rm(list=ls(all=T))
gc() used (Mb) gc trigger (Mb) max used (Mb)
Ncells 559509 29.9 1276470 68.2 644254 34.5
Vcells 985724 7.6 8388608 64.0 1635077 12.5Aula 7 - Regressão 2
1 Introdução
- Vamos fazer o uso de um modelo GAM, e ver qual ajuste vai se adequar melhor aos dados.
2 Uso do GAM
2.1 Impotando o banco de dados e visualizando
O banco de Dados se encontra no pacote UsingR, e o nome do banco de dados é fat, e a descrição do banco é: “A data set containing many physical measurements of 252 males. Most of the variables can be measured with a scale or tape measure. Can they be used to predict the percentage of body fat? If so, this offers an easy alternative to an underwater weighing technique.”
As variáveis são as seguintes:
case: Case Numberbody.fat: Percent body fat using Brozek’s equation, 457/Density - 414.2body.fat.siri: Percent body fat using Siri’s equation, 495/Density - 450density: Density (gm/cm^2)age: Age (yrs)weight: Weight (lbs)height: Height (inches)BMI: Adiposity index = Weight/Height^2 (kg/m^2)ffweight: Fat Free Weight = (1 - fraction of body fat) * Weight, using Brozek’s formula (lbs)neck: Neck circumference (cm)chest: Chest circumference (cm)abdomen: Abdomen circumference (cm) “at the umbilicus and level with the iliac crest”hip: Hip circumference (cm)thigh: Thigh circumference (cm)knee: Knee circumference (cm)ankle: Ankle circumference (cm)bicep: Extended biceps circumference (cm)forearm: Forearm circumference (cm)wrist: Wrist circumference (cm) “distal to the styloid processes”
library(dplyr)
Attaching package: 'dplyr'The following objects are masked from 'package:stats':
filter, lagThe following objects are masked from 'package:base':
intersect, setdiff, setequal, union2.1.1 Visualizando algumas observações do banco
UsingR::fat %>%
slice_head(n = 10) %>%
gt::gt()| case | body.fat | body.fat.siri | density | age | weight | height | BMI | ffweight | neck | chest | abdomen | hip | thigh | knee | ankle | bicep | forearm | wrist |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 12.6 | 12.3 | 1.0708 | 23 | 154.25 | 67.75 | 23.7 | 134.9 | 36.2 | 93.1 | 85.2 | 94.5 | 59.0 | 37.3 | 21.9 | 32.0 | 27.4 | 17.1 |
| 2 | 6.9 | 6.1 | 1.0853 | 22 | 173.25 | 72.25 | 23.4 | 161.3 | 38.5 | 93.6 | 83.0 | 98.7 | 58.7 | 37.3 | 23.4 | 30.5 | 28.9 | 18.2 |
| 3 | 24.6 | 25.3 | 1.0414 | 22 | 154.00 | 66.25 | 24.7 | 116.0 | 34.0 | 95.8 | 87.9 | 99.2 | 59.6 | 38.9 | 24.0 | 28.8 | 25.2 | 16.6 |
| 4 | 10.9 | 10.4 | 1.0751 | 26 | 184.75 | 72.25 | 24.9 | 164.7 | 37.4 | 101.8 | 86.4 | 101.2 | 60.1 | 37.3 | 22.8 | 32.4 | 29.4 | 18.2 |
| 5 | 27.8 | 28.7 | 1.0340 | 24 | 184.25 | 71.25 | 25.6 | 133.1 | 34.4 | 97.3 | 100.0 | 101.9 | 63.2 | 42.2 | 24.0 | 32.2 | 27.7 | 17.7 |
| 6 | 20.6 | 20.9 | 1.0502 | 24 | 210.25 | 74.75 | 26.5 | 167.0 | 39.0 | 104.5 | 94.4 | 107.8 | 66.0 | 42.0 | 25.6 | 35.7 | 30.6 | 18.8 |
