time
# colour-coded by MET
aes(y = F1n, x = times_norm, col=MET, group=MET) +
facet_grid(Gram~Region)+
geom_smooth()+
theme_light() +
ylab("Normalised F1")+
xlab("Normalised time")+
scale_x_continuous("Normalised time", breaks = c(0, 0.25, 0.5, 0.75)) +
theme(strip.text.x = element_text(color = "black"), strip.text.y = element_text(color = "black"),
text = element_text(size = 12), legend.position = "top")+
scale_color_manual(values = cols, name = "Metaphony")+
ggtitle ("Stem-/e/")
b=v.mean.F1 %>% filter(Stem_vowel == "o") %>%
ggplot +
# plot F1 as a function of normalised time
# colour-coded by MET
aes(y = F1n, x = times_norm, col=MET, group=MET) +
facet_grid(Gram~Region)+
geom_smooth()+
theme_light() +
ylab("Normalised F1")+
xlab("Normalised time")+
scale_x_continuous("Normalised time", breaks = c(0, 0.25, 0.5, 0.75)) +
theme(strip.text.x = element_text(color = "black"), strip.text.y = element_text(color = "black"),
text = element_text(size = 12), legend.position = "top")+
scale_color_manual(values = cols, name = "Metaphony")+
ggtitle ("Stem-/o/")
grid.arrange(a, b, nrow=2)
k0, comparison between MET = T vs MET = F, by region and grammatical category:
D = D %>%
mutate(MET = ifelse(Suffix_vowel %in%
c("i", "u"), T, F))
D$Region = factor(D$Region, levels = c("MM", "ZZ", "MZ"))
cols.gram = c("blue", "red")
D %>%
ggplot +
aes(y = X0, x = MET, fill = Gram) +
geom_violin(position = position_dodge(0.8), color = NA, alpha=0.2) +
geom_boxplot(width=0.3, alpha = 0.7, cex=.5, position=position_dodge(.8)) +
facet_wrap(.~Region) +
coord_cartesian(ylim = c(-2, 2)) +
theme_light() + xlab("Metaphony") + ylab(expression(k[0]))+
theme(strip.text.x = element_text(color = "black"), strip.text.y = element_text(color = "black"),
text = element_text(size = 12), legend.position = "top") +
scale_fill_manual(values = cols.gram, name = "Grammatical category")
k1, comparison between all four suffix vowels, by region and grammatical category:
D %>%
ggplot +
aes(y = X1, x = MET, fill = Gram) +
geom_violin(position = position_dodge(0.8), color = NA, alpha=0.2) +
geom_boxplot(width=0.3, alpha = 0.7, cex=.5, position=position_dodge(.8)) +
facet_wrap(.~Region) +
coord_cartesian(ylim = c(-1.3, 1.3)) +
theme_light() + xlab("Metaphony") + ylab(expression(k[1]))+
theme(strip.text.x = element_text(color = "black"), strip.text.y = element_text(color = "black"),
text = element_text(size = 12), legend.position = "top") +
scale_fill_manual(values = cols.gram, name = "Grammatical category")
From the plots above it is clearly visible that verbs show overall less metaphony than both adjectives and nouns together. Also, we can see that metaphony/coarticulatory effects are less marked (if not absent) in verbs. The statistical analysis below confirms that these differences are significant.
1.2. Statistics
## Backward reduced random-effect table:
##
## Eliminated npar logLik AIC LRT Df Pr(>Chisq)
## <none> 22 -17702 35448
## Region in (Region | Stem) 0 17 -18557 37147 1709.25 5 < 2.2e-16
## MET in (MET | speaker) 0 20 -17784 35608 164.44 2 < 2.2e-16
##
## <none>
## Region in (Region | Stem) ***
## MET in (MET | speaker) ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Backward reduced fixed-effect table:
## Degrees of freedom method: Satterthwaite
##
## Eliminated Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## Region:Gram:MET 0 37.993 18.996 2 16710 43.8 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Model found:
## X0 ~ Region * Gram * MET + (Region | Stem) + (MET | speaker)## Backward reduced random-effect table:
##
## Eliminated npar logLik AIC LRT Df Pr(>Chisq)
## <none> 22 -1085.7 2215.3
## Region in (Region | Stem) 0 17 -1488.7 3011.4 806.05 5 < 2.2e-16
## MET in (MET | speaker) 0 20 -1138.2 2316.3 104.97 2 < 2.2e-16
##
## <none>
## Region in (Region | Stem) ***
## MET in (MET | speaker) ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Backward reduced fixed-effect table:
## Degrees of freedom method: Satterthwaite
##
## Eliminated Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## Region:Gram:MET 0 2.2324 1.1162 2 15704 17.749 1.996e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Model found:
## X1 ~ Region * Gram * MET + (Region | Stem) + (MET | speaker)Models found by step() coincide with the ones suggested:
D %>%
lmer(X0 ~ Region * Gram * MET + (Region | Stem) + (MET | speaker),
control = lmerControl(
optimizer ='optimx', optCtrl=list(method='nlminb')), .) %>% anova()## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## Region 0.549 0.275 2 57.1 0.6330 0.534700
## Gram 2.429 2.429 1 56.0 5.6012 0.021429 *
## MET 82.070 82.070 1 202.3 189.2289 < 2.2e-16 ***
## Region:Gram 0.046 0.023 2 53.5 0.0531 0.948292
## Region:MET 6.018 3.009 2 198.3 6.9380 0.001224 **
## Gram:MET 154.438 154.438 1 17067.3 356.0887 < 2.2e-16 ***
## Region:Gram:MET 37.993 18.996 2 16709.6 43.8002 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1D %>%
lmer(X1 ~ Region * Gram * MET + (Region | Stem) + (MET | speaker),
control = lmerControl(
optimizer ='optimx', optCtrl=list(method='nlminb')), .) %>% anova()## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## Region 0.3586 0.1793 2 88.8 2.8509 0.063096 .
