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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: enter image description here

I then try to interpret the gam:

summary(speed.gammer$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:

summary(speed.gammer$mer)

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?

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