| 7 | 19.0 | 19.2 | 1.0549 | 26 | 181.00 | 69.75 | 26.2 | 146.6 | 36.4 | 105.1 | 90.7 | 100.3 | 58.4 | 38.3 | 22.9 | 31.9 | 27.8 | 17.7 |
| 8 | 12.8 | 12.4 | 1.0704 | 25 | 176.00 | 72.50 | 23.6 | 153.6 | 37.8 | 99.6 | 88.5 | 97.1 | 60.0 | 39.4 | 23.2 | 30.5 | 29.0 | 18.8 |
| 9 | 5.1 | 4.1 | 1.0900 | 25 | 191.00 | 74.00 | 24.6 | 181.3 | 38.1 | 100.9 | 82.5 | 99.9 | 62.9 | 38.3 | 23.8 | 35.9 | 31.1 | 18.2 |
| 10 | 12.0 | 11.7 | 1.0722 | 23 | 198.25 | 73.50 | 25.8 | 174.4 | 42.1 | 99.6 | 88.6 | 104.1 | 63.1 | 41.7 | 25.0 | 35.6 | 30.0 | 19.2 |
UsingR::fat %>%
slice_tail(n = 12) %>%
gt::gt()| case | body.fat | body.fat.siri | density | age | weight | height | BMI | ffweight | neck | chest | abdomen | hip | thigh | knee | ankle | bicep | forearm | wrist |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 241 | 17.0 | 17.0 | 1.0599 | 65 | 127.50 | 65.75 | 20.8 | 105.9 | 34.7 | 93.0 | 79.7 | 87.6 | 50.7 | 33.4 | 20.1 | 28.5 | 24.8 | 16.5 |
| 242 | 33.6 | 35.0 | 1.0207 | 65 | 224.50 | 68.25 | 33.9 | 149.2 | 38.8 | 119.6 | 118.0 | 114.3 | 61.3 | 42.1 | 23.4 | 34.9 | 30.1 | 19.4 |
| 243 | 29.3 | 30.4 | 1.0304 | 66 | 234.25 | 72.00 | 31.8 | 165.6 | 41.4 | 119.7 | 109.0 | 109.1 | 63.7 | 42.4 | 24.6 | 35.6 | 30.7 | 19.5 |
| 244 | 31.4 | 32.6 | 1.0256 | 67 | 227.75 | 72.75 | 30.3 | 156.3 | 41.3 | 115.8 | 113.4 | 109.8 | 65.6 | 46.0 | 25.4 | 35.3 | 29.8 | 19.5 |
| 245 | 28.1 | 29.0 | 1.0334 | 67 | 199.50 | 68.50 | 29.9 | 143.6 | 40.7 | 118.3 | 106.1 | 101.6 | 58.2 | 38.8 | 24.1 | 32.1 | 29.3 | 18.5 |
| 246 | 15.3 | 15.2 | 1.0641 | 68 | 155.50 | 69.25 | 22.8 | 131.8 | 36.3 | 97.4 | 84.3 | 94.4 | 54.3 | 37.5 | 22.6 | 29.2 | 27.3 | 18.5 |
| 247 | 29.1 | 30.2 | 1.0308 | 69 | 215.50 | 70.50 | 30.5 | 152.7 | 40.8 | 113.7 | 107.6 | 110.0 | 63.3 | 44.0 | 22.6 | 37.5 | 32.6 | 18.8 |
| 248 | 11.5 | 11.0 | 1.0736 | 70 | 134.25 | 67.00 | 21.1 | 118.9 | 34.9 | 89.2 | 83.6 | 88.8 | 49.6 | 34.8 | 21.5 | 25.6 | 25.7 | 18.5 |
| 249 | 32.3 | 33.6 | 1.0236 | 72 | 201.00 | 69.75 | 29.1 | 136.1 | 40.9 | 108.5 | 105.0 | 104.5 | 59.6 | 40.8 | 23.2 | 35.2 | 28.6 | 20.1 |
| 250 | 28.3 | 29.3 | 1.0328 | 72 | 186.75 | 66.00 | 30.2 | 133.9 | 38.9 | 111.1 | 111.5 | 101.7 | 60.3 | 37.3 | 21.5 | 31.3 | 27.2 | 18.0 |
| 251 | 25.3 | 26.0 | 1.0399 | 72 | 190.75 | 70.50 | 27.0 | 142.6 | 38.9 | 108.3 | 101.3 | 97.8 | 56.0 | 41.6 | 22.7 | 30.5 | 29.4 | 19.8 |
| 252 | 30.7 | 31.9 | 1.0271 | 74 | 207.50 | 70.00 | 29.8 | 143.7 | 40.8 | 112.4 | 108.5 | 107.1 | 59.3 | 42.2 | 24.6 | 33.7 | 30.0 | 20.9 |
2.1.2 Estatísticas Descritivas
visdat::vis_dat(UsingR::fat)
Verificando se existe algum valor ausente:
visdat::vis_miss(UsingR::fat, sort_miss = TRUE)
Conforme observado, temos todo o conjunto de dados completo sem nenhum NA.
