Fit GAMs to Ascocyta blight spatiotemporal development data
Ihsan Khaliq
2021-02-26
Spatiotemporal_development_GAMs.RmdImport data
dat <-
read_excel(
system.file("extdata", "SpatioTemporalSpreadData.xlsx",
package = "spatiotemporaldynamics"),
sheet = 1
)Examine data
str(dat)## tibble [1,800 × 18] (S3: tbl_df/tbl/data.frame)
## $ location : chr [1:1800] "Billa Billa" "Billa Billa" "Billa Billa" "Billa Billa" ...
## $ assessment_date : POSIXct[1:1800], format: "2020-07-02" "2020-07-02" ...
## $ assessment_number: num [1:1800] 1 1 1 1 1 1 1 1 1 1 ...
## $ plot_number : num [1:1800] 1 1 1 1 1 1 1 1 1 1 ...
## $ distance : num [1:1800] 0 9 9 9 9 9 9 9 9 6 ...
## $ quadrat : chr [1:1800] "F" "N9" "NE9" "E9" ...
## $ direction : chr [1:1800] "NA" "North" "NorthEast" "East" ...
## $ infected_plants : num [1:1800] 0 0 0 0 0 0 0 0 0 0 ...
## $ total_plants : num [1:1800] 36 48 27 57 53 41 39 31 36 54 ...
## $ incidence : num [1:1800] 0 0 0 0 0 0 0 0 0 0 ...
## $ min_temp : num [1:1800] 3.99 3.99 3.99 3.99 3.99 ...
## $ max_temp : num [1:1800] 20 20 20 20 20 ...
## $ avg_temp : num [1:1800] 12 12 12 12 12 ...
## $ avg_wind_speed : num [1:1800] 1.52 1.52 1.52 1.52 1.52 ...
## $ total_rain : num [1:1800] 1 1 1 1 1 1 1 1 1 1 ...
## $ min_rh : num [1:1800] 35.2 35.2 35.2 35.2 35.2 ...
## $ max_rh : num [1:1800] 82.7 82.7 82.7 82.7 82.7 ...
## $ avg_rh : num [1:1800] 58.9 58.9 58.9 58.9 58.9 ...Combine direction & location columns to get information on whether the rate of disease progress was signficantly faster in quadrats located in a particular direction
dat<-
unite(dat, direc_loc, c(location, direction), remove = FALSE) Re-check class
sapply(dat, class)## $direc_loc
## [1] "factor"
##
## $location
## [1] "factor"
##
## $assessment_date
## [1] "POSIXct" "POSIXt"
##
## $assessment_number
## [1] "numeric"
##
## $plot_number
## [1] "numeric"
##
## $distance
## [1] "numeric"
##
## $quadrat
## [1] "factor"
##
## $direction
## [1] "factor"
##
## $infected_plants
## [1] "numeric"
##
## $total_plants
## [1] "numeric"
##
## $incidence
## [1] "numeric"
##
## $min_temp
## [1] "numeric"
##
## $max_temp
## [1] "numeric"
##
## $avg_temp
## [1] "numeric"
##
## $avg_wind_speed
## [1] "numeric"
##
## $total_rain
## [1] "numeric"
##
## $min_rh
## [1] "numeric"
##
## $max_rh
## [1] "numeric"
##
## $avg_rh
## [1] "numeric"Fit univariate GAMs
Use ‘set.seed()’ for reproducibility purposes
set.seed(42)Model_1 s(distance)
##
## Family: gaussian
## Link function: identity
##
## Formula:
## incidence ~ s(distance, k = 4)
##
## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 19.3025 0.8242 23.42 <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(distance) 2.935 2.997 55.02 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## R-sq.(adj) = 0.0849 Deviance explained = 8.64%
## -REML = 8953.3 Scale est. = 1222.8 n = 1800
plot(
model_1,
pages = 1,
residuals = TRUE,
shade = TRUE,
seWithMean = TRUE,
shift = coef(model_1)[1]
)
Model_2 s(total_rain)
##
## Family: gaussian
## Link function: identity
##
## Formula:
## incidence ~ s(total_rain, k = 16)
##
## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 19.3025 0.4788 40.31 <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(total_rain) 14.35 14.8 272 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## R-sq.(adj) = 0.691 Deviance explained = 69.4%
## -REML = 8023.9 Scale est. = 412.71 n = 1800
plot(
model_2,
residuals = TRUE,
pages = 1,
shade = TRUE,
seWithMean = TRUE,
shift = coef(model_2)[1]
)
Model_3 assessment_number
##
## Family: gaussian
## Link function: identity
##
## Formula:
## incidence ~ assessment_number
##
## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -20.8905 1.4975 -13.95 <2e-16 ***
## assessment_number 7.9503 0.2618 30.37 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## R-sq.(adj) = 0.339 Deviance explained = 33.9%
## -REML = 8658.6 Scale est. = 883.65 n = 1800
plot(
model_3,
all.terms = TRUE,
residuals = TRUE,
pages = 1,
shade = TRUE,
seWithMean = TRUE,
shift = coef(model_3)
)
Model_4 s(avg_wind_speed)
##
## Family: gaussian
## Link function: identity
##
## Formula:
## incidence ~ s(avg_wind_speed, k = 18)
##
## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 19.3025 0.4772 40.45 <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(avg_wind_speed) 15.84 16.01 253.9 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## R-sq.(adj) = 0.693 Deviance explained = 69.6%
