I am new to gam, and most of my knowledge comes from this document http://www3.nd.edu/~mclark19/learn/GAMS.pdf. Now I am using generalized addictive model with random effects to model some data, where I want to see how "speedChange" correlates with "response" in my dataset, with consideration of random effects "user.id"
The code I run is shown as follows:
speed.gammer <- gamm4(response ~ s(speedChange) , data= t, random=~(1|user.id))
The gam can be plotted as follows:
I then try to interpret the gam:
which gives the following :
Family: gaussian Link function: identity Formula: response ~ s(speedChange) Parametric coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 2.30618 0.01482 155.6 <2e-16 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Approximate significance of smooth terms: edf Ref.df F p-value s(speedChange) 5.875 5.875 28.61 <2e-16 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 R-sq.(adj) = 0.0263 lmer.REML = 14688 Scale est. = 0.57643 n = 5619
From what I understand from the output, I learned that speedChange is significantly correlates with response, and the non-linear relationship is as shown in the plot. I know the R-squared is small, but that's not what I want to ask. I actually don't understand the mer model.
If I run:
I got the following results:
Linear mixed model fit by REML ['lmerMod'] REML criterion at convergence: 14687.7 Scaled residuals: Min 1Q Median 3Q Max -2.5908 -0.6500 -0.0454 0.5880 3.7110 Random effects: Groups Name Variance Std.Dev. user.id (Intercept) 0.2853 0.5342 Xr s(speedChange) 56.4011 7.5101 Residual 0.5764 0.7592 Number of obs: 5619, groups: user.id, 3042; Xr, 8 Fixed effects: Estimate Std. Error t value X(Intercept) 2.306181 0.014823 155.58 Xs(speedChange)Fx1 -0.008977 0.115045 -0.08 Correlation of Fixed Effects: X(Int) Xs(spdCh)F1 0.004
I understand this is an lmerMod. I understand the output for lmer function, but not here. I don't understand what "X" means in the fixed effects. From the t-value it seems that the Intercept is significant but not the speedChange. I want to report the result of my analysis, but what is the relationship between the gam results and this mer result? How can I interpret the mer result of
Xs(speedChange)Fx1 -0.008977 0.115045 -0.08
together with the gam result:
s(speedChange) 5.875 5.875 28.61 <2e-16 ***
I don't see any documents that help me to understand the output in order to report the result. Could someone help?