Main_Hourly_SES_MARS <- read_csv("G:/Analyses/Main_Hourly_SES_MARS.csv", 
                                 col_types = cols(datetime = col_datetime(format = "%m/%d/%Y %H:%M"), 
                                                  justdate = col_date(format = "%m/%d/%Y"), 
                                                  sunrise = col_datetime(format = "%m/%d/%Y %H:%M"), 
                                                  sunset = col_datetime(format = "%m/%d/%Y %H:%M")))
View(Main_Hourly_SES_MARS)
colnames(Main_Hourly_SES_MARS)
# [1] "datetime"           "atn"                "mooninterp"         "hour"               "year"               "month"              "day"               
# [8] "Year-Week"          "justdate"           "ABSdayssincesolst"  "moonbins"           "Pred"               "tidal_diff"         "dayssincesolstice" 
# [15] "NUMdayssincesolst"  "sunrisedecimalhour" "sunsetdecimalhour"  "sunrise"            "sunset"   

SES_atn <- gam(log1p(Main_Hourly_SES_MARS$atn) ~  s(mooninterp) + s(hour) +s(Pred) +s(tidal_diff), data = Main_Hourly_SES_MARS, method = "REML")
summary(SES_atn)

SES_atn <- gam(log1p(Main_Hourly_SES_MARS$atn) ~  s(mooninterp) + s(hour) +s(Pred) +s(tidal_diff), data = Main_Hourly_SES_MARS, method = "REML")
# > summary(SES_atn)

# Family: gaussian 
# Link function: identity 
# 
# Formula:
#   log1p(Main_Hourly_SES_MARS$atn) ~ s(mooninterp) + s(hour) + s(Pred) + 
#   s(tidal_diff)
# 
# Parametric coefficients:
#   Estimate Std. Error t value Pr(>|t|)    
# (Intercept) 0.274108   0.003761   72.89   <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(mooninterp) 6.984  8.050 11.486  < 2e-16 ***
#   s(hour)       6.932  8.028 24.101  < 2e-16 ***
#   s(Pred)       4.720  5.862  7.221 9.27e-07 ***
#   s(tidal_diff) 7.536  8.477  8.537  < 2e-16 ***
#   ---
#   Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
# 
# R-sq.(adj) =   0.19   Deviance explained = 20.2%
# -REML = -702.13  Scale est. = 0.023943  n = 1693
# > gam.check(SES_atn)
# 
# Method: REML   Optimizer: outer newton
# full convergence after 8 iterations.
# Gradient range [-1.462809e-09,2.042002e-10]
# (score -702.1343 & scale 0.02394286).
# Hessian positive definite, eigenvalue range [1.531319,844.0379].
# Model rank =  37 / 37 
# 
# Basis dimension (k) checking results. Low p-value (k-index<1) may
# indicate that k is too low, especially if edf is close to k'.
# 
#                 k'  edf k-index p-value    
# s(mooninterp) 9.00 6.98    1.00    0.54    
# s(hour)       9.00 6.93    0.84  <2e-16 ***
#   s(Pred)       9.00 4.72    1.00    0.47    
# s(tidal_diff) 9.00 7.54    0.55  <2e-16 ***
#   ---
#   Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1