## Gram 0.0076 0.0076 1 56.0 0.1201 0.730266
## MET 1.1152 1.1152 1 201.8 17.7336 3.827e-05 ***
## Region:Gram 0.3483 0.1742 2 51.0 2.7696 0.072132 .
## Region:MET 0.6157 0.3078 2 195.3 4.8953 0.008425 **
## Gram:MET 3.9447 3.9447 1 17030.8 62.7285 2.518e-15 ***
## Region:Gram:MET 2.2324 1.1162 2 15704.5 17.7493 1.996e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1For both models, there is an interesting three-way interaction between region, suffix vowel, and grammatical category. This is why we do a post-hoc test.
#emm_options(pbkrtest.limit = 17259)
D %>%
lmer(X0 ~ Region * Gram * MET + (Region | Stem) + (MET | speaker),
control = lmerControl(
optimizer ='optimx', optCtrl=list(method='nlminb')), .) %>%
emmeans(., ~ MET * Region|Gram) %>%
pairs(., simple = "each", combine=T) %>%
as.data.frame() %>%
filter(p.value <= 0.05) %>%
as_tibble() %>%
mutate(p.value = round(p.value, 4)) %>%
print(., n = nrow(.), max_extra_cols = ncol(.))## Note: D.f. calculations have been disabled because the number of observations exceeds 3000.
## To enable adjustments, add the argument 'pbkrtest.limit = 17259' (or larger)
## [or, globally, 'set emm_options(pbkrtest.limit = 17259)' or larger];
## but be warned that this may result in large computation time and memory use.## Note: D.f. calculations have been disabled because the number of observations exceeds 3000.
## To enable adjustments, add the argument 'lmerTest.limit = 17259' (or larger)
## [or, globally, 'set emm_options(lmerTest.limit = 17259)' or larger];
## but be warned that this may result in large computation time and memory use.## # A tibble: 8 × 9
## Region Gram MET contrast estimate SE df z.ratio p.value
## <chr> <chr> <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 MM NAdj . FALSE - TRUE 0.504 0.0440 Inf 11.4 0
## 2 ZZ NAdj . FALSE - TRUE 0.641 0.0477 Inf 13.4 0
## 3 MZ NAdj . FALSE - TRUE 1.08 0.0350 Inf 30.9 0
## 4 . NAdj TRUE MM - MZ 0.351 0.0780 Inf 4.50 0.0002
## 5 . NAdj TRUE ZZ - MZ 0.220 0.0702 Inf 3.13 0.0412
## 6 MM . TRUE NAdj - V -0.743 0.201 Inf -3.70 0.0053
## 7 ZZ . TRUE NAdj - V -0.723 0.214 Inf -3.38 0.0175
## 8 MZ . TRUE NAdj - V -1.02 0.253 Inf -4.03 0.0013D %>%
lmer(X1 ~ Region * Gram * MET + (Region | Stem) + (MET | speaker),
control = lmerControl(
optimizer ='optimx', optCtrl=list(method='nlminb')), .) %>%
emmeans(., ~ MET * Region|Gram) %>%
pairs(., simple = "each", combine=T) %>%
as.data.frame() %>%
filter(p.value <= 0.05) %>%
as_tibble() %>%
mutate(p.value = round(p.value, 4)) %>%
print(., n = nrow(.), max_extra_cols = ncol(.))## Note: D.f. calculations have been disabled because the number of observations exceeds 3000.
## To enable adjustments, add the argument 'pbkrtest.limit = 17259' (or larger)
## [or, globally, 'set emm_options(pbkrtest.limit = 17259)' or larger];
## but be warned that this may result in large computation time and memory use.
## Note: D.f. calculations have been disabled because the number of observations exceeds 3000.
## To enable adjustments, add the argument 'lmerTest.limit = 17259' (or larger)
## [or, globally, 'set emm_options(lmerTest.limit = 17259)' or larger];
## but be warned that this may result in large computation time and memory use.## # A tibble: 4 × 9
## Region Gram MET contrast estimate SE df z.ratio p.value
## <chr> <chr> <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 ZZ NAdj . FALSE - TRUE 0.213 0.0171 Inf 12.4 0
## 2 MZ NAdj . FALSE - TRUE 0.0567 0.0122 Inf 4.63 0.0001
## 3 . NAdj TRUE MM - ZZ 0.282 0.0349 Inf 8.06 0
## 4 . NAdj TRUE ZZ - MZ -0.217 0.0304 Inf -7.12 0As regards the differences between regions, results are in line with FPCA analysis by Greca et al. 2024: k1 plays a role mainly for ZZ in nouns and adjectives, while differences in k0 are significant between the regions MM-MZ and ZZ-MZ.
However, for MET=T vs F, k-score differences between regions are significant only for nouns and adjectives. Also, differences between grammatical categories are significant in metaphonic contexts for all three regions. In line with the previous plots, this confirms that verbs show overall significantly less metaphony than nouns and adjectives in all regions.
Consequently, the next step is to zoom into different verb lexical stems, to check whether there are differences between (and within) verbs (following Lausberg 1939; see Introduction in the paper).
2. Differences between verbal lexical stems
We plot verbal lexical stems separately by person: this is because, following Lausberg (1939), we may have metaphony in some persons but not in others, or metaphony in all persons, or no metaphony in any person. “Person” includes the suffix vowels grouped into three levels: non-high /a, e/ suffixes (morphologically marking the third person singular); high front /i/ (second person singular); high back /u/ (first person singular).
Below the code to order the verbal stems in conjugation order and to generate the new variable “Person”.
