8 Summarizing models

Let’s further inspect our first model:

levels(f0_df$Tone)

## [1] "1" "2" "3" "4"

levels(f0_df$Gender)

## [1] "F" "M"

summary(m00_gam)

## 
## Family: gaussian 
## Link function: identity 
## 
## Formula:
## F0_st ~ Tone + Gender
## 
## Parametric coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  1.28292    0.05758   22.28   <2e-16 ***
## Tone2       -1.92844    0.07257  -26.57   <2e-16 ***
## Tone3       -5.20632    0.07243  -71.88   <2e-16 ***
## Tone4       -1.75915    0.07483  -23.51   <2e-16 ***
## GenderM      0.77784    0.05193   14.98   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## R-sq.(adj) =   0.28   Deviance explained =   28%
## -REML =  36673  Scale est. = 9.6754    n = 14357

The first two lines show the levels of our factors. The first level of Tone is “1” and the first level of Gender is “F”. These first levels are important because they usually determine the “reference” of our model.

The summary shows a table of parametric coefficients. The first row is the Intercept, i.e., the value of F0_st for the reference levels of our factors. In this case, the Estimate column indicates that the average F0 is 1.283 semitones higher than the speakers’ median F0 for female speakers producing Tone 1.

The Tone2 entry shows that Tone 2 is 1.928 semitones lower than Tone 1 for female speakers, while Tone 3 is about 5.2 semitones lower, and Tone 4 is 1.76 semitones lower than Tone 1 for female speakers. GenderM, indicates that, keeping Tone constant, male speakers produce tones that are 0.778 semitones higher than female tones. So, according to this model a male speaker producing a Tone 1 will have on average an f0 2.06 semitones higher than the median f0 of that speaker (1.283+0.778=2.061):

Mean F0 in semitones relative to the speaker-specific median F0.
	Female	Male
Tone 1	1.283	2.061
Tone 2	−0.646	0.132
Tone 3	−3.923	−3.145
Tone 4	−0.476	0.301

Note that the gender difference is the same for every tone since the model only includes the two independent factors and not their interaction.

The standard errors indicate the uncertainty around the estimates, the \(t\)-values indicate how far the estimates are from zero (in standard-error units), and the \(p\)-value, the probability of finding such a difference by chance.

Additionally, the summary also provides a measure of the adjusted \(R^2\) and the deviance explained. This model only accounts for 28% of the observed variation of F0 in semitones. This is not necessarily bad, but we could do better, based on experience.

The other entries (-REML, Scale est., and n) are not usually reported. They indicate the Restricted Maximum Likelihood—a method to estimate variance—, the residual variance, and the number of observations used for fitting the model.