## -REML = 8025.1 Scale est. = 409.95 n = 1800
plot(
model_4,
residuals = TRUE,
pages = 1,
shade = TRUE,
seWithMean = TRUE,
shift = coef(model_4)[1]
)
Model_5 s(avg_rh)
##
## Family: gaussian
## Link function: identity
##
## Formula:
## incidence ~ s(avg_rh, k = 18)
##
## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 19.3025 0.4767 40.49 <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(avg_rh) 16.97 17 239.8 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## R-sq.(adj) = 0.694 Deviance explained = 69.7%
## -REML = 8059.5 Scale est. = 409.08 n = 1800
plot(model_5,
residuals = TRUE,
pages = 1,
shade = TRUE,
seWithMean = TRUE,
shift = coef(model_5)[1])
Model_6 s(avg _temp)
##
## Family: gaussian
## Link function: identity
##
## Formula:
## incidence ~ s(avg_temp, k = 18)
##
## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 19.3025 0.4773 40.44 <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(avg_temp) 12.88 14.32 283.9 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## R-sq.(adj) = 0.693 Deviance explained = 69.5%
## -REML = 7993.9 Scale est. = 410.08 n = 1800
plot(
model_6,
residuals = TRUE,
pages = 1,
shade = TRUE,
seWithMean = TRUE,
shift = coef(model_6)[1]
)
Model_6.1 s(avg _temp, by = location)
model_6.1 <-
gam(incidence ~ s(avg_temp, by = location, k = 18),
data = dat,
method = "REML")
summary(model_6.1)##
## Family: gaussian
## Link function: identity
##
## Formula:
## incidence ~ s(avg_temp, by = location, k = 18)
##
## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 16.6065 0.8576 19.36 <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(avg_temp):locationBilla Billa 6.230 6.748 336.7 <2e-16 ***
## s(avg_temp):locationTosari 7.725 7.933 227.8 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## R-sq.(adj) = 0.694 Deviance explained = 69.6%
## -REML = 7993.1 Scale est. = 409.34 n = 1800
plot(
model_6.1,
residuals = TRUE,
pages = 1,
shade = TRUE,
seWithMean = TRUE,
shift = coef(model_6.1)[1]
)
Model_7 location
##
## Family: gaussian
## Link function: identity
##
## Formula:
## incidence ~ location
##
## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 17.149 1.154 14.86 < 2e-16 ***
## locationTosari 4.845 1.731 2.80 0.00517 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## R-sq.(adj) = 0.00379 Deviance explained = 0.434%
## -REML = 9025.3 Scale est. = 1331.1 n = 1800
plot(
model_7,
residuals = TRUE,
all.terms = TRUE,
pages = 1,
shade = TRUE,
seWithMean = TRUE,
shift = coef(model_7)[1]
)
Fit multivariate GAMs
Model_8 (All variables)
model_8 <-
gam(
incidence ~ s(total_rain, k = 16) +
s(distance, k = 4) +
s(avg_wind_speed, k = 18) +
s(avg_rh, k = 18) +
s(avg_temp, k = 18) +
location +
assessment_number +
direc_loc,
data = dat,
method = "REML"
)
summary(model_8)##
## Family: gaussian
## Link function: identity
##
## Formula:
## incidence ~ s(total_rain, k = 16) + s(distance, k = 4) + s(avg_wind_speed,
## k = 18) + s(avg_rh, k = 18) + s(avg_temp, k = 18) + location +
## assessment_number + direc_loc
##
## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 21.51093 6.94148 3.099 0.00197 **
## locationTosari -7.28480 8.90499 -0.818 0.41343
## assessment_number -0.07815 1.10438 -0.071 0.94359
## direc_locBilla Billa_NA 26.79034 6.71232 3.991 6.84e-05 ***
## direc_locBilla Billa_North -0.03499 2.09472 -0.017 0.98668
## direc_locBilla Billa_NorthEast -1.87407 2.09472 -0.895 0.37109
## direc_locBilla Billa_NorthWest -1.70319 2.09472 -0.813 0.41628
## direc_locBilla Billa_South -3.55843 2.09472 -1.699 0.08954 .
## direc_locBilla Billa_SouthEast -4.99762 2.09472 -2.386 0.01715 *
## direc_locBilla Billa_SouthWest -2.96581 2.09472 -1.416 0.15700
## direc_locBilla Billa_West -0.62089 2.09472 -0.296 0.76695
## direc_locTosari_East 12.05864 2.34197 5.149 2.91e-07 ***
## direc_locTosari_NA 49.71240 6.87381 7.232 7.05e-13 ***
## direc_locTosari_North 3.31796 2.34197 1.417 0.15673
## direc_locTosari_NorthEast 18.16437 2.34197 7.756 1.47e-14 ***
## direc_locTosari_NorthWest -3.28803 2.34197 -1.404 0.16051
## direc_locTosari_South -4.32432 2.34197 -1.846 0.06499 .
## direc_locTosari_SouthEast 0.00000 0.00000 NA NA
## direc_locTosari_SouthWest -3.34241 2.34197 -1.427 0.15370
## direc_locTosari_West -3.91910 2.34197 -1.673 0.09442 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(total_rain) 2.030 2.138 2.768 0.0314 *
