Análisis temporal de parámetros bioquímcos del Puerto Bahía Blanca
AP
18/11/2019
Serie temporal
302 observaciones de 6 variables bioquímicas (pH, oxígeno disuelto, DBO, Na, Namon) en tres zonas. En cada zona, 2 o 3 puntos de muestreo que se siguieron en el tiempo, de 2003 a 2015. Dataset completo, se imputaron datos faltantes por random forest y datos censurados por izquierda (zCompositions)
Estadística descriptiva
Cantidad de muestreos por zona, año, mes
| zona | anio | Total | ||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 2003 | 2004 | 2005 | 2006 | 2007 | 2008 | 2009 | 2010 | 2011 | 2012 | 2013 | 2014 | 2015 | ||
| 1-GALVAN | 14 | 4 | 4 | 5 | 9 | 8 | 7 | 15 | 8 | 19 | 10 | 11 | 7 | 121 |
| 2-WHITE | 22 | 5 | 2 | 2 | 8 | 15 | 17 | 11 | 8 | 16 | 12 | 13 | 9 | 140 |
| 3-BELGRyROS | 0 | 0 | 0 | 3 | 3 | 4 | 7 | 4 | 3 | 8 | 6 | 1 | 2 | 41 |
| Total | 36 | 9 | 6 | 10 | 20 | 27 | 31 | 30 | 19 | 43 | 28 | 25 | 18 | 302 |
| zona | lugar | Total | |||||||
|---|---|---|---|---|---|---|---|---|---|
| Oleaginosa Moreno | Sector cangrejales |
Terminal 5 y 6 Pto. Galvan |
ADM Agro | MMC | TBB |
B20 y B21 y Vaciadero |
E/ B23 y B 24 | ||
| 1-GALVAN | 22 | 59 | 40 | 0 | 0 | 0 | 0 | 0 | 121 |
| 2-WHITE | 0 | 0 | 0 | 32 | 41 | 67 | 0 | 0 | 140 |
| 3-BELGRyROS | 0 | 0 | 0 | 0 | 0 | 0 | 26 | 15 | 41 |
| Total | 22 | 59 | 40 | 32 | 41 | 67 | 26 | 15 | 302 |
pH
- Missing: 1 (0.3%).
- Datos censurados: 0
Gráficos de perfiles
## `geom_smooth()` using method = 'loess' and formula 'y ~ x'
## `geom_smooth()` using method = 'loess' and formula 'y ~ x'
Modelos temporales - GAM
Usamos Cyclic cubic regression splines (cc): - uses knots - can only be used for single covariates - computationally less expensive - has the same start and end point, e.g. for modelling seasonality
Smooth functions are usually centered to mean zero taken over the set of covariate values
R2-value is as usual the proportion of variance explained by the model.
Scale estimate is the variance of the residual.
the p-values are only approximate and should be handled with care.
edf (effective degrees of freedom). I.e, edf = 3 indicates that the fit is similar to a GLM with a cubic function.
Modelo 1. sin factor aleat (lugar) sin interacción
##
## Family: gaussian
## Link function: identity
##
## Formula:
## ph_imp ~ s(mes, bs = "cc", k = 4) + s(anio, bs = "ps", k = 12) +
## zona
##
## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 7.87122 0.02096 375.470 <2e-16 ***
## zona2-WHITE -0.01377 0.02883 -0.478 0.633
## zona3-BELGRyROS 0.05565 0.04230 1.316 0.189
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(mes) 1.912 2.000 18.16 1.46e-08 ***
## s(anio) 9.005 9.587 28.38 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## R-sq.(adj) = 0.53 Deviance explained = 55.1%
## GCV = 0.054646 Scale est. = 0.052128 n = 302##
## Family: gaussian
## Link function: identity
##
## Formula:
## ph_imp ~ s(mes, bs = "cc", k = 4) + s(anio, bs = "ps", k = 12) +
## zona
##
## Parametric Terms:
## df F p-value
## zona 2 1.386 0.252
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(mes) 1.912 2.000 18.16 1.46e-08