# put verbs in latin conjugation order
# (NB: /vol/ comes from "volo, vis, velle", an irregular verb; in Italian it belongs to the second conjugation):
D_verb = D %>% filter(Gram == "V")
D_verb$Stem = factor(D_verb$Stem, levels = c("pens", "trov", "ten", "vol", "dorm", "ess", "mor"))
# Create variable "Person" as described above and in the Method section of the paper
D_third = D_verb %>% filter(Suffix_vowel %in% c("a", "e"))
D_third$Person <- "3rd"
D_second = D_verb %>% filter(Suffix_vowel == "i")
D_second$Person <- "2nd"
D_first = D_verb %>% filter(Suffix_vowel == "u")
D_first$Person <- "1st"
D_verb= rbind(D_third, D_second, D_first)
# colours for the plots
cols.suff = c("darkgrey", "orange","darkgreen")2.1 Overview: violin plots
Comparison between MM and MZ:
D_verb %>% filter(Region %in% c( "MM", "MZ") & !Stem %in% c( "mor", "vol")) %>%
ggplot +
aes(y = X0, x = Person, fill = Person) +
geom_violin(position = position_dodge(0.8), color = NA, alpha=0.4, width=1) +
geom_boxplot(width=0.4, alpha = 0.7, cex=.5, position=position_dodge(.8)) +
ylab(expression(k[0]))+
xlab("")+
geom_hline(yintercept=0, linetype="longdash", size=0.3)+
facet_grid(Region~Stem) +
coord_cartesian(ylim = c(-2, 2)) +
theme_light() +
scale_fill_manual(values = cols.suff,
name = "Person")+
theme(strip.text.x = element_text(color = "black"), strip.text.y = element_text(color = "black"),
text = element_text(size = 10), legend.position = "top") 
Mormanno, k0
/pens/: 1. Latin conjugation. There is a slight coarticulatory effect of suffix-/u/ pulling the signal’s mean downwards, otherwise no visible effects of suffix vowel. Please also consider that the 2. pers. sg. suffix here is /asi/ (yellow violin plot), so it is no surprise that coarticulatorily we have similar effects to suffix-/a/ (grey violin plot).
/trov/: 1. Latin conjugation. We find a very similar situation to /pens/.
/ten/: 2. Latin conjugation. k0 is slightly lower for both 1. and (surprisingly, given we are dealing with an /e/-suffix) 3. person singular, but differences do not look significant.
/dorm/: 4. Latin conjugation. There is no raising at all. Indeed, all values point to vowel lowering.
/ess/: 4. Latin conjugation. Values suggest the presence of mid-high /e/ in the stem, with slight raising for the second person singular (but differences do no appear to be significant). NB this could also be linked to the fact that often the pronunciation is rather /jE/ or /je/, so that the mean raises a bit compared to other dialects.
To sum-up: in Mormanno, vowel stems present overall mid-low vowels (with only 2 exceptions, /vol, ess/). Probably, the presence of raising before /u/-suffixes (which is however not that consistent) is due to “gradient” coarticulatory effects.
Mittelzone, k0
/pens/: 1. conjugation. Differences do not look significant.
/trov/: 1. conjugation. Differences do not look significant.
/ten/: 2. conjugation. Differences do not look significant.
/dorm/: 4. conjugation. Differences do not look significant. However, there may be a slight raising (part of the violin plots below 0)
/ess/: 4. conjugation. Values point to generalised vowel raising, especially marked in the second and third persons. Please also notice that, similarly as in other regions, the first person sg. may have a diphthongal vowel quality [jesk@], and this may lower the whole signal’s mean.
There is a very big variation in the scores (very long violin plots). For MZ, there may be a loss of metaphony for /dorm/ compared to the data by Lausberg (general high means, although many tokens appear below the 0-line), while the observations by Lausberg fit our data for /ess/ (less metaphony in the 1. person and metaphonic vowel raising in the other two).
Zwischenzone, k1 (signal’s slope, indirectly degree of diphthongisation)
values below 0 suggest more opening diphthongisation /O/ > [wo, uo]; /E/ > [jE, ie].
D_verb %>% filter(Region == "ZZ" & !Stem %in% c( "mor", "vol")) %>%
ggplot +
aes(y = X1, x = Person, fill = Person) +
geom_violin(position = position_dodge(0.8), color = NA, alpha=0.4, width=1) +
geom_boxplot(width=0.4, alpha = 0.7, cex=.5, position=position_dodge(.8)) +
ylab(expression(k[1]))+
xlab("")+
geom_hline(yintercept=0, linetype="longdash", size=0.3)+
facet_grid(Region~Stem) +
coord_cartesian(ylim = c(-1.3, 1)) +
theme_light() +
scale_fill_manual(values = cols.suff,
name = "Person")+
theme(strip.text.x = element_text(color = "black"), strip.text.y = element_text(color = "black"),
text = element_text(size = 10), legend.position = "top") 
/pens/: 1. conjugation. Apparently no significant differences between suffixes.
/trov/: 1. conjugation. Apparently no significant differences between suffixes.
/ten/: 2. conjugation. By observing the grey and yellow violin plots this would suggest that the 2. and 3. (suffix-/e/) p. singular may show metaphonic diphthongisation.
/dorm/: 4. conjugation. It looks like all three persons may diphthong, with slightly lower k1 values in the first two persons. This is not exactly in line with what described by Lausberg for two villages of the ZZ (one of which, Verbicaro, is also represented in our data). However, please also remember that the signal’s means for the verb were high (open stem vowels).
/ess/: 4. conjugation: the values indicate no diphthongisation.
In general, the presence of long violin plots points to great variation within the data. To sum-up: general diphthongisation for /dorm/ (an evolution compared to the data by Lausberg?) and unexpected metaphony of the 2. and 3. persons in /ten/. There may be slight metaphony in the second person of /vol/.
General summary: a general tendency to metaphonise less for all verbs also compared to the data by Lausberg.
To check what differences are significant or not, we need statistics.
2.2. Statistics
We test whether the differences above are significant: the hypothesis is that that are significant differences for some verbs between different persons. We test this hypothesis separately by DCT-score.