## s(distance) 1.928 1.995 32.592 <2e-16 ***
## s(avg_wind_speed) 1.003 1.005 2.920 0.0873 .
## s(avg_rh) 2.255 2.485 1.386 0.1973
## s(avg_temp) 7.811 8.555 30.928 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Rank: 88/89
## R-sq.(adj) = 0.803 Deviance explained = 80.7%
## -REML = 7544.3 Scale est. = 263.27 n = 1800
plot(
model_8,
all.terms = TRUE,
pages = 1,
shade = TRUE,
seWithMean = TRUE,
shift = coef(model_8)[1]
)
Model_9 (Fit different smooths for each term by location)
Same as model_8 but different smooths have been considered for each term BY LOCATION
model_9 <-
gam(
incidence ~ s(total_rain, k = 16, by = location) +
s(distance, k = 4, by = location) +
s(avg_wind_speed, k = 18, by = location) +
s(avg_temp, k = 18, by = location) +
s(avg_rh, k = 18, by = location) +
assessment_number +
location +
direc_loc,
data = dat,
method = "REML"
)
summary(model_9)##
## Family: gaussian
## Link function: identity
##
## Formula:
## incidence ~ s(total_rain, k = 16, by = location) + s(distance,
## k = 4, by = location) + s(avg_wind_speed, k = 18, by = location) +
## s(avg_temp, k = 18, by = location) + s(avg_rh, k = 18, by = location) +
## assessment_number + location + direc_loc
##
## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 23.87951 19.68772 1.213 0.22533
## assessment_number 0.01882 2.00906 0.009 0.99253
## locationTosari -29.67809 63.82349 -0.465 0.64199
## direc_locBilla Billa_NA 38.04027 3.17199 11.993 < 2e-16 ***
## direc_locBilla Billa_North -0.03499 2.05813 -0.017 0.98644
## direc_locBilla Billa_NorthEast -1.87407 2.05813 -0.911 0.36265
## direc_locBilla Billa_NorthWest -1.70319 2.05813 -0.828 0.40804
## direc_locBilla Billa_South -3.55843 2.05813 -1.729 0.08399 .
## direc_locBilla Billa_SouthEast -4.99762 2.05813 -2.428 0.01527 *
## direc_locBilla Billa_SouthWest -2.96581 2.05813 -1.441 0.14976
## direc_locBilla Billa_West -0.62089 2.05813 -0.302 0.76293
## direc_locTosari_East 15.97774 2.30106 6.944 5.35e-12 ***
## direc_locTosari_NA 39.81465 13.13429 3.031 0.00247 **
## direc_locTosari_North 7.23706 2.30106 3.145 0.00169 **
## direc_locTosari_NorthEast 22.08346 2.30106 9.597 < 2e-16 ***
## direc_locTosari_NorthWest 0.63106 2.30106 0.274 0.78392
## direc_locTosari_South -0.40523 2.30106 -0.176 0.86023
## direc_locTosari_SouthEast 3.91910 2.30106 1.703 0.08871 .
## direc_locTosari_SouthWest 0.57669 2.30106 0.251 0.80214
## direc_locTosari_West 0.00000 0.00000 NA NA
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(total_rain):locationBilla Billa 1.001 1.001 0.033 0.8557
## s(total_rain):locationTosari 1.002 1.003 231.379 < 2e-16 ***
## s(distance):locationBilla Billa 1.000 1.000 5.369 0.0206 *
## s(distance):locationTosari 1.965 1.999 46.326 < 2e-16 ***
## s(avg_wind_speed):locationBilla Billa 1.480 1.516 0.486 0.5476
## s(avg_wind_speed):locationTosari 3.256 3.382 3.633 0.0128 *
## s(avg_temp):locationBilla Billa 4.426 4.517 5.974 2.64e-05 ***
## s(avg_temp):locationTosari 1.000 1.000 64.132 < 2e-16 ***
## s(avg_rh):locationBilla Billa 1.000 1.000 0.392 0.5317
## s(avg_rh):locationTosari 1.482 1.543 2.991 0.0315 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Rank: 157/158
## R-sq.(adj) = 0.81 Deviance explained = 81.4%
## -REML = 7502.9 Scale est. = 254.15 n = 1800
plot(
model_9,
all.terms = TRUE,
pages = 1,
shade = TRUE,
seWithMean = TRUE,
shift = coef(model_9)[1]
)
Model_10 (Remove by argument from avg_rh and avg_wind_speed)
Remove by argument from avg_rh and avg_wind_speed as they are only weakly significant for Tosari only.
model_10 <-
gam(
incidence ~ s(total_rain, k = 16, by = location) +
s(distance, k = 4, by = location) +
s(avg_wind_speed, k = 18) +
s(avg_temp, k = 18, by = location) +
s(avg_rh, k = 18) +
assessment_number +
location +
direc_loc,
data = dat,
method = "REML"
)
summary(model_10)##
## Family: gaussian
## Link function: identity
##
## Formula:
## incidence ~ s(total_rain, k = 16, by = location) + s(distance,
## k = 4, by = location) + s(avg_wind_speed, k = 18) + s(avg_temp,
## k = 18, by = location) + s(avg_rh, k = 18) + assessment_number +
## location + direc_loc
##
## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 10.19418 6.91442 1.474 0.14057