## s(anio) 9.005 9.587 28.38 < 2e-16## Summary:
## * zona : factor; set to the value(s): 1-GALVAN, 2-WHITE, 3-BELGRyROS.
## * mes : numeric predictor; set to the value(s): 6.
## * anio : numeric predictor; with 30 values ranging from 2003.000000 to 2015.000000.
## Summary:
## * zona : factor; set to the value(s): 1-GALVAN, 2-WHITE, 3-BELGRyROS.
## * mes : numeric predictor; with 30 values ranging from 1.000000 to 12.000000.
## * anio : numeric predictor; set to the value(s): 2010.
##
## Method: GCV Optimizer: magic
## Smoothing parameter selection converged after 6 iterations.
## The RMS GCV score gradient at convergence was 1.650149e-06 .
## The Hessian was positive definite.
## Model rank = 16 / 16
##
## 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(mes) 2.00 1.91 0.53 <2e-16 ***
## s(anio) 11.00 9.01 0.55 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Modelo 2. Con aleat con interacción año x zona
##
## Family: gaussian
## Link function: identity
##
## Formula:
## ph_imp ~ s(mes, bs = "cc", k = 4) + s(anio, bs = "ps", k = 12,
## by = zona) + zona + s(lugar, bs = "re")
##
## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 7.86680 0.02101 374.384 <2e-16 ***
## zona2-WHITE -0.01019 0.02875 -0.354 0.723
## zona3-BELGRyROS 0.07656 0.49820 0.154 0.878
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(mes) 1.897e+00 2.000 17.07 3.58e-08 ***
## s(anio):zona1-GALVAN 8.082e+00 8.874 12.60 < 2e-16 ***
## s(anio):zona2-WHITE 8.596e+00 9.246 11.76 < 2e-16 ***
## s(anio):zona3-BELGRyROS 6.342e+00 6.907 10.84 2.67e-12 ***
## s(lugar) 6.063e-09 7.000 0.00 0.792
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## R-sq.(adj) = 0.542 Deviance explained = 58.3%
## GCV = 0.056038 Scale est. = 0.050858 n = 302##
## Family: gaussian
## Link function: identity
##
## Formula:
## ph_imp ~ s(mes, bs = "cc", k = 4) + s(anio, bs = "ps", k = 12,
## by = zona) + zona + s(lugar, bs = "re")
##
## Parametric Terms:
## df F p-value
## zona 2 0.076 0.926
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(mes) 1.897e+00 2.000e+00 17.07 3.58e-08