## [1] 1813# Analysis
#k0
D_verb %>% filter (!Stem %in% c( "mor", "vol")) %>%
lmer(X0 ~ Stem * Person * Region + (1 | speaker),
control = lmerControl(
optimizer ='optimx', optCtrl=list(method='nlminb')), .) %>% anova()## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## Stem 203.062 50.766 4 1709.50 152.6272 < 2.2e-16 ***
## Person 2.334 1.167 2 1711.85 3.5089 0.030144 *
## Region 3.070 1.535 2 78.76 4.6151 0.012726 *
## Stem:Person 5.834 0.729 8 1696.98 2.1923 0.025485 *
## Stem:Region 77.776 9.722 8 1710.27 29.2292 < 2.2e-16 ***
## Person:Region 5.241 1.310 4 1711.95 3.9391 0.003459 **
## Stem:Person:Region 11.395 0.712 16 1697.14 2.1413 0.005335 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1#k1
D_verb %>% filter (!Stem %in% c( "mor", "vol")) %>%
lmer(X1 ~ Stem * Person * Region + (1 | speaker),
control = lmerControl(
optimizer ='optimx', optCtrl=list(method='nlminb')), .) %>% anova()## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## Stem 22.5897 5.6474 4 1727.20 103.2767 < 2.2e-16 ***
## Person 0.6426 0.3213 2 1731.75 5.8760 0.002862 **
## Region 0.1388 0.0694 2 78.82 1.2691 0.286756
## Stem:Person 3.8868 0.4859 8 1707.38 8.8850 5.481e-12 ***
## Stem:Region 2.2349 0.2794 8 1728.31 5.1089 2.624e-06 ***
## Person:Region 0.2385 0.0596 4 1731.20 1.0902 0.359721
## Stem:Person:Region 1.8196 0.1137 16 1707.70 2.0797 0.007190 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Below the post-hoc tests for each of the models above (Reminder: the first persons is indicated by /u/-suffixed forms; /e, a/ suffixes correspond to the third person; /i/-suffixes indicate the second person):
# k0
D_verb %>% filter (!Stem %in% c( "mor", "vol")) %>%
lmer(X0 ~ Stem * Person * Region + (1 | speaker),
control = lmerControl(
optimizer ='optimx', optCtrl=list(method='nlminb')), .) %>%
emmeans(., ~ Person * Region | Stem) %>%
pairs(., simple = "each", combine=T) %>%
as.data.frame() %>%
filter(p.value <= 0.05) %>%
as_tibble() %>%
mutate(p.value = round(p.value, 4)) %>%
print(., n = nrow(.), max_extra_cols = ncol(.))## # A tibble: 60 × 9
## Region Stem Person contrast estimate SE df t.ratio p.value
## <chr> <chr> <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 ZZ ten . 1st - 3rd -0.586 0.156 1696. -3.77 0.0304
## 2 ZZ ten . 2nd - 3rd -0.659 0.156 1696. -4.24 0.0043
## 3 MZ ess . 1st - 2nd 0.479 0.122 1692. 3.93 0.0159
## 4 . ten 2nd MM - ZZ 0.660 0.165 617. 4.00 0.0128
## 5 . ten 2nd ZZ - MZ -0.823 0.149 570. -5.53 0
## 6 . dorm 1st MM - MZ 0.739 0.131 537. 5.66 0
## 7 . dorm 1st ZZ - MZ 0.723 0.149 563. 4.86 0.0003
## 8 . dorm 2nd MM - MZ 0.821 0.142 695. 5.78 0
## 9 . dorm 2nd ZZ - MZ 0.715 0.152 605. 4.71 0.0005
## 10 . dorm 3rd MM - MZ 0.800 0.146 730. 5.48 0
## 11 . dorm 3rd ZZ - MZ 0.752 0.153 606. 4.91 0.0002
## 12 . ess 2nd MM - MZ 0.724 0.165 978. 4.40 0.0022
## 13 . ess 3rd MM - MZ 0.787 0.152 813. 5.18 0
## 14 MM . 1st pens - ess 0.524 0.131 1707. 3.99 0.0126
## 15 MM . 1st trov - ess 0.631 0.138 1728. 4.59 0.0009
## 16 MM . 1st ten - ess 0.568 0.124 1719. 4.56 0.001
## 17 MM . 1st dorm - ess 0.811 0.126 1712. 6.46 0
## 18 MM . 2nd pens - ess 0.870 0.155 1705. 5.63 0
## 19 MM . 2nd trov - ess 0.937 0.161 1710. 5.80 0
## 20 MM . 2nd ten - ess 0.812 0.154 1723. 5.28 0
## 21 MM . 2nd dorm - ess 0.958 0.156 1712. 6.14 0
## 22 MM . 3rd pens - ess 0.643 0.142 1699. 4.52 0.0012
## 23 MM . 3rd trov - ess 0.865 0.158 1697. 5.48 0
## 24 MM . 3rd ten - ess 0.578 0.137 1716. 4.22 0.0047
## 25 MM . 3rd dorm - ess 0.807 0.145 1701. 5.55 0
## 26 ZZ . 1st pens - ess 0.764 0.156 1697. 4.89 0.0002
## 27 ZZ . 1st trov - ten 0.596 0.149 1693. 3.99 0.0124
## 28 ZZ . 1st trov - ess 1.17 0.155 1693. 7.59 0
## 29 ZZ . 1st ten - dorm -0.614 0.147 1692. -4.19 0.0053
## 30 ZZ . 1st ten - ess 0.577 0.152 1696. 3.79 0.0281
## 31 ZZ . 1st dorm - ess 1.19 0.152 1692. 7.83 0
## 32 ZZ . 2nd pens - ess 0.676 0.162 1700. 4.17 0.0056
## 33 ZZ . 2nd trov - ten 0.625 0.160 1695. 3.92 0.0168
## 34 ZZ . 2nd trov - ess 0.921 0.170 1702. 5.43 0
## 35 ZZ . 2nd ten - dorm -0.700 0.149 1691. -4.69 0.0005
## 36 ZZ . 2nd dorm - ess 0.997 0.160 1698. 6.23 0
## 37 ZZ . 