- Verificando o tipo das variáveis
glimpse(UsingR::fat)Rows: 252
Columns: 19
$ case <int> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 1…
$ body.fat <dbl> 12.6, 6.9, 24.6, 10.9, 27.8, 20.6, 19.0, 12.8, 5.1, 12.0…
$ body.fat.siri <dbl> 12.3, 6.1, 25.3, 10.4, 28.7, 20.9, 19.2, 12.4, 4.1, 11.7…
$ density <dbl> 1.0708, 1.0853, 1.0414, 1.0751, 1.0340, 1.0502, 1.0549, …
$ age <int> 23, 22, 22, 26, 24, 24, 26, 25, 25, 23, 26, 27, 32, 30, …
$ weight <dbl> 154.25, 173.25, 154.00, 184.75, 184.25, 210.25, 181.00, …
$ height <dbl> 67.75, 72.25, 66.25, 72.25, 71.25, 74.75, 69.75, 72.50, …
$ BMI <dbl> 23.7, 23.4, 24.7, 24.9, 25.6, 26.5, 26.2, 23.6, 24.6, 25…
$ ffweight <dbl> 134.9, 161.3, 116.0, 164.7, 133.1, 167.0, 146.6, 153.6, …
$ neck <dbl> 36.2, 38.5, 34.0, 37.4, 34.4, 39.0, 36.4, 37.8, 38.1, 42…
$ chest <dbl> 93.1, 93.6, 95.8, 101.8, 97.3, 104.5, 105.1, 99.6, 100.9…
$ abdomen <dbl> 85.2, 83.0, 87.9, 86.4, 100.0, 94.4, 90.7, 88.5, 82.5, 8…
$ hip <dbl> 94.5, 98.7, 99.2, 101.2, 101.9, 107.8, 100.3, 97.1, 99.9…
$ thigh <dbl> 59.0, 58.7, 59.6, 60.1, 63.2, 66.0, 58.4, 60.0, 62.9, 63…
$ knee <dbl> 37.3, 37.3, 38.9, 37.3, 42.2, 42.0, 38.3, 39.4, 38.3, 41…
$ ankle <dbl> 21.9, 23.4, 24.0, 22.8, 24.0, 25.6, 22.9, 23.2, 23.8, 25…
$ bicep <dbl> 32.0, 30.5, 28.8, 32.4, 32.2, 35.7, 31.9, 30.5, 35.9, 35…
$ forearm <dbl> 27.4, 28.9, 25.2, 29.4, 27.7, 30.6, 27.8, 29.0, 31.1, 30…
$ wrist <dbl> 17.1, 18.2, 16.6, 18.2, 17.7, 18.8, 17.7, 18.8, 18.2, 19…- Com a função
skimdo pacoteskimr, temos um resumo da estatística descritiva do banco utilizado.