## s(anio):zona1-GALVAN 8.082e+00 8.874e+00 12.60 < 2e-16
## s(anio):zona2-WHITE 8.596e+00 9.246e+00 11.76 < 2e-16
## s(anio):zona3-BELGRyROS 6.342e+00 6.907e+00 10.84 2.67e-12
## s(lugar) 6.063e-09 7.000e+00 0.00 0.792## Summary:
## * zona : factor; set to the value(s): 1-GALVAN, 2-WHITE, 3-BELGRyROS.
## * mes : numeric predictor; set to the value(s): 6.
## * anio : numeric predictor; with 30 values ranging from 2003.000000 to 2015.000000.
## * lugar : factor; set to the value(s): TBB.
## Summary:
## * zona : factor; set to the value(s): 1-GALVAN, 2-WHITE, 3-BELGRyROS.
## * mes : numeric predictor; set to the value(s): 6.
## * anio : numeric predictor; with 30 values ranging from 2003.000000 to 2015.000000.
## * lugar : factor; set to the value(s): TBB.
## Summary:
## * zona : factor; set to the value(s): 1-GALVAN, 2-WHITE, 3-BELGRyROS.
## * mes : numeric predictor; with 30 values ranging from 1.000000 to 12.000000.
## * anio : numeric predictor; set to the value(s): 2010.
## * lugar : factor; set to the value(s): TBB.
##
## Method: GCV Optimizer: magic
## Smoothing parameter selection converged after 14 iterations.
## The RMS GCV score gradient at convergence was 3.672533e-08 .
## The Hessian was positive definite.
## Model rank = 46 / 46
##
## 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(mes) 2.00e+00 1.90e+00 0.49 <2e-16 ***
## s(anio):zona1-GALVAN 1.10e+01 8.08e+00 0.50 <2e-16 ***
## s(anio):zona2-WHITE 1.10e+01 8.60e+00 0.50 <2e-16 ***
## s(anio):zona3-BELGRyROS 1.10e+01 6.34e+00 0.50 <2e-16 ***
## s(lugar) 8.00e+00 6.06e-09 NA NA
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## s(mes) s(anio)
## 0.07272963 1.38608596
Modelo 3. Con aleat sin inter año x zona
##
## Family: gaussian
## Link function: identity
##
## Formula:
## ph_imp ~ s(mes, bs = "cc", k = 4) + s(anio, bs = "ps", k = 12) +
## zona + s(lugar, bs = "re")
##
## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 7.87122 0.02096 375.470 <2e-16 ***
## zona2-WHITE -0.01377 0.02883 -0.478 0.633
## zona3-BELGRyROS 0.05565 0.04230 1.316 0.189
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(mes) 1.912e+00 2.000 18.16 1.46e-08 ***
## s(anio) 9.005e+00 9.587 28.38 < 2e-16 ***
## s(lugar) 9.102e-09 6.000 0.00 0.961
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## R-sq.(adj) = 0.53 Deviance explained = 55.1%
## GCV = 0.054646 Scale est. = 0.052128 n = 302##
## Family: gaussian
## Link function: identity
##
## Formula:
## ph_imp ~ s(mes, bs = "cc", k = 4) + s(anio, bs = "ps", k = 12) +
## zona + s(lugar, bs = "re")
##
## Parametric Terms:
## df F p-value
## zona 2 1.386 0.252
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(mes) 1.912e+00 2.000e+00 18.16 1.46e-08
## s(anio) 9.005e+00 9.587e+00 28.38 < 2e-16
## s(lugar) 9.102e-09 6.000e+00 0.00 0.961## Summary:
## * zona : factor; set to the value(s): 1-GALVAN, 2-WHITE, 3-BELGRyROS.
## * mes : numeric predictor; set to the value(s): 6.
## * anio : numeric predictor; with 30 values ranging from 2003.000000 to 2015.000000.
## * lugar : factor; set to the value(s): TBB.
## Summary:
## * zona : factor; set to the value(s): 1-GALVAN, 2-WHITE, 3-BELGRyROS.
## * mes : numeric predictor; with 30 values ranging from 1.000000 to 12.000000.
## * anio : numeric predictor; set to the value(s): 2010.
## * lugar : factor; set to the value(s): TBB.
##
## Method: GCV Optimizer: magic
## Smoothing parameter selection converged after 7 iterations.
## The RMS GCV score gradient at convergence was 2.485368e-07 .
## The Hessian was positive definite.
## Model rank = 24 / 24
##
## 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(mes) 2.00e+00 1.91e+00 0.53 <2e-16 ***
## s(anio) 1.10e+01 9.01e+00 0.55 <2e-16 ***
## s(lugar) 8.00e+00 9.10e-09 NA NA
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## s(mes) s(anio)
## 0.07272963 1.38608596## df AIC
## m1 14.91695 -19.49948
## m10 28.91714 -13.99359
## m11 14.91720 -19.49950| ph_imp | |||
|---|---|---|---|
| Predictors | Estimates | CI | p |
| (Intercept) | 7.87 | 7.83 – 7.91 | <0.001 |
| zona (2-WHITE) | -0.01 | -0.07 – 0.04 | 0.633 |
| zona (3-BELGRyROS) | 0.06 | -0.03 – 0.14 | 0.189 |
| Smooth term (mes) | 1.91 | <0.001 | |
| Smooth term (anio) | 9.01 | <0.001 | |
| Observations | 302 | ||
| R2 Nagelkerke | 0.564 | ||
- Interacción NS.Factor aleatorio no parece aportar. No hay diferencias entre sitios, pero sí entre años y meses => m1
DBO
- Missing: 1 (0.3%).
- Datos censurados: 53%
Gráficos de perfiles
## `geom_smooth()` using method = 'loess' and formula 'y ~ x'
## `geom_smooth()` using method = 'loess' and formula 'y ~ x'
Modelos temporales - GAM
Modelo 1. sin factor aleat (lugar) sin interacción
##
## Family: gaussian
## Link function: identity
##
## Formula:
## dbo_imp ~ s(mes, bs = "cc", k = 4) + s(anio, bs = "ps", k = 12) +
## zona
##
## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 10.0022 0.5253 19.040 <2e-16 ***
## zona2-WHITE -0.2973 0.7221 -0.412 0.681
## zona3-BELGRyROS -0.5639 1.0569 -0.534 0.594
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(mes) 1.425 2.000 2.899 0.0177 *
## s(anio) 7.345 8.263 53.530 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## R-sq.(adj) = 0.6 Deviance explained = 61.4%
## GCV = 34.167 Scale est. = 32.835 n = 302##
## Family: gaussian
## Link function: identity
##
## Formula:
## dbo_imp ~ s(mes, bs = "cc", k = 4) + s(anio, bs = "ps", k = 12) +
## zona
##
## Parametric Terms:
## df F p-value
## zona 2 0.17 0.844
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(mes) 1.425 2.000 2.899 0.0177
