[R] Interpretation of gam intercept parameter

[Lidia Dobria]

Dear All:

I apologize for asking such an elementary question, but I could not find an adequate response on line. I am hoping to receive some help with the interpretation of the Intercept coefficient in the gam model below.
 
I1 through I3 are dummy coded "Item difficulty" parameters in a data set that includes 4 items. If the Intercept is the value of Y when all other terms are 0, am I correct in assuming that it also equals the difficulty of item 4 (dummy coded 0 0 0 )?

Thank you for your help.
Lidia


Family: gaussian 
Link function: identity 

Formula:
Score ~ I1 + I2 + I3 + s(TimeI1, bs = "cr", k = 7) +
s(TimeI2, bs = "cr", k = 7) + s(TimeI3, bs = "cr", k = 7)

Parametric coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  4.70968    0.09547  49.330  < 2e-16 ***
I1          -0.22188    0.21767  -1.019 0.308157    
I2           0.51236    0.16592   3.088 0.002042 ** 
I3          -0.60697    0.18258  -3.324 0.000902 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 
 
Approximate significance of smooth terms:
             edf Ref.df     F  p-value    
s(TimeI1) 3.820  3.820 4.587 0.001331 ** 
s(TimeI2) 2.491  2.491 6.271 0.000784 ***
s(TimeI3) 3.481  3.481 8.997 1.54e-06 ***
---

Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 
R-sq.(adj) =  0.057  Scale est. = 2.131     n = 2079