skimr::skim(UsingR::fat)| Name | UsingR::fat |
| Number of rows | 252 |
| Number of columns | 19 |
| _______________________ | |
| Column type frequency: | |
| numeric | 19 |
| ________________________ | |
| Group variables | None |
Variable type: numeric
| skim_variable | n_missing | complete_rate | mean | sd | p0 | p25 | p50 | p75 | p100 | hist |
|---|---|---|---|---|---|---|---|---|---|---|
| case | 0 | 1 | 126.50 | 72.89 | 1.0 | 63.75 | 126.50 | 189.25 | 252.00 | ▇▇▇▇▇ |
| body.fat | 0 | 1 | 18.94 | 7.75 | 0.0 | 12.80 | 19.00 | 24.60 | 45.10 | ▂▇▇▃▁ |
| body.fat.siri | 0 | 1 | 19.15 | 8.37 | 0.0 | 12.47 | 19.20 | 25.30 | 47.50 | ▃▇▇▃▁ |
| density | 0 | 1 | 1.06 | 0.02 | 1.0 | 1.04 | 1.05 | 1.07 | 1.11 | ▁▅▇▆▁ |
| age | 0 | 1 | 44.88 | 12.60 | 22.0 | 35.75 | 43.00 | 54.00 | 81.00 | ▅▇▇▃▁ |
| weight | 0 | 1 | 178.92 | 29.39 | 118.5 | 159.00 | 176.50 | 197.00 | 363.15 | ▆▇▂▁▁ |
| height | 0 | 1 | 70.15 | 3.66 | 29.5 | 68.25 | 70.00 | 72.25 | 77.75 | ▁▁▁▂▇ |
| BMI | 0 | 1 | 25.44 | 3.65 | 18.1 | 23.10 | 25.05 | 27.33 | 48.90 | ▆▇▁▁▁ |
| ffweight | 0 | 1 | 143.71 | 18.23 | 105.9 | 131.35 | 141.55 | 153.88 | 240.50 | ▃▇▂▁▁ |
| neck | 0 | 1 | 37.99 | 2.43 | 31.1 | 36.40 | 38.00 | 39.42 | 51.20 | ▂▇▃▁▁ |
| chest | 0 | 1 | 100.82 | 8.43 | 79.3 | 94.35 | 99.65 | 105.38 | 136.20 | ▂▇▅▁▁ |
| abdomen | 0 | 1 | 92.56 | 10.78 | 69.4 | 84.57 | 90.95 | 99.33 | 148.10 | ▃▇▂▁▁ |
| hip | 0 | 1 | 99.90 | 7.16 | 85.0 | 95.50 | 99.30 | 103.53 | 147.70 | ▆▇▁▁▁ |
| thigh | 0 | 1 | 59.41 | 5.25 | 47.2 | 56.00 | 59.00 | 62.35 | 87.30 | ▃▇▃▁▁ |
| knee | 0 | 1 | 38.59 | 2.41 | 33.0 | 36.98 | 38.50 | 39.92 | 49.10 | ▃▇▅▁▁ |
| ankle | 0 | 1 | 23.10 | 1.69 | 19.1 | 22.00 | 22.80 | 24.00 | 33.90 | ▃▇▁▁▁ |
| bicep | 0 | 1 | 32.27 | 3.02 | 24.8 | 30.20 | 32.05 | 34.32 | 45.00 | ▂▇▆▁▁ |
| forearm | 0 | 1 | 28.66 | 2.02 | 21.0 | 27.30 | 28.70 | 30.00 | 34.90 | ▁▂▇▆▁ |
| wrist | 0 | 1 | 18.23 | 0.93 | 15.8 | 17.60 | 18.30 | 18.80 | 21.40 | ▂▆▇▂▁ |
2.2 Primeiro Ajuste
Vamos fazer o primeiro ajuste, considerando a variável dependente body.fat, e o parâmetro te, nas variáveis independentes, logo em seguida vamos analisar os resultados.
fit1<-mgcv::gam(body.fat ~ te(age) + te(weight) + te(height) + te(BMI) + te(neck) + te(chest) + te(abdomen) + te(hip) + te(thigh) + te(knee) + te(ankle) + te(bicep) + te(forearm) + te(wrist), data=UsingR::fat)2.2.1 Resultados
summary(fit1)
Family: gaussian
Link function: identity
Formula:
body.fat ~ te(age) + te(weight) + te(height) + te(BMI) + te(neck) +
te(chest) + te(abdomen) + te(hip) + te(thigh) + te(knee) +
te(ankle) + te(bicep) + te(forearm) + te(wrist)
Parametric coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 18.9385 0.2322 81.55 <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
te(age) 1.000 1.000 6.216 0.013381 *
te(weight) 1.000 1.000 0.121 0.728618
te(height) 1.000 1.000 0.693 0.406014
te(BMI) 2.076 2.647 0.810 0.402917
te(neck) 1.336 1.591 3.816 0.087699 .