3rd pens - ess 0.614 0.167 1700. 3.68 0.0428
## 38 ZZ . 3rd trov - ess 1.07 0.177 1696. 6.02 0
## 39 ZZ . 3rd ten - ess 0.987 0.172 1695. 5.75 0
## 40 ZZ . 3rd dorm - ess 1.05 0.165 1698. 6.37 0
## 41 MZ . 1st pens - dorm 0.625 0.103 1697. 6.08 0
## 42 MZ . 1st pens - ess 0.986 0.115 1708. 8.56 0
## 43 MZ . 1st trov - dorm 0.786 0.105 1696. 7.51 0
## 44 MZ . 1st trov - ess 1.15 0.117 1711. 9.79 0
## 45 MZ . 1st ten - dorm 0.562 0.0972 1700. 5.78 0
## 46 MZ . 1st ten - ess 0.923 0.110 1709. 8.38 0
## 47 MZ . 2nd pens - dorm 0.785 0.108 1694. 7.25 0
## 48 MZ . 2nd pens - ess 1.65 0.119 1701. 13.8 0
## 49 MZ . 2nd trov - dorm 0.880 0.106 1698. 8.28 0
## 50 MZ . 2nd trov - ess 1.74 0.117 1707. 14.8 0
## 51 MZ . 2nd ten - dorm 0.838 0.101 1699. 8.30 0
## 52 MZ . 2nd ten - ess 1.70 0.112 1708. 15.1 0
## 53 MZ . 2nd dorm - ess 0.861 0.113 1703. 7.63 0
## 54 MZ . 3rd pens - dorm 0.620 0.111 1696. 5.56 0
## 55 MZ . 3rd pens - ess 1.41 0.116 1699. 12.2 0
## 56 MZ . 3rd trov - dorm 0.587 0.108 1696. 5.45 0
## 57 MZ . 3rd trov - ess 1.38 0.113 1710. 12.2 0
## 58 MZ . 3rd ten - dorm 0.746 0.105 1702. 7.08 0
## 59 MZ . 3rd ten - ess 1.54 0.110 1706. 13.9 0
## 60 MZ . 3rd dorm - ess 0.794 0.112 1699. 7.11 0# k1
D_verb %>% filter (!Stem %in% c( "mor", "vol")) %>%
lmer(X1 ~ Stem * Person * Region + (1 | speaker),
control = lmerControl(
optimizer ='optimx', optCtrl=list(method='nlminb')), .) %>%
emmeans(., ~ Person * Region | Stem) %>%
pairs(., simple = "each", combine=T) %>%
as.data.frame() %>%
filter(p.value <= 0.05) %>%
as_tibble() %>%
mutate(p.value = round(p.value, 4)) %>%
print(., n = nrow(.), max_extra_cols = ncol(.))## # A tibble: 36 × 9
## Region Stem Person contrast estimate SE df t.ratio p.value
## <chr> <chr> <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 ZZ ten . 1st - 2nd 0.399 0.0594 1692. 6.72 0
## 2 ZZ ten . 1st - 3rd 0.348 0.0630 1700. 5.52 0
## 3 MZ ten . 1st - 2nd 0.189 0.0395 1708. 4.79 0.0003
## 4 MZ ten . 1st - 3rd 0.215 0.0402 1711. 5.35 0
## 5 MM . 1st pens - dorm 0.398 0.0506 1703. 7.88 0
## 6 MM . 1st trov - dorm 0.317 0.0529 1730. 5.99 0
## 7 MM . 1st ten - dorm 0.216 0.0474 1709. 4.55 0.001
## 8 MM . 1st dorm - ess -0.255 0.0507 1734. -5.03 0.0001
## 9 MM . 2nd pens - ten 0.204 0.0557 1737. 3.66 0.0475
## 10 MM . 2nd pens - dorm 0.394 0.0567 1719. 6.95 0
## 11 MM . 2nd trov - dorm 0.273 0.0594 1708. 4.59 0.0008
## 12 MM . 2nd dorm - ess -0.255 0.0630 1730. -4.05 0.0095
## 13 MM . 3rd pens - trov 0.278 0.0620 1712. 4.48 0.0014
## 14 MM . 3rd pens - ten 0.273 0.0532 1751. 5.13 0.0001
## 15 MM . 3rd pens - dorm 0.376 0.0569 1725. 6.61 0
## 16 MM . 3rd dorm - ess -0.226 0.0588 1712. -3.84 0.0232
## 17 ZZ . 1st pens - dorm 0.404 0.0611 1701. 6.61 0
## 18 ZZ . 1st trov - dorm 0.374 0.0605 1693. 6.18 0
## 19 ZZ . 1st ten - dorm 0.444 0.0594 1694. 7.47 0
## 20 ZZ . 1st dorm - ess -0.293 0.0616 1695. -4.75 0.0004
## 21 ZZ . 2nd pens - ten 0.428 0.0612 1706. 7.00 0
## 22 ZZ . 2nd pens - dorm 0.499 0.0622 1710. 8.02 0
## 23 ZZ . 2nd trov - ten 0.380 0.0646 1704. 5.89 0
## 24 ZZ . 2nd trov - dorm 0.452 0.0655 1702. 6.89 0
## 25 ZZ . 2nd ten - ess -0.252 0.0639 1710. -3.95 0.0149
## 26 ZZ . 2nd dorm - ess -0.323 0.0648 1705. -4.99 0.0001
## 27 ZZ . 3rd pens - ten 0.346 0.0640 1701. 5.40 0
## 28 ZZ . 3rd pens - dorm 0.343 0.0610 1696. 5.62 0
## 29 MZ . 1st pens - dorm 0.244 0.0416 1706. 5.88 0
## 30 MZ . 1st pens - ess 0.177 0.0466 1726. 3.80 0.0273
## 31 MZ . 1st trov - dorm 0.156 0.0424 1706. 3.69 0.0422
## 32 MZ . 1st ten - dorm 0.214 0.0393 1710. 5.43 0
## 33 MZ . 2nd pens - ten 0.216 0.0438 1720. 4.93 0.0002
## 34 MZ . 2nd pens - dorm 0.209 0.0439 1702. 4.76 0.0004
## 35 MZ . 3rd pens - ten 0.274 0.0448 1729. 6.11 0
## 36 MZ . 3rd pens - dorm 0.259 0.0451 1706. 5.73 0The statistics confirms that differences observed before between persons are significant for /ten/ in ZZ (both k0 and k1) and slightly so in /ess/ in MZ (k0, 1st vs 2nd person). In all other cases, either are the effects non-significant, or metaphony is levelled to the whole paradigm, or it does not apply at all (see also Sections 3.2 and 3.3 in the paper).