## assessment_number 0.80848 1.08405 0.746 0.45589
## locationTosari -3.95894 6.15431 -0.643 0.52013
## direc_locBilla Billa_NA 38.04033 3.17106 11.996 < 2e-16 ***
## direc_locBilla Billa_North -0.03499 2.05761 -0.017 0.98643
## direc_locBilla Billa_NorthEast -1.87407 2.05761 -0.911 0.36253
## direc_locBilla Billa_NorthWest -1.70319 2.05761 -0.828 0.40792
## direc_locBilla Billa_South -3.55843 2.05761 -1.729 0.08391 .
## direc_locBilla Billa_SouthEast -4.99762 2.05761 -2.429 0.01525 *
## direc_locBilla Billa_SouthWest -2.96581 2.05761 -1.441 0.14965
## direc_locBilla Billa_West -0.62089 2.05761 -0.302 0.76288
## direc_locTosari_East 15.40105 2.30048 6.695 2.89e-11 ***
## direc_locTosari_NA 39.23775 13.13408 2.987 0.00285 **
## direc_locTosari_North 6.66037 2.30048 2.895 0.00384 **
## direc_locTosari_NorthEast 21.50677 2.30048 9.349 < 2e-16 ***
## direc_locTosari_NorthWest 0.05438 2.30048 0.024 0.98114
## direc_locTosari_South -0.98191 2.30048 -0.427 0.66956
## direc_locTosari_SouthEast 3.34241 2.30048 1.453 0.14642
## direc_locTosari_SouthWest 0.00000 0.00000 NA NA
## direc_locTosari_West -0.57669 2.30048 -0.251 0.80209
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(total_rain):locationBilla Billa 1.000 1.000 0.906 0.3413
## s(total_rain):locationTosari 3.438 3.773 282.039 <2e-16 ***
## s(distance):locationBilla Billa 1.000 1.000 5.373 0.0206 *
## s(distance):locationTosari 1.965 1.999 46.348 <2e-16 ***
## s(avg_wind_speed) 1.001 1.001 0.489 0.4846
## s(avg_temp):locationBilla Billa 5.603 6.147 26.984 <2e-16 ***
## s(avg_temp):locationTosari 1.002 1.003 0.337 0.5630
## s(avg_rh) 1.002 1.003 0.808 0.3692
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Rank: 123/124
## R-sq.(adj) = 0.81 Deviance explained = 81.3%
## -REML = 7506 Scale est. = 254.03 n = 1800
plot(
model_10,
all.terms = TRUE,
pages = 1,
shade = TRUE,
seWithMean = TRUE,
shift = coef(model_10)[1]
)
Model_11 (Interaction between total_rain and avg_wind_speed)
model_11 <-
gam(
incidence ~ s(total_rain, avg_wind_speed, k = 18, by = location) +
s(distance, k = 4, by = location) +
s(avg_temp, k = 18, by = location) +
s(avg_rh, k = 18) +
assessment_number +
location +
direc_loc,
data = dat,
method = "REML"
)
summary(model_11)##
## Family: gaussian
## Link function: identity
##
## Formula:
## incidence ~ s(total_rain, avg_wind_speed, k = 18, by = location) +
## s(distance, k = 4, by = location) + s(avg_temp, k = 18, by = location) +
## s(avg_rh, k = 18) + assessment_number + location + direc_loc
##
## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 11.22801 8.44070 1.330 0.18362
## assessment_number 0.59818 1.24450 0.481 0.63082
## locationTosari 0.00000 0.00000 NA NA
## direc_locBilla Billa_NA 38.03938 3.17360 11.986 < 2e-16 ***
## direc_locBilla Billa_North -0.03499 2.05789 -0.017 0.98644
## direc_locBilla Billa_NorthEast -1.87407 2.05789 -0.911 0.36259
## direc_locBilla Billa_NorthWest -1.70319 2.05789 -0.828 0.40799
## direc_locBilla Billa_South -3.55843 2.05789 -1.729 0.08395 .
## direc_locBilla Billa_SouthEast -4.99762 2.05789 -2.429 0.01526 *
## direc_locBilla Billa_SouthWest -2.96581 2.05789 -1.441 0.14971
## direc_locBilla Billa_West -0.62089 2.05789 -0.302 0.76291
## direc_locTosari_East 11.29817 6.66889 1.694 0.09041 .
## direc_locTosari_NA 35.13498 14.09731 2.492 0.01278 *
## direc_locTosari_North 2.55749 6.66889 0.383 0.70140
## direc_locTosari_NorthEast 17.40390 6.66889 2.610 0.00914 **
## direc_locTosari_NorthWest -4.04850 6.66889 -0.607 0.54388
## direc_locTosari_South -5.08479 6.66889 -0.762 0.44588
## direc_locTosari_SouthEast -0.76047 6.66889 -0.114 0.90923
## direc_locTosari_SouthWest -4.10288 6.66889 -0.615 0.53848
## direc_locTosari_West -4.67956 6.66889 -0.702 0.48296
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(total_rain,avg_wind_speed):locationBilla Billa 2.003 2.004 0.168 0.8454
## s(total_rain,avg_wind_speed):locationTosari 4.693 4.941 202.992 <2e-16
## s(distance):locationBilla Billa 1.002 1.003 5.349 0.0207
## s(distance):locationTosari 1.965 1.999 46.337 <2e-16
## s(avg_temp):locationBilla Billa 5.181 5.512 25.048 <2e-16
## s(avg_temp):locationTosari 1.001 1.002 0.162 0.6890
## s(avg_rh) 1.003 1.005 0.854 0.3566
##
## s(total_rain,avg_wind_speed):locationBilla Billa
## s(total_rain,avg_wind_speed):locationTosari ***
## s(distance):locationBilla Billa *
## s(distance):locationTosari ***
## s(avg_temp):locationBilla Billa ***
## s(avg_temp):locationTosari
## s(avg_rh)
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Rank: 110/111
## R-sq.(adj) = 0.81 Deviance explained = 81.4%
## -REML = 7504 Scale est. = 254.09 n = 1800
plot(model_11, scheme = 1, pages = 1)
Comments on model_11
The effect of avg_wind_speed is not significant at its own in model_10, but significant in interaction with total_rain for Tosari only
Add confidence interval to the interaction visualisation/predictions
vis.gam(
x = model_11,
view = c("total_rain", "avg_wind_speed"),
plot.type = "persp",
se = 2,
theta = 135
)
The plot indicates the number of standard errors (2 in this case) away from the average prediction to plot high and low prediction surfaces
Model_12 Try tensor interactions instead of smooth interactions
Tensor smooths let us model interactions that operate on different scales. Tensor interaction takes longer to run the model, and requires more data.