te(chest) 1.000 1.000 0.984 0.322169
te(abdomen) 4.000 4.000 25.794 < 2e-16 ***
te(hip) 3.324 3.680 2.182 0.163367
te(thigh) 2.880 3.421 1.553 0.305784
te(knee) 1.750 2.187 0.733 0.480100
te(ankle) 1.000 1.000 0.579 0.447634
te(bicep) 3.606 3.896 2.186 0.075074 .
te(forearm) 1.000 1.000 1.429 0.233174
te(wrist) 1.734 2.155 8.458 0.000234 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
R-sq.(adj) = 0.774 Deviance explained = 79.8%
GCV = 15.269 Scale est. = 13.591 n = 252Podemos ver, com o primeiro ajuste, o resultado de que, tivemos um R^2 ajustado de 77.4%, e uma explicação de Desvio de 79.8%, que são bons valores para o modelo ajustado. Todavia, prosseguiremos em busca do melhor modelo ajustado.
2.3 Segundo ajuste
Vamos fazer o segundo ajuste, considerando a variável dependente body.fat, e o parâmetro t2, nas variáveis independentes, logo em seguida vamos analisar os resultados.
fit2<-mgcv::gam(body.fat ~ t2(age) + t2(weight) + t2(height) + t2(BMI) + t2(neck) + t2(chest) + t2(abdomen) +t2(hip) + t2(thigh) + t2(knee) + t2(ankle) + t2(bicep) + t2(forearm) + t2(wrist), data=UsingR::fat)2.3.1 Resultados
summary(fit2)
Family: gaussian
Link function: identity
Formula:
body.fat ~ t2(age) + t2(weight) + t2(height) + t2(BMI) + t2(neck) +
t2(chest) + t2(abdomen) + t2(hip) + t2(thigh) + t2(knee) +
t2(ankle) + t2(bicep) + t2(forearm) + t2(wrist)
Parametric coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 18.9385 0.2323 81.51 <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
t2(age) 1.000 1.000 6.134 0.0140 *
t2(weight) 1.000 1.000 0.142 0.7067
t2(height) 1.000 1.000 0.652 0.4204
t2(BMI) 2.085 2.653 0.535 0.6423
t2(neck) 1.339 1.594 0.837 0.5339
t2(chest) 1.000 1.000 0.989 0.3211
t2(abdomen) 4.000 4.000 25.890 <2e-16 ***
t2(hip) 3.167 3.627 1.925 0.2097
t2(thigh) 2.890 3.420 1.540 0.2067
t2(knee) 1.753 2.188 0.489 0.5731
t2(ankle) 1.000 1.000 0.593 0.4419
t2(bicep) 3.515 3.859 1.855 0.1050
t2(forearm) 1.000 1.000 1.501 0.2217
t2(wrist) 1.737 2.157 5.658 0.0257 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
R-sq.(adj) = 0.774 Deviance explained = 79.7%
GCV = 15.269 Scale est. = 13.604 n = 252Podemos ver, com o segundo ajuste, o resultado de que, tivemos um R^2 ajustado de 77.4%, e uma explicação de Desvio de 79.7%, que são bons valores para o modelo ajustado. Todavia, prosseguiremos em busca do melhor modelo ajustado.