3. Revisions: Alternative LMER models with four fixed factors
3.1. Statistics: step()-tests
Reviewer 2 suggested: “I recommend that the authors include an interaction between vowel and dialect as a predictor in the regression model(s)”, since (citing the editor) “differences in nouns/adjectives versus verbs could be because of different proportions of /e/ and /o/ in the lexical categories”.
A note: our models had “(lexical) stem” as a RF, so part of variation between /e/ and /o/-stemmed words was already considered in our previous models.
library(lmerTest)
library(emmeans)
D %>%
lmer(X0 ~ Region * Gram * MET * Stem_vowel + (Region | Stem) + (MET| speaker), .) %>% step()## boundary (singular) fit: see help('isSingular')## Backward reduced random-effect table:
##
## Eliminated npar logLik AIC LRT Df Pr(>Chisq)
## <none> 34 -17641 35349
## Region in (Region | Stem) 0 29 -18485 37028 1688.42 5 < 2.2e-16
## MET in (MET | speaker) 0 32 -17725 35513 168.03 2 < 2.2e-16
##
## <none>
## Region in (Region | Stem) ***
## MET in (MET | speaker) ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Backward reduced fixed-effect table:
## Degrees of freedom method: Satterthwaite
##
## Eliminated Sum Sq Mean Sq NumDF DenDF F value
## Region:Gram:MET:Stem_vowel 1 1.094 0.5472 2 16268.1 1.2699
## Region:Gram:Stem_vowel 2 0.707 0.3534 2 48.7 0.8202
## Region:MET:Stem_vowel 3 2.507 1.2534 2 8792.5 2.9090
## Region:Stem_vowel 4 0.994 0.4968 2 49.3 1.1528
## Region:Gram:MET 0 37.980 18.9900 2 16721.5 44.0694
## Gram:MET:Stem_vowel 0 9.131 9.1311 1 16968.7 21.1902
## Pr(>F)
## Region:Gram:MET:Stem_vowel 0.28087
## Region:Gram:Stem_vowel 0.44634
## Region:MET:Stem_vowel 0.05458 .
## Region:Stem_vowel 0.32412
## Region:Gram:MET < 2.2e-16 ***
## Gram:MET:Stem_vowel 4.189e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Model found:
## X0 ~ Region + Gram + MET + Stem_vowel + (Region | Stem) + (MET | speaker) + Region:Gram + Region:MET + Gram:MET + Gram:Stem_vowel + MET:Stem_vowel + Region:Gram:MET + Gram:MET:Stem_vowel## Backward reduced random-effect table:
##
## Eliminated npar logLik AIC LRT Df Pr(>Chisq)
## <none> 34 -1078.2 2224.3
## Region in (Region | Stem) 0 29 -1349.9 2757.8 543.46 5 < 2.2e-16
## MET in (MET | speaker) 0 32 -1130.8 2325.6 105.34 2 < 2.2e-16
##
## <none>
## Region in (Region | Stem) ***
## MET in (MET | speaker) ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Backward reduced fixed-effect table:
## Degrees of freedom method: Satterthwaite
##
## Eliminated Sum Sq Mean Sq NumDF DenDF F value
## Region:Gram:MET:Stem_vowel 1 0.29073 0.14537 2 14471.9 2.3177
## Region:Gram:Stem_vowel 2 0.08186 0.04093 2 42.9 0.6525
## Region:Gram:MET 0 2.16861 1.08431 2 14280.0 17.2870
## Region:MET:Stem_vowel 0 0.43591 0.21795 2 4109.7 3.4748
## Gram:MET:Stem_vowel 0 0.69124 0.69124 1 16934.8 11.0204
## Pr(>F)
## Region:Gram:MET:Stem_vowel 0.098538 .
## Region:Gram:Stem_vowel 0.525815
## Region:Gram:MET 3.173e-08 ***
## Region:MET:Stem_vowel 0.031058 *
## Gram:MET:Stem_vowel 0.000903 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Model found:
## X1 ~ Region + Gram + MET + Stem_vowel + (Region | Stem) + (MET | speaker) + Region:Gram + Region:MET + Gram:MET + Region:Stem_vowel + Gram:Stem_vowel + MET:Stem_vowel + Region:Gram:MET + Region:MET:Stem_vowel + Gram:MET:Stem_vowelSo the stem vowel seems to play a role (3-way interaction between Gram, MET, and Stem vowel).