## s(anio) 7.345 8.263 53.530 <2e-16## Summary:
## * zona : factor; set to the value(s): 1-GALVAN, 2-WHITE, 3-BELGRyROS.
## * mes : numeric predictor; set to the value(s): 6.
## * anio : numeric predictor; with 30 values ranging from 2003.000000 to 2015.000000.
## Summary:
## * zona : factor; set to the value(s): 1-GALVAN, 2-WHITE, 3-BELGRyROS.
## * mes : numeric predictor; with 30 values ranging from 1.000000 to 12.000000.
## * anio : numeric predictor; set to the value(s): 2010.
##
## Method: GCV Optimizer: magic
## Smoothing parameter selection converged after 6 iterations.
## The RMS GCV score gradient at convergence was 6.336818e-05 .
## The Hessian was positive definite.
## Model rank = 16 / 16
##
## 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(mes) 2.00 1.43 0.80 <2e-16 ***
## s(anio) 11.00 7.35 0.78 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Modelo 2. Con aleat con interacción año x zona
##
## Family: gaussian
## Link function: identity
##
## Formula:
## dbo_imp ~ s(mes, bs = "cc", k = 4) + s(anio, bs = "ps", k = 12,
## by = zona) + zona + s(lugar, bs = "re")
##
## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 10.1228 0.5755 17.590 <2e-16 ***
## zona2-WHITE -0.5197 0.7911 -0.657 0.512
## zona3-BELGRyROS -12.3749 34.3970 -0.360 0.719
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(mes) 1.1793 2.000 2.162 0.0264 *
## s(anio):zona1-GALVAN 6.1751 7.165 28.366 < 2e-16 ***
## s(anio):zona2-WHITE 6.6608 7.615 34.479 < 2e-16 ***
## s(anio):zona3-BELGRyROS 7.3008 7.672 4.928 9.54e-06 ***
## s(lugar) 0.8067 5.000 0.212 0.2549
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## R-sq.(adj) = 0.634 Deviance explained = 66.3%
## GCV = 32.775 Scale est. = 30.049 n = 302##
## Family: gaussian
## Link function: identity
##
## Formula:
## dbo_imp ~ s(mes, bs = "cc", k = 4) + s(anio, bs = "ps", k = 12,
## by = zona) + zona + s(lugar, bs = "re")
##
## Parametric Terms:
## df F p-value
## zona 2 0.278 0.758
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(mes) 1.1793 2.0000 2.162 0.0264