model_12 <-
gam(
incidence ~ s(total_rain, avg_wind_speed, k = 18, by = location) +
s(distance, k = 4, by = location) +
s(avg_temp, k = 18, by = location) +
s(avg_rh, k = 18) +
assessment_number +
location +
direc_loc,
data = dat,
method = "REML"
)
summary(model_12)##
## Family: gaussian
## Link function: identity
##
## Formula:
## incidence ~ s(total_rain, avg_wind_speed, k = 18, by = location) +
## s(distance, k = 4, by = location) + s(avg_temp, k = 18, by = location) +
## s(avg_rh, k = 18) + assessment_number + location + direc_loc
##
## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 11.22801 8.44070 1.330 0.18362
## assessment_number 0.59818 1.24450 0.481 0.63082
## locationTosari 0.00000 0.00000 NA NA
## direc_locBilla Billa_NA 38.03938 3.17360 11.986 < 2e-16 ***
## direc_locBilla Billa_North -0.03499 2.05789 -0.017 0.98644
## direc_locBilla Billa_NorthEast -1.87407 2.05789 -0.911 0.36259
## direc_locBilla Billa_NorthWest -1.70319 2.05789 -0.828 0.40799
## direc_locBilla Billa_South -3.55843 2.05789 -1.729 0.08395 .
## direc_locBilla Billa_SouthEast -4.99762 2.05789 -2.429 0.01526 *
## direc_locBilla Billa_SouthWest -2.96581 2.05789 -1.441 0.14971
## direc_locBilla Billa_West -0.62089 2.05789 -0.302 0.76291
## direc_locTosari_East 11.29817 6.66889 1.694 0.09041 .
## direc_locTosari_NA 35.13498 14.09731 2.492 0.01278 *
## direc_locTosari_North 2.55749 6.66889 0.383 0.70140
## direc_locTosari_NorthEast 17.40390 6.66889 2.610 0.00914 **
## direc_locTosari_NorthWest -4.04850 6.66889 -0.607 0.54388
## direc_locTosari_South -5.08479 6.66889 -0.762 0.44588
## direc_locTosari_SouthEast -0.76047 6.66889 -0.114 0.90923
## direc_locTosari_SouthWest -4.10288 6.66889 -0.615 0.53848
## direc_locTosari_West -4.67956 6.66889 -0.702 0.48296
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(total_rain,avg_wind_speed):locationBilla Billa 2.003 2.004 0.168 0.8454
## s(total_rain,avg_wind_speed):locationTosari 4.693 4.941 202.992 <2e-16
## s(distance):locationBilla Billa 1.002 1.003 5.349 0.0207
## s(distance):locationTosari 1.965 1.999 46.337 <2e-16
## s(avg_temp):locationBilla Billa 5.181 5.512 25.048 <2e-16
## s(avg_temp):locationTosari 1.001 1.002 0.162 0.6890
## s(avg_rh) 1.003 1.005 0.854 0.3566
##
## s(total_rain,avg_wind_speed):locationBilla Billa
## s(total_rain,avg_wind_speed):locationTosari ***
## s(distance):locationBilla Billa *
## s(distance):locationTosari ***
## s(avg_temp):locationBilla Billa ***
## s(avg_temp):locationTosari
## s(avg_rh)
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Rank: 110/111
## R-sq.(adj) = 0.81 Deviance explained = 81.4%
## -REML = 7504 Scale est. = 254.09 n = 1800
plot(model_12, scheme = 1, pages = 1)
Model_13
Same as model_10 but relative humidity removed.
model_13 <-
gam(
incidence ~ s(total_rain, k = 16, by = location) +
s(distance, k = 4, by = location) +
s(avg_temp, k = 18, by = location) +
s(avg_wind_speed, k = 18) +
assessment_number +
location +
direc_loc,
data = dat,
method = "REML"
)
summary(model_13)##
## Family: gaussian
## Link function: identity
##
## Formula:
## incidence ~ s(total_rain, k = 16, by = location) + s(distance,
## k = 4, by = location) + s(avg_temp, k = 18, by = location) +
## s(avg_wind_speed, k = 18) + assessment_number + location +
## direc_loc
##
## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -41.44525 14.85023 -2.791 0.005313 **