3.2. LMER: anova() and post-hoc tests
k0:
library(lmerTest)
library(emmeans)
D %>% lmer(X0 ~ Region * Gram * MET * Stem_vowel + (Region | Stem) + (MET| speaker),
control = lmerControl(
optimizer ='optimx', optCtrl=list(method='nlminb')), .) %>% anova()## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## Region 0.681 0.341 2 54.2 0.7904 0.4588286
## Gram 3.757 3.757 1 53.6 8.7195 0.0046645 **
## MET 71.778 71.778 1 209.5 166.5977 < 2.2e-16 ***
## Stem_vowel 3.233 3.233 1 53.6 7.5031 0.0083462 **
## Region:Gram 0.063 0.032 2 50.7 0.0735 0.9292099
## Region:MET 6.014 3.007 2 205.2 6.9798 0.0011679 **
## Gram:MET 134.149 134.149 1 17067.4 311.3640 < 2.2e-16 ***
## Region:Stem_vowel 0.692 0.346 2 50.5 0.8036 0.4533592
## Gram:Stem_vowel 0.779 0.779 1 53.6 1.8090 0.1842884
## MET:Stem_vowel 6.109 6.109 1 16963.9 14.1788 0.0001668 ***
## Region:Gram:MET 38.404 19.202 2 16462.3 44.5686 < 2.2e-16 ***
## Region:Gram:Stem_vowel 0.471 0.236 2 50.5 0.5469 0.5821348
## Region:MET:Stem_vowel 0.863 0.432 2 16268.1 1.0021 0.3671378
## Gram:MET:Stem_vowel 9.816 9.816 1 16960.0 22.7821 1.83e-06 ***
## Region:Gram:MET:Stem_vowel 1.094 0.547 2 16268.0 1.2700 0.2808572
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1We can apply the same model also to k1:
library(lmerTest)
library(emmeans)
D %>%
lmer(X1 ~ Region * Gram * MET * Stem_vowel + (Region | Stem) + (MET| speaker), control = lmerControl(
optimizer ='optimx', optCtrl=list(method='nlminb')), .) %>% anova()## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## Region 0.4129 0.2065 2 82.2 3.2919 0.042144 *
## Gram 0.0049 0.0049 1 53.6 0.0775 0.781757
## MET 1.3028 1.3028 1 214.0 20.7718 8.695e-06 ***
## Stem_vowel 0.0289 0.0289 1 53.5 0.4603 0.500385
## Region:Gram 0.4166 0.2083 2 45.8 3.3208 0.044999 *
## Region:MET 0.6735 0.3368 2 205.9 5.3694 0.005332 **
## Gram:MET 4.1091 4.1091 1 17016.9 65.5147 6.154e-16 ***
## Region:Stem_vowel 0.3069 0.1535 2 45.5 2.4469 0.097889 .
## Gram:Stem_vowel 0.0016 0.0016 1 53.5 0.0262 0.871998
## MET:Stem_vowel 0.1246 0.1246 1 16929.9 1.9859 0.158783
## Region:Gram:MET 1.9617 0.9808 2 14763.1 15.6385 1.642e-07 ***
## Region:Gram:Stem_vowel 0.0683 0.0342 2 45.5 0.5448 0.583713
## Region:MET:Stem_vowel 0.1010 0.0505 2 14473.9 0.8051 0.447058
## Gram:MET:Stem_vowel 0.5526 0.5526 1 16924.1 8.8113 0.002998 **
## Region:Gram:MET:Stem_vowel 0.2907 0.1454 2 14471.9 2.3176 0.098543 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1The 4-way interaction is never significant, but the interaction between Gram, MET, and stem vowel is significant for both models.
Post-hoc tests for k0:
#emm_options(pbkrtest.limit = 17259)
D %>%
lmer(X0 ~ Region * Gram * MET * Stem_vowel + (Region | Stem) + (MET| speaker),
control = lmerControl(
optimizer ='optimx', optCtrl=list(method='nlminb')), .) %>%
emmeans(., ~ Stem_vowel * MET|Gram) %>%
pairs(., simple = "each", combine=T) %>%
as.data.frame() %>%
filter(p.value <= 0.05) %>%
as_tibble() %>%
mutate(p.value = round(p.value, 4)) %>%
print(., n = nrow(.), max_extra_cols = ncol(.))## Note: D.f. calculations have been disabled because the number of observations exceeds 3000.
## To enable adjustments, add the argument 'pbkrtest.limit = 17259' (or larger)
## [or, globally, 'set emm_options(pbkrtest.limit = 17259)' or larger];
## but be warned that this may result in large computation time and memory use.## Note: D.f. calculations have been disabled because the number of observations exceeds 3000.
## To enable adjustments, add the argument 'lmerTest.limit = 17259' (or larger)
## [or, globally, 'set emm_options(lmerTest.limit = 17259)' or larger];
## but be warned that this may result in large computation time and memory use.## NOTE: Results may be misleading due to involvement in interactions## # A tibble: 6 × 9
## MET Gram Stem_vowel contrast estimate SE df z.ratio p.value
## <chr> <chr> <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 FALSE NAdj . e - o -0.804 0.109 Inf -7.36 0
## 2 TRUE NAdj . e - o -0.472 0.109 Inf -4.33 0.0002
## 3 . NAdj e FALSE - TRUE 0.542 0.0308 Inf 17.6 0
## 4 . NAdj o FALSE - TRUE 0.874 0.0275 Inf 31.8 0
## 5 TRUE . e NAdj - V -0.925 0.233 Inf -3.96 0.0009
## 6 TRUE . o NAdj - V -0.690 0.208 Inf -3.32 0.0109There are differences between F1 means in /e/ and /o/ in both metaphonic and non-metaphonic contexts. However, such differences are significant only for N/Adj, not for verbs.
Same post-hoc texts for k1:
#emm_options(pbkrtest.limit = 17259)
D %>%
lmer(X1 ~ Region * Gram * MET * Stem_vowel + (Region | Stem) + (MET| speaker),
control = lmerControl(
optimizer ='optimx', optCtrl=list(method='nlminb')), .) %>%
emmeans(., ~ Stem_vowel * MET|Gram) %>%
pairs(., simple = "each", combine=T) %>%
as.data.frame() %>%
filter(p.value <= 0.05) %>%
as_tibble() %>%
mutate(p.value = round(p.value, 4)) %>%
print(., n = nrow(.), max_extra_cols = ncol(.))## Note: D.f. calculations have been disabled because the number of observations exceeds 3000.
## To enable adjustments, add the argument 'pbkrtest.limit = 17259' (or larger)
## [or, globally, 'set emm_options(pbkrtest.limit = 17259)' or larger];
## but be warned that this may result in large computation time and memory use.## Note: D.f. calculations have been disabled because the number of observations exceeds 3000.