## s(anio):zona1-GALVAN 6.1751 7.1651 28.366 < 2e-16
## s(anio):zona2-WHITE 6.6608 7.6151 34.479 < 2e-16
## s(anio):zona3-BELGRyROS 7.3008 7.6718 4.928 9.54e-06
## s(lugar) 0.8067 5.0000 0.212 0.2549## Summary:
## * zona : factor; set to the value(s): 1-GALVAN, 2-WHITE, 3-BELGRyROS.
## * mes : numeric predictor; set to the value(s): 6.
## * anio : numeric predictor; with 30 values ranging from 2003.000000 to 2015.000000.
## * lugar : factor; set to the value(s): TBB.
## Summary:
## * zona : factor; set to the value(s): 1-GALVAN, 2-WHITE, 3-BELGRyROS.
## * mes : numeric predictor; set to the value(s): 6.
## * anio : numeric predictor; with 30 values ranging from 2003.000000 to 2015.000000.
## * lugar : factor; set to the value(s): TBB.
## Summary:
## * zona : factor; set to the value(s): 1-GALVAN, 2-WHITE, 3-BELGRyROS.
## * mes : numeric predictor; with 30 values ranging from 1.000000 to 12.000000.
## * anio : numeric predictor; set to the value(s): 2010.
## * lugar : factor; set to the value(s): TBB.
##
## Method: GCV Optimizer: magic
## Smoothing parameter selection converged after 8 iterations.
## The RMS GCV score gradient at convergence was 5.329104e-06 .
## The Hessian was positive definite.
## Model rank = 46 / 46
##
## 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(mes) 2.000 1.179 0.72 <2e-16 ***
## s(anio):zona1-GALVAN 11.000 6.175 0.66 <2e-16 ***
## s(anio):zona2-WHITE 11.000 6.661 0.66 <2e-16 ***
## s(anio):zona3-BELGRyROS 11.000 7.301 0.66 <2e-16 ***
## s(lugar) 8.000 0.807 NA NA
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## s(mes) s(anio)
## 0.6098124 11.3243255
Modelo 3. Con aleat sin inter año x zona
##
## Family: gaussian
## Link function: identity
##
## Formula:
## dbo_imp ~ s(mes, bs = "cc", k = 4) + s(anio, bs = "ps", k = 12) +
## zona + s(lugar, bs = "re")
##
## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 10.0022 0.5253 19.040 <2e-16 ***
## zona2-WHITE -0.2973 0.7221 -0.412 0.681
## zona3-BELGRyROS -0.5639 1.0569 -0.534 0.594
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(mes) 1.425e+00 2.000 2.899 0.0177 *
## s(anio) 7.345e+00 8.263 53.530 <2e-16 ***
## s(lugar) 2.387e-09 6.000 0.000 0.4537
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## R-sq.(adj) = 0.6 Deviance explained = 61.4%
## GCV = 34.167 Scale est. = 32.835 n = 302##
## Family: gaussian
## Link function: identity
##
## Formula:
## dbo_imp ~ s(mes, bs = "cc", k = 4) + s(anio, bs = "ps", k = 12) +
## zona + s(lugar, bs = "re")
##
## Parametric Terms:
## df F p-value
## zona 2 0.17 0.844
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(mes) 1.425e+00 2.000e+00 2.899 0.0177
## s(anio) 7.345e+00 8.263e+00 53.530 <2e-16
## s(lugar) 2.387e-09 6.000e+00 0.000 0.4537## Summary:
## * zona : factor; set to the value(s): 1-GALVAN, 2-WHITE, 3-BELGRyROS.
## * mes : numeric predictor; set to the value(s): 6.
## * anio : numeric predictor; with 30 values ranging from 2003.000000 to 2015.000000.
## * lugar : factor; set to the value(s): TBB.
## Summary:
## * zona : factor; set to the value(s): 1-GALVAN, 2-WHITE, 3-BELGRyROS.
## * mes : numeric predictor; with 30 values ranging from 1.000000 to 12.000000.
## * anio : numeric predictor; set to the value(s): 2010.
## * lugar : factor; set to the value(s): TBB.
##
## Method: GCV Optimizer: magic
## Smoothing parameter selection converged after 12 iterations.
## The RMS GCV score gradient at convergence was 1.663502e-06 .
## The Hessian was positive definite.
## Model rank = 24 / 24
##
## 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(mes) 2.00e+00 1.43e+00 0.80 <2e-16 ***
## s(anio) 1.10e+01 7.35e+00 0.78 <2e-16 ***
## s(lugar) 8.00e+00 2.39e-09 NA NA
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## s(mes) s(anio)
## 0.6098124 11.3243255## df AIC
## m1 12.77031 1925.008
## m10 26.12279 1910.707
## m11 12.77031 1925.008| dbo_imp | |||
|---|---|---|---|
| Predictors | Estimates | CI | p |
| (Intercept) | 10.00 | 8.97 – 11.04 | <0.001 |
| zona (2-WHITE) | -0.30 | -1.72 – 1.12 | 0.681 |
| zona (3-BELGRyROS) | -0.56 | -2.64 – 1.52 | 0.594 |
| Smooth term (mes) | 1.43 | 0.018 | |
| Smooth term (anio) | 7.35 | <0.001 | |
| Observations | 302 | ||
| R2 Nagelkerke | 1.000 | ||
- Modelar varianzas. datos censurados
Oxígeno disuelto
- Missing: 9 (2.98%)
- Datos censurados: 0%
Gráficos de perfiles
## `geom_smooth()` using method = 'loess' and formula 'y ~ x'
## `geom_smooth()` using method = 'loess' and formula 'y ~ x'
Modelos temporales - GAM
Modelo 1. sin factor aleat (lugar) sin interacción
##
## Family: gaussian
## Link function: identity
##
## Formula:
## odis_imp ~ s(mes, bs = "cc", k = 4) + s(anio, bs = "ps", k = 12) +
## zona
##
## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 7.037265 0.095235 73.893 < 2e-16 ***
## zona2-WHITE -0.004527 0.130958 -0.035 0.97245
## zona3-BELGRyROS 0.591462 0.192390 3.074 0.00231 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(mes) 1.981 2.00 73.49 <2e-16 ***
## s(anio) 9.926 10.45 46.45 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## R-sq.(adj) = 0.708 Deviance explained = 72.1%
## GCV = 1.1305 Scale est. = 1.0747 n = 302##
## Family: gaussian
## Link function: identity
##
## Formula:
## odis_imp ~ s(mes, bs = "cc", k = 4) + s(anio, bs = "ps", k = 12) +
## zona
##
## Parametric Terms:
## df F p-value
## zona 2 5.476 0.00463
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(mes) 1.981 2.000 73.49 <2e-16
