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I am new to mixed models and have some trouble interpreting my model output.

I am investigating realisations of the vowel in words such as NURSE. For this I measured Formant values (F1/F2). In this case I am interested in F2. Without going into too much detail, I coded three contexts <Er, Ir, Vr> and want to see how the speakers F2 values vary in each context. I created a model (below) with a cross random predictor (phoneme|individual). the F2 values were normalised (zscores).

lmer <- lmer(F2 ~ (phoneme|individual) + (1|word) + age + frequency + (1|zduration), data = nurse_female). Linear mixed model fit by REML ['lmerMod'] Formula: F2 ~ (phoneme | individual) + age Data: nurse_female REML criterion at convergence: 686.3 Scaled residuals: Min 1Q Median 3Q Max -5.4834 -0.3934 0.0302 0.4440 3.3055 Random effects: Groups Name Variance Std.Dev. Corr individual (Intercept) 0.4461 0.6679 phonemeIr 0.8407 0.9169 -0.86 phonemeVr 1.9711 1.4040 -0.95 0.93 Residual 0.3388 0.5821 Number of obs: 334, groups: individual, 23 Fixed effects: Estimate Std. Error t value (Intercept) 1.395335 0.263929 5.287 age -0.016893 0.004959 -3.406 Correlation of Fixed Effects: (Intr) age -0.969 > plot(nurse_female_F2.lmer8) > summary(nurse_female_F2.lmer8) Linear mixed model fit by REML ['lmerMod'] Formula: F2 ~ (phoneme | individual) + (1 | word) + age + frequency + (1 | zduration) Data: nurse_female REML criterion at convergence: 654.4 Scaled residuals: Min 1Q Median 3Q Max -2.09203 -0.20332 0.03263 0.25273 1.37056 Random effects: Groups Name Variance Std.Dev. Corr zduration (Intercept) 0.27779 0.5271 word (Intercept) 0.04488 0.2118 individual (Intercept) 0.34181 0.5846 phonemeIr 0.54227 0.7364 -0.82 phonemeVr 1.52090 1.2332 -0.93 0.91 Residual 0.06326 0.2515 Number of obs: 334, groups: zduration, 280; word, 116; individual, 23 Fixed effects: Estimate Std. Error t value (Intercept) 1.79167 0.32138 5.575 age -0.01596 0.00508 -3.142 frequencylow -0.37587 0.18560 -2.025 frequencymid -1.18901 0.27738 -4.286 frequencyvery high -0.68365 0.26564 -2.574 Correlation of Fixed Effects: (Intr) age frqncyl frqncym age -0.811 frequencylw -0.531 -0.013 frequencymd -0.333 -0.006 0.589 frqncyvryhg -0.356 0.000 0.627 0.389

I checked model fit with a residual plot, checked that each effect is significant using anova tests. I also created a random effects plot for the crossed random effect.

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My question is now, how to I interpret the variance? Is it right to say that for Vr all speakers vary in their F2 between 0 and 1.97? And would be correct to say speaker 50 realises a mean F2 value of about 1,75 but has a max and min F2 of ca -3 and -.5?

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  • $\begingroup$ First this is not crossed random effects. You have random intercepts for individuals and random slopes for phoneme. However you have not fitted fixed effects for phoneme which is probably a mistake. Normally you fit fixed effects and if you have reason to think they vary by participant you can add random slopes. $\endgroup$ Commented Aug 15, 2020 at 16:01
  • $\begingroup$ I've seen the three similar posts over the past day. Maybe some back and forth discussion would be helpful? If you'd like, you can contact me, information can be found through my profile? $\endgroup$ Commented Aug 15, 2020 at 19:13

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Robert is right, these are not crossed random effects, but I think I understand the data enough that I can answer the other parts of your question. If you are interested in how phoneme changes across the different contexts, you need to have it has a fixed effect.

Something like this:

fit <- lmer(F2 ~ (phoneme|individual) + (1|word) + phoneme + age + frequency + (1|zduration), data = nurse_female)

As for the last question You have plotted the different individuals for each phoneme. So the (Intercept) category corresponds to the phoneme . The model above will allow you to plot the difference between the different F2 values of the three phonemes taking into account the differences between participants and that participants may not all produce the phonemes with equal differences between the three levels. You can then plot the fixed effects to see the differences of the "average" participant. For example, the code below would plot all fixed effects using the effects package.

library(effects) plot(allEffects(fit))
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  • $\begingroup$ Thank you so much! That already helped massively! $\endgroup$ Commented Aug 16, 2020 at 9:52
  • $\begingroup$ Glad I could help! $\endgroup$ Commented Aug 17, 2020 at 0:29

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