## To enable adjustments, add the argument 'lmerTest.limit = 17259' (or larger)
## [or, globally, 'set emm_options(lmerTest.limit = 17259)' or larger];
## but be warned that this may result in large computation time and memory use.## NOTE: Results may be misleading due to involvement in interactions## # A tibble: 2 × 9
## MET Gram Stem_vowel contrast estimate SE df z.ratio p.value
## <chr> <chr> <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 . NAdj e FALSE - TRUE 0.139 0.0112 Inf 12.4 0
## 2 . NAdj o FALSE - TRUE 0.0741 0.00987 Inf 7.50 0To sum-up : there are some differences in vowel height/F1 mean for /e/ vs /o/ in N/Adj only, no matter the suffix context. The verbs are not affected by these. So the results about differences in metaphony between N/Adj and verbs are still valid.
4. Relationship between stem and suffix vowel height
4.1 Data preparation
suff.df contains mean values (across all time points) of suffix vowels, when they were not deleted.
We only wish to analyse nouns and adjectives (Nadj)
Join suff.df to d.df
# Rename the variables so they have
# different names from `D_basic`
sx.df = suff.df %>%
rename(F1nx = F1n, F1x = F1) %>%
select(bundle, F1nx, F1x)
# Join to D_basic
f.df = left_join(d.df, sx.df, by = "bundle")
# extract at temporal midpoint
f5.df = f.df %>% filter(times_norm== .5)
# should have same number of rows as bundle count
nrow(f5.df) == length(unique(d.df$bundle))## [1] TRUE## [1] 0.35985524.2 Regression of F1 at stem midpoint and F1 in suffix vowel
We wish to determine whether there is a predictable relationship between F1-stem and F1-suffix within each suffix vowel.
Remove ‘ZZ’
An information for the method part: How many tokens with phonetically realised suffixes?
## [1] 8223NB: the statistical models below ignore rows for which there are no suffix vowel formant data.
This is the model:
f5.lmer = f5.df %>%
lmer(F1n ~ F1nx * Region * Suffix_vowel +
+ (Region|Stem) +
(1|speaker), .)
anova(f5.lmer)## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## F1nx 22.49 22.485 1 6902.7 83.1346 < 2.2e-16 ***
## Region 0.47 0.470 1 57.3 1.7391 0.192503
## Suffix_vowel 329.01 109.670 3 7541.0 405.4817 < 2.2e-16 ***
## F1nx:Region 1.98 1.983 1 6916.6 7.3331 0.006786 **
## F1nx:Suffix_vowel 0.75 0.250 3 7539.6 0.9234 0.428475
## Region:Suffix_vowel 58.46 19.486 3 6462.6 72.0448 < 2.2e-16 ***
## F1nx:Region:Suffix_vowel 0.81 0.268 3 7549.6 0.9923 0.395255
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Test slopes for significance together with F1nx interaction with Region:
emtrends(f5.lmer, pairwise ~ Region, by = 'Suffix_vowel', var = 'F1nx') %>%
# or e.g. rbind(adjust = "bonferroni") %>%
rbind(adjust = "sidak") %>%
summary(., infer=T)## Suffix_vowel Region contrast F1nx.trend SE df asymp.LCL asymp.UCL z.ratio
## a MM . 0.10909 0.0372 Inf 0.00275 0.215 2.932
## a MZ . 0.05602 0.0218 Inf -0.00631 0.118 2.569
## e MM . 0.11917 0.0410 Inf 0.00208 0.236 2.909
## e MZ . 0.11566 0.0285 Inf 0.03412 0.197 4.054
## i MM . 0.15915 0.0418 Inf 0.03968 0.279 3.807
## i MZ . 0.05084 0.0209 Inf -0.00884 0.111 2.435
## u MM . 0.17902 0.0374 Inf 0.07222 0.286 4.790
## u MZ . 0.08470 0.0238 Inf 0.01673 0.153 3.561
## a . MM - MZ 0.05307 0.0431 Inf -0.07014 0.176 1.231
## e . MM - MZ 0.00351 0.0499 Inf -0.13910 0.146 0.070
## i . MM - MZ 0.10831 0.0467 Inf -0.02523 0.242 2.318
## u . MM - MZ 0.09432 0.0443 Inf -0.03225 0.221 2.130
## p.value
## 0.0397
## 0.1159
## 0.0427
## 0.0006
## 0.0017
## 0.1649
## <.0001
## 0.0044
## 0.9480
## 1.0000
## 0.2196
## 0.3331
##
## Degrees-of-freedom method: asymptotic
## Confidence level used: 0.95
## Conf-level adjustment: sidak method for 12 estimates
## P value adjustment: sidak method for 12 testsHere is a plot (Figure 7 in the paper):
theme_phon =
function(atextx = 18, atexty = 18, atitlex=
18, atitley = 18, ptitle=24, strip.text.x = 24,
lpos = "bottom", othertext=24, ltitle =24){
theme(
axis.text.x = element_text(size=atextx),
axis.title.x = element_text(size=atitley),
axis.text.y = element_text(size=atexty),
axis.title.y = element_text(size=atitley),
plot.title = element_text(size = ptitle),
legend.position=lpos,
legend.title = ltitle,
strip.text.x =element_text(size=strip.text.x),
text = element_text(size=othertext))
}n =30; k = 22; i = 20; textsize = 30
col.values = c(rep("darkgreen", 2),
rep("red", 2), rep("blue", 2), rep("black", 2))
lty.values = rep(c(1, 3), 4)
lwd = 1.5
regmodel = f5.lmer %>%
emmip(., Region * Suffix_vowel ~ F1nx,
cov.reduce = range, plotit=F) %>%
emmip_ggplot(., Region * Suffix_vowel ~ F1nx,
cov.reduce = range,
linearg=list(linewidth=lwd)) +
scale_color_manual(values = col.values) +
scale_linetype_manual(values = lty.values) +
ylab("Normalized F1 in stem vowel") +
xlab("Normalized F1 in suffix vowel") +
theme_light() +
theme_phon(lpos="top",
atextx=i,
atexty=i,
atitlex=k,
atitley=k,
strip.text.x = k,
ptitle=n,
ltitle=element_blank(),
othertext=n)
ggsave(filename = "regression.png",
plot = regmodel,
width = 20,
height = 20,
units = "cm")
regmodel