## s(anio) 9.926 10.446 46.45 <2e-16## Summary:
## * zona : factor; set to the value(s): 1-GALVAN, 2-WHITE, 3-BELGRyROS.
## * mes : numeric predictor; set to the value(s): 6.
## * anio : numeric predictor; with 30 values ranging from 2003.000000 to 2015.000000.
## Summary:
## * zona : factor; set to the value(s): 1-GALVAN, 2-WHITE, 3-BELGRyROS.
## * mes : numeric predictor; with 30 values ranging from 1.000000 to 12.000000.
## * anio : numeric predictor; set to the value(s): 2010.
##
## Method: GCV Optimizer: magic
## Smoothing parameter selection converged after 7 iterations.
## The RMS GCV score gradient at convergence was 3.402339e-06 .
## The Hessian was positive definite.
## Model rank = 16 / 16
##
## 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(mes) 2.00 1.98 0.38 <2e-16 ***
## s(anio) 11.00 9.93 0.42 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Modelo 2. Con aleat con interacción año x zona
##
## Family: gaussian
## Link function: identity
##
## Formula:
## odis_imp ~ s(mes, bs = "cc", k = 4) + s(anio, bs = "ps", k = 12,
## by = zona) + zona + s(lugar, bs = "re")
##
## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 6.99657 0.09733 71.884 <2e-16 ***
## zona2-WHITE 0.01547 0.13321 0.116 0.908
## zona3-BELGRyROS 0.80124 1.74408 0.459 0.646
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(mes) 1.990e+00 2.000 63.67 < 2e-16 ***
## s(anio):zona1-GALVAN 7.484e+00 8.393 20.81 < 2e-16 ***
## s(anio):zona2-WHITE 8.204e+00 8.944 24.44 < 2e-16 ***
## s(anio):zona3-BELGRyROS 5.956e+00 6.617 12.12 2.85e-13 ***
## s(lugar) 8.169e-10 8.000 0.00 0.629
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## R-sq.(adj) = 0.703 Deviance explained = 72.8%
## GCV = 1.1996 Scale est. = 1.0938 n = 302##
## Family: gaussian
## Link function: identity
##
## Formula:
## odis_imp ~ s(mes, bs = "cc", k = 4) + s(anio, bs = "ps", k = 12,
## by = zona) + zona + s(lugar, bs = "re")
##
## Parametric Terms:
## df F p-value
## zona 2 0.11 0.896
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(mes) 1.990e+00 2.000e+00 63.67 < 2e-16