## assessment_number 9.13265 1.62278 5.628 2.12e-08 ***
## locationTosari 16.26187 16.87546 0.964 0.335358
## direc_locBilla Billa_NA 38.04010 3.17244 11.991 < 2e-16 ***
## direc_locBilla Billa_North -0.03499 2.05817 -0.017 0.986439
## direc_locBilla Billa_NorthEast -1.87407 2.05817 -0.911 0.362658
## direc_locBilla Billa_NorthWest -1.70319 2.05817 -0.828 0.408053
## direc_locBilla Billa_South -3.55843 2.05817 -1.729 0.083997 .
## direc_locBilla Billa_SouthEast -4.99762 2.05817 -2.428 0.015274 *
## direc_locBilla Billa_SouthWest -2.96581 2.05817 -1.441 0.149765
## direc_locBilla Billa_West -0.62089 2.05817 -0.302 0.762938
## direc_locTosari_East 16.38296 2.30111 7.120 1.57e-12 ***
## direc_locTosari_NA 40.21989 13.13431 3.062 0.002230 **
## direc_locTosari_North 7.64228 2.30111 3.321 0.000915 ***
## direc_locTosari_NorthEast 22.48869 2.30111 9.773 < 2e-16 ***
## direc_locTosari_NorthWest 1.03629 2.30111 0.450 0.652518
## direc_locTosari_South 0.00000 0.00000 NA NA
## direc_locTosari_SouthEast 4.32432 2.30111 1.879 0.060377 .
## direc_locTosari_SouthWest 0.98191 2.30111 0.427 0.669640
## direc_locTosari_West 0.40523 2.30111 0.176 0.860235
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(total_rain):locationBilla Billa 1.003 1.003 0.770 0.3808
## s(total_rain):locationTosari 1.000 1.000 133.768 < 2e-16 ***
## s(distance):locationBilla Billa 1.000 1.001 5.365 0.0206 *
## s(distance):locationTosari 1.965 1.999 46.324 < 2e-16 ***
## s(avg_temp):locationBilla Billa 2.792 2.899 2.189 0.1377
## s(avg_temp):locationTosari 1.009 1.011 58.740 < 2e-16 ***
## s(avg_wind_speed) 8.664 9.002 5.167 5.07e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Rank: 106/107
## R-sq.(adj) = 0.81 Deviance explained = 81.4%
## -REML = 7517 Scale est. = 254.16 n = 1800
Model_14
Same as model_13 but considering the interaction between total rain and wind speed.
model_14 <-
gam(
incidence ~ s(total_rain, avg_wind_speed, k = 18, by = location) +
s(distance, k = 4, by = location) +
s(avg_temp, k = 18, by = location) +
assessment_number +
location +
direc_loc,
data = dat,
method = "REML"
)
summary(model_14)##
## Family: gaussian
## Link function: identity
##
## Formula:
## incidence ~ s(total_rain, avg_wind_speed, k = 18, by = location) +
## s(distance, k = 4, by = location) + s(avg_temp, k = 18, by = location) +
## assessment_number + location + direc_loc
##
## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 24.59770 29.71854 0.828 0.40796
## assessment_number 1.19570 1.04337 1.146 0.25195
## locationTosari 16.83229 31.50177 0.534 0.59318
## direc_locBilla Billa_NA 38.03945 3.17375 11.986 < 2e-16 ***
## direc_locBilla Billa_North -0.03499 2.05808 -0.017 0.98644
## direc_locBilla Billa_NorthEast -1.87407 2.05808 -0.911 0.36264
## direc_locBilla Billa_NorthWest -1.70319 2.05808 -0.828 0.40803
## direc_locBilla Billa_South -3.55843 2.05808 -1.729 0.08398 .
## direc_locBilla Billa_SouthEast -4.99762 2.05808 -2.428 0.01527 *
## direc_locBilla Billa_SouthWest -2.96581 2.05808 -1.441 0.14975
## direc_locBilla Billa_West -0.62089 2.05808 -0.302 0.76293
## direc_locTosari_East -23.83694 13.13360 -1.815 0.06970 .
## direc_locTosari_NA 0.00000 0.00000 NA NA
## direc_locTosari_North -32.57762 13.13360 -2.480 0.01321 *
## direc_locTosari_NorthEast -17.73121 13.13360 -1.350 0.17717
## direc_locTosari_NorthWest -39.18361 13.13360 -2.983 0.00289 **
## direc_locTosari_South -40.21990 13.13360 -3.062 0.00223 **
## direc_locTosari_SouthEast -35.89558 13.13360 -2.733 0.00634 **
## direc_locTosari_SouthWest -39.23799 13.13360 -2.988 0.00285 **
## direc_locTosari_West -39.81467 13.13360 -3.032 0.00247 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(total_rain,avg_wind_speed):locationBilla Billa 7.855 7.981 203.787 <2e-16
## s(total_rain,avg_wind_speed):locationTosari 4.738 4.953 268.585 <2e-16
## s(distance):locationBilla Billa 1.002 1.003 5.349 0.0207
## s(distance):locationTosari 1.965 1.999 46.328 <2e-16
## s(avg_temp):locationBilla Billa 1.000 1.000 0.102 0.7496
## s(avg_temp):locationTosari 1.001 1.001 0.585 0.4456
##
## s(total_rain,avg_wind_speed):locationBilla Billa ***
## s(total_rain,avg_wind_speed):locationTosari ***
## s(distance):locationBilla Billa *
## s(distance):locationTosari ***
## s(avg_temp):locationBilla Billa
## s(avg_temp):locationTosari
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Rank: 93/94
## R-sq.(adj) = 0.81 Deviance explained = 81.4%
## -REML = 7512.1 Scale est. = 254.14 n = 1800
Model_15
Same as model_13 but without wind speed.
model_15 <-
gam(
incidence ~ s(total_rain, k = 16, by = location) +
s(distance, k = 4, by = location) +
s(avg_temp, k = 18, by = location) +
assessment_number +
location + direc_loc,
data = dat,
method = "REML"
)
summary(model_15)##
## Family: gaussian
## Link function: identity
##
## Formula:
## incidence ~ s(total_rain, k = 16, by = location) + s(distance,
## k = 4, by = location) + s(avg_temp, k = 18, by = location) +
## assessment_number + location + direc_loc
##
## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.97249 5.21760 0.761 0.44654