2.4 Terceiro ajuste
Vamos fazer o terceiro ajuste, considerando a variável dependente body.fat, e o parâmetro s, nas variáveis independentes, logo em seguida vamos analisar os resultados.
fit3<-mgcv::gam(body.fat ~ s(age) + s(weight) + s(height) + s(BMI) + s(neck) + s(chest) + s(abdomen) + s(hip) + s(thigh) + s(knee) + s(ankle) + s(bicep) + s(forearm) + s(wrist), data=UsingR::fat)2.4.1 Resultados
summary(fit3)
Family: gaussian
Link function: identity
Formula:
body.fat ~ s(age) + s(weight) + s(height) + s(BMI) + s(neck) +
s(chest) + s(abdomen) + s(hip) + s(thigh) + s(knee) + s(ankle) +
s(bicep) + s(forearm) + s(wrist)
Parametric coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 18.9385 0.2256 83.96 <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(age) 5.423 6.567 2.075 0.051891 .
s(weight) 1.000 1.000 0.175 0.676352
s(height) 1.000 1.000 0.199 0.655765
s(BMI) 2.452 3.173 0.925 0.482472
s(neck) 1.494 1.842 1.867 0.104184
s(chest) 1.000 1.000 0.563 0.453853
s(abdomen) 6.547 7.425 14.779 < 2e-16 ***
s(hip) 7.439 8.261 2.130 0.047066 *
s(thigh) 2.361 3.065 0.490 0.665215
s(knee) 1.437 1.760 0.368 0.566256
s(ankle) 2.844 3.503 0.820 0.618727
s(bicep) 4.558 5.557 1.791 0.081062 .
s(forearm) 1.000 1.000 2.156 0.143457
s(wrist) 1.806 2.268 7.208 0.000558 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
R-sq.(adj) = 0.787 Deviance explained = 82.1%
GCV = 15.338 Scale est. = 12.821 n = 252Podemos ver, com o terceiro ajuste, o resultado de que, tivemos um R^2 ajustado de 78.7%, e uma explicação de Desvio de 82.1%. Ou seja, temos que o terceiro modelo foi o que melhor se adequou aos dados, sendo assim, tomaremos o parâmetro s de suavização como o parâmetro a ser utilizado no ajuste da GAM.
2.5 Ajuste do modelo final.
Devido ao número excessivo de variáveis, é observado que no ajuste acima algumas variáveis não são significativas para o ajuste, considerando o nível de significância de 5%, foi observado que apenas as variáveis abaixo são significativas.
abdomen: Abdomen circumference (cm) “at the umbilicus and level with the iliac crest”hip: Hip circumference (cm)wrist: Wrist circumference (cm) “distal to the styloid processes”
Sendo assim, ajustaremos um modelo apenas com essas variáveis.
ajuste_final <- mgcv::gam(body.fat~s(abdomen)+s(hip)+s(wrist), data = UsingR::fat)2.5.1 Resultados
summary(ajuste_final)
Family: gaussian
Link function: identity
Formula:
body.fat ~ s(abdomen) + s(hip) + s(wrist)
Parametric coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 18.9385 0.2433 77.85 <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(abdomen) 5.387 6.490 51.025 < 2e-16 ***
s(hip) 6.986 8.005 3.266 0.00145 **
s(wrist) 1.267 1.486 22.070 2.38e-07 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
R-sq.(adj) = 0.752 Deviance explained = 76.5%
GCV = 15.834 Scale est. = 14.914 n = 2522.6 Análise gráfica residual
Uma importante parte é a análise gráfica para saber se o modelo ficou bem ajustado.
par(mfrow = c(1,3))
plot(ajuste_final)
par(mfrow = c(2,2))
mgcv::gam.check(ajuste_final)
Method: GCV Optimizer: magic
Smoothing parameter selection converged after 8 iterations.
The RMS GCV score gradient at convergence was 4.538414e-06 .
The Hessian was positive definite.
Model rank = 28 / 28
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(abdomen) 9.00 5.39 1.02 0.56
s(hip) 9.00 6.99 1.03 0.66
s(wrist) 9.00 1.27 1.06 0.833 Conclusão
O uso de GAM (Modelos aditivos generalizados) se mostrou muito eficiente no ajuste dos dados, quando utilizado o parâmetro de suavização spline, sendo assim, obtivemos um bom modelo ajustado, onde os valores preditos estão coerentes com os valores observados, tendo uma diminuição no erro, um bom coeficiente de determinação, evidenciando a importância do modelo ajustado, e que os residuos aparentemente seguem uma distribuição normal.