## s(anio):zona1-GALVAN 7.484e+00 8.393e+00 20.81 < 2e-16
## s(anio):zona2-WHITE 8.204e+00 8.944e+00 24.44 < 2e-16
## s(anio):zona3-BELGRyROS 5.956e+00 6.617e+00 12.12 2.85e-13
## s(lugar) 8.169e-10 8.000e+00 0.00 0.629## Summary:
## * zona : factor; set to the value(s): 1-GALVAN, 2-WHITE, 3-BELGRyROS.
## * mes : numeric predictor; set to the value(s): 6.
## * anio : numeric predictor; with 30 values ranging from 2003.000000 to 2015.000000.
## * lugar : factor; set to the value(s): TBB.
## Summary:
## * zona : factor; set to the value(s): 1-GALVAN, 2-WHITE, 3-BELGRyROS.
## * mes : numeric predictor; set to the value(s): 6.
## * anio : numeric predictor; with 30 values ranging from 2003.000000 to 2015.000000.
## * lugar : factor; set to the value(s): TBB.
## Summary:
## * zona : factor; set to the value(s): 1-GALVAN, 2-WHITE, 3-BELGRyROS.
## * mes : numeric predictor; with 30 values ranging from 1.000000 to 12.000000.
## * anio : numeric predictor; set to the value(s): 2010.
## * lugar : factor; set to the value(s): TBB.
##
## Method: GCV Optimizer: magic
## Smoothing parameter selection converged after 14 iterations.
## The RMS GCV score gradient at convergence was 6.641957e-08 .
## The Hessian was positive definite.
## Model rank = 46 / 46
##
## 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(mes) 2.00e+00 1.99e+00 0.39 <2e-16 ***
## s(anio):zona1-GALVAN 1.10e+01 7.48e+00 0.43 <2e-16 ***
## s(anio):zona2-WHITE 1.10e+01 8.20e+00 0.43 <2e-16 ***
## s(anio):zona3-BELGRyROS 1.10e+01 5.96e+00 0.43 <2e-16 ***
## s(lugar) 8.00e+00 8.17e-10 NA NA
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## s(mes) s(anio)
## 0.7381032 14.5303443
Modelo 3. Con aleat sin inter año x zona
##
## Family: gaussian
## Link function: identity
##
## Formula:
## odis_imp ~ s(mes, bs = "cc", k = 4) + s(anio, bs = "ps", k = 12) +
## zona + s(lugar, bs = "re")
##
## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 7.037274 0.095234 73.895 < 2e-16 ***
## zona2-WHITE -0.004538 0.130956 -0.035 0.97238
## zona3-BELGRyROS 0.591428 0.192387 3.074 0.00231 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(mes) 1.981e+00 2.00 73.49 <2e-16 ***
## s(anio) 9.929e+00 10.45 46.45 <2e-16 ***
## s(lugar) 7.268e-10 8.00 0.00 0.897
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## R-sq.(adj) = 0.708 Deviance explained = 72.1%
## GCV = 1.1305 Scale est. = 1.0747 n = 302##
## Family: gaussian
## Link function: identity
##
## Formula:
## odis_imp ~ s(mes, bs = "cc", k = 4) + s(anio, bs = "ps", k = 12) +
## zona + s(lugar, bs = "re")
##
## Parametric Terms:
## df F p-value
## zona 2 5.476 0.00464
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(mes) 1.981e+00 2.000e+00 73.49 <2e-16
## s(anio) 9.929e+00 1.045e+01 46.45 <2e-16
## s(lugar) 7.268e-10 8.000e+00 0.00 0.897## Summary:
## * zona : factor; set to the value(s): 1-GALVAN, 2-WHITE, 3-BELGRyROS.
## * mes : numeric predictor; set to the value(s): 6.
## * anio : numeric predictor; with 30 values ranging from 2003.000000 to 2015.000000.
## * lugar : factor; set to the value(s): TBB.
## Summary:
## * zona : factor; set to the value(s): 1-GALVAN, 2-WHITE, 3-BELGRyROS.
## * mes : numeric predictor; with 30 values ranging from 1.000000 to 12.000000.
## * anio : numeric predictor; set to the value(s): 2010.
## * lugar : factor; set to the value(s): TBB.
##
## Method: GCV Optimizer: magic
## Smoothing parameter selection converged after 12 iterations.
## The RMS GCV score gradient at convergence was 1.359304e-07 .
## The Hessian was positive definite.
## Model rank = 24 / 24
##
## 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(mes) 2.00e+00 1.98e+00 0.38 <2e-16 ***
## s(anio) 1.10e+01 9.93e+00 0.43 <2e-16 ***
## s(lugar) 8.00e+00 7.27e-10 NA NA
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## s(mes) s(anio)
## 0.7381032 14.5303443## df AIC
## m1 15.90773 895.3262
## m10 27.63393 911.4995
## m11 15.91062 895.3189| odis_imp | |||
|---|---|---|---|
| Predictors | Estimates | CI | p |
| (Intercept) | 7.04 | 6.85 – 7.22 | <0.001 |
| zona (2-WHITE) | -0.00 | -0.26 – 0.25 | 0.972 |
| zona (3-BELGRyROS) | 0.59 | 0.21 – 0.97 | 0.002 |
| Smooth term (mes) | 1.98 | <0.001 | |
| Smooth term (anio) | 9.93 | <0.001 | |
| Observations | 302 | ||
| R2 Nagelkerke | 0.953 | ||
- No interacción. Diferencias entre zonas