## assessment_number 2.01680 0.71049 2.839 0.00458 **
## locationTosari -3.62075 3.24067 -1.117 0.26402
## direc_locBilla Billa_NA 38.04020 3.17171 11.994 < 2e-16 ***
## direc_locBilla Billa_North -0.03499 2.05786 -0.017 0.98644
## direc_locBilla Billa_NorthEast -1.87407 2.05786 -0.911 0.36258
## direc_locBilla Billa_NorthWest -1.70319 2.05786 -0.828 0.40798
## direc_locBilla Billa_South -3.55843 2.05786 -1.729 0.08395 .
## direc_locBilla Billa_SouthEast -4.99762 2.05786 -2.429 0.01526 *
## direc_locBilla Billa_SouthWest -2.96581 2.05786 -1.441 0.14970
## direc_locBilla Billa_West -0.62089 2.05786 -0.302 0.76290
## direc_locTosari_East 15.97774 2.30075 6.945 5.32e-12 ***
## direc_locTosari_NA 39.81454 13.13416 3.031 0.00247 **
## direc_locTosari_North 7.23706 2.30075 3.146 0.00169 **
## direc_locTosari_NorthEast 22.08346 2.30075 9.598 < 2e-16 ***
## direc_locTosari_NorthWest 0.63106 2.30075 0.274 0.78390
## direc_locTosari_South -0.40523 2.30075 -0.176 0.86021
## direc_locTosari_SouthEast 3.91910 2.30075 1.703 0.08867 .
## direc_locTosari_SouthWest 0.57669 2.30075 0.251 0.80211
## direc_locTosari_West 0.00000 0.00000 NA NA
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(total_rain):locationBilla Billa 1.350 1.516 0.270 0.6027
## s(total_rain):locationTosari 3.497 3.841 262.965 <2e-16 ***
## s(distance):locationBilla Billa 1.000 1.001 5.369 0.0206 *
## s(distance):locationTosari 1.965 1.999 46.338 <2e-16 ***
## s(avg_temp):locationBilla Billa 5.735 6.280 150.640 <2e-16 ***
## s(avg_temp):locationTosari 1.052 1.091 1.241 0.2878
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Rank: 89/90
## R-sq.(adj) = 0.81 Deviance explained = 81.3%
## -REML = 7510.4 Scale est. = 254.09 n = 1800
plot(
model_15,
all.terms = TRUE,
pages = 1,
shade = TRUE,
seWithMean = TRUE,
shift = coef(model_15)[1]
)
Model_16
Add the effect avg_rh to model_15 if a better fit can be achieved
model_16 <-
gam(
incidence ~ s(total_rain, k = 16, by = location) +
s(distance, k = 4, by = location) +
s(avg_temp, k = 18, by = location) +
s(avg_rh, k = 18) +
assessment_number +
location +
direc_loc,
data = dat,
method = "REML"
)
summary(model_16)##
## Family: gaussian
## Link function: identity
##
## Formula:
## incidence ~ s(total_rain, k = 16, by = location) + s(distance,
## k = 4, by = location) + s(avg_temp, k = 18, by = location) +
## s(avg_rh, k = 18) + assessment_number + location + direc_loc
##
## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 7.45091 5.88619 1.266 0.205741
## assessment_number 1.01397 1.04820 0.967 0.333508
## locationTosari -1.49542 3.68806 -0.405 0.685177
## direc_locBilla Billa_NA 38.04023 3.17118 11.996 < 2e-16 ***
## direc_locBilla Billa_North -0.03499 2.05756 -0.017 0.986435
## direc_locBilla Billa_NorthEast -1.87407 2.05756 -0.911 0.362514
## direc_locBilla Billa_NorthWest -1.70319 2.05756 -0.828 0.407913
## direc_locBilla Billa_South -3.55843 2.05756 -1.729 0.083905 .
## direc_locBilla Billa_SouthEast -4.99762 2.05756 -2.429 0.015244 *
## direc_locBilla Billa_SouthWest -2.96581 2.05756 -1.441 0.149643
## direc_locBilla Billa_West -0.62089 2.05756 -0.302 0.762869
## direc_locTosari_East 16.38296 2.30042 7.122 1.55e-12 ***
## direc_locTosari_NA 40.21964 13.13405 3.062 0.002230 **
## direc_locTosari_North 7.64228 2.30042 3.322 0.000912 ***
## direc_locTosari_NorthEast 22.48869 2.30042 9.776 < 2e-16 ***
## direc_locTosari_NorthWest 1.03629 2.30042 0.450 0.652420
## direc_locTosari_South 0.00000 0.00000 NA NA
## direc_locTosari_SouthEast 4.32432 2.30042 1.880 0.060300 .
## direc_locTosari_SouthWest 0.98191 2.30042 0.427 0.669547
## direc_locTosari_West 0.40523 2.30042 0.176 0.860194
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(total_rain):locationBilla Billa 1.002 1.003 0.871 0.3502
## s(total_rain):locationTosari 3.443 3.779 324.700 <2e-16 ***
## s(distance):locationBilla Billa 1.000 1.000 5.371 0.0206 *
## s(distance):locationTosari 1.965 1.999 46.350 <2e-16 ***
## s(avg_temp):locationBilla Billa 5.702 6.274 29.741 <2e-16 ***
## s(avg_temp):locationTosari 1.013 1.022 0.154 0.7116
## s(avg_rh) 1.002 1.003 1.293 0.2556
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Rank: 106/107
## R-sq.(adj) = 0.81 Deviance explained = 81.3%
## -REML = 7508 Scale est. = 254.01 n = 1800
plot(
model_16,
all.terms = TRUE,
pages = 1,
shade = TRUE,
seWithMean = TRUE,
shift = coef(model_16)[1]
)
Compare the models
AIC, BIC
models <- list(
model_1 = model_1,
model_2 = model_2,
model_3 = model_3,
model_4 = model_4,
model_5 = model_5,
model_6 = model_6,
model_6.1 = model_6.1,
model_7 = model_7,
model_8 = model_8,
model_9 = model_9,
model_10 = model_10,
model_11 = model_11,
model_12 = model_12,
model_13 = model_13,
model_14 = model_14,
model_15 = model_15,
model_16 = model_16
)
map_df(models, glance, .id = "model") %>%
arrange(AIC)## # A tibble: 17 x 8
## model df logLik AIC BIC deviance df.residual nobs
## <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <int>
## 1 model_16 34.1 -7521. 15112. 15307. 448554. 1766. 1800
## 2 model_15 33.6 -7521. 15114. 15310. 448818. 1766. 1800
## 3 model_10 35.0 -7520. 15114. 15316. 448353. 1765. 1800
## 4 model_11 35.8 -7520. 15114. 15318. 448260. 1764. 1800
## 5 model_12 35.8 -7520. 15114. 15318. 448260. 1764. 1800
## 6 model_13 36.4 -7520. 15115. 15322. 448236. 1764. 1800
## 7 model_14 36.6 -7520. 15115. 15324. 448164. 1763. 1800
## 8 model_9 36.6 -7520. 15115. 15324. 448171. 1763. 1800
## 9 model_8 34.0 -7553. 15178. 15377. 464929. 1766. 1800
## 10 model_6.1 15.0 -7960. 15953. 16044. 730695. 1785. 1800
## 11 model_5 18.0 -7958. 15953. 16058. 728998. 1782. 1800
## 12 model_6 13.9 -7962. 15955. 16040. 732449. 1786. 1800
## 13 model_4 16.8 -7960. 15956. 16055. 731007. 1783. 1800
## 14 model_2 15.4 -7967. 15967. 16057. 736538. 1785. 1800
## 15 model_3 2. -8659. 17323. 17340. 1588802. 1798 1800
## 16 model_1 3.94 -8950. 17910. 17938. 2196139. 1796. 1800
## 17 model_7 2.00 -9027. 18061. 18077. 2393383. 1798 1800R2
enframe(
c(
model_1 = summary(model_1)$r.sq,
model_2 = summary(model_2)$r.sq,
model_3 = summary(model_3)$r.sq,
model_4 = summary(model_4)$r.sq,
model_5 = summary(model_5)$r.sq,
model_6 = summary(model_6)$r.sq,
model_6.1 = summary(model_6.1)$r.sq,
model_7 = summary(model_7)$r.sq,
model_8 = summary(model_8)$r.sq,
model_9 = summary(model_9)$r.sq,
model_10 = summary(model_10)$r.sq,
model_11 = summary(model_11)$r.sq,
model_12 = summary(model_12)$r.sq,
model_13 = summary(model_13)$r.sq,
model_14 = summary(model_14)$r.sq,
model_15 = summary(model_15)$r.sq,
model_16 = summary(model_16)$r.sq
)
) %>%
arrange(desc(value))## # A tibble: 17 x 2
## name value
## <chr> <dbl>
## 1 model_16 0.810
## 2 model_10 0.810
## 3 model_15 0.810
## 4 model_11 0.810
## 5 model_12 0.810
## 6 model_14 0.810
## 7 model_9 0.810
## 8 model_13 0.810
## 9 model_8 0.803
## 10 model_5 0.694
## 11 model_6.1 0.694
## 12 model_4 0.693
## 13 model_6 0.693
## 14 model_2 0.691
## 15 model_3 0.339
## 16 model_1 0.0849
## 17 model_7 0.00379ANOVA
anova(
model_1,
model_2,
model_3,
model_4,
model_5,
model_6,
model_6.1,
model_7,
model_8,
model_9,
model_10,
model_11,
model_12,
model_13,
model_14,
model_15,
model_
)## Error in anova.gam(model_1, model_2, model_3, model_4, model_5, model_6, : object 'model_' not found
Perform checks on the best fitting model_16
gam.check and concurvity
gam.check(model_16)
##
## Method: REML Optimizer: outer newton
## full convergence after 11 iterations.
## Gradient range [-0.001914579,0.004457845]
## (score 7508.032 & scale 254.0128).
## Hessian positive definite, eigenvalue range [9.299123e-05,886.5037].
## Model rank = 106 / 107
##
## 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(total_rain):locationBilla Billa 15.00 1.00 0.71 <2e-16 ***
## s(total_rain):locationTosari 15.00 3.44 0.71 <2e-16 ***
## s(distance):locationBilla Billa 3.00 1.00 0.45 <2e-16 ***
## s(distance):locationTosari 3.00 1.97 0.45 <2e-16 ***
## s(avg_temp):locationBilla Billa 17.00 5.70 0.72 <2e-16 ***
## s(avg_temp):locationTosari 17.00 1.01 0.72 <2e-16 ***
## s(avg_rh) 17.00 1.00 0.71 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Comments on the model check
The model fit could have been much better if we had enough basis function for total_rain, distance and avg_temp and avg_rh (shown by significant result in the diagnostic function).
concurvity(model_15, full=TRUE)## para s(total_rain):locationBilla Billa s(total_rain):locationTosari
## worst 1 1.146525 2.839383e+30
## observed 1 1.000000 2.922429e+00
## estimate 1 1.000000 1.000000e+00
## s(distance):locationBilla Billa s(distance):locationTosari
## worst 1.0000000 1.0000000
## observed 0.2210998 0.3684495
## estimate 0.2280612 0.2012842
## s(avg_temp):locationBilla Billa s(avg_temp):locationTosari
## worst 1.127943 7.104991e+29
## observed 1.000000 9.783470e-01
## estimate 1.000000 1.000000e+00
Comments on model_8 and model_9
Fitting different smooths for each term by location in
model_9improved the adjusted R^2 and percent deviance explained values. Noam Ross encourages this practice in his own words,