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Introduction

  • Read data

  • Rename the levels of zona:

    • Pyric herbivorism (HP, from spanish Herbivorismo pírico): old Quemado con pastoreo
    • Prescribed Fires (QP, from spanish Quemas Prescritas): old Quemado sin pastoreo

Modelo Efectos de la quema

Cobertura vegetal

\[Cobertura \sim treat + meses + treat \times meses\]

Tabla ANOVA

ANOVA Efectos Quema, variable = Cobertura
Df Sum Sq Mean Sq F value Pr(>F)
treat 1 71 70.868 0.189 0.664
meses 5 85906 17181.183 45.938 0.000
treat:meses 5 965 192.905 0.516 0.764
Residuals 372 139132 374.012 NA NA

Visualizando el modelo

Version Author Date
8d3328b ajpelu 2022-02-03

¿Es el modelo válido?

Version Author Date
8d3328b ajpelu 2022-02-03
Warning: Autocorrelated residuals detected (p < .001).
Warning: Variances differ between groups (Bartlett Test, p = 0.000).
Warning: Non-normality of residuals detected (p < .001).
OK: No outliers detected.

No, se detectan varios problemas:

  • No homogeneidad varianza,
  • Problemas de linealirad,
  • Correlaciones (problamente temporales) entre datos

Por tanto, las conclusiones que se obtuvieran de este modelado no son válidas!!. Alternativas: Modelos GLMMs, Modelos GAMMs, … ver Zuur et al. (2013)

Tabla posthoc

Post-hoc Efectos Quema, variable = Cobertura
treat meses contrast estimate SE df t.ratio p.value
HP . 5 - (-1) -41.1094 4.8348 372 -8.5027 0.0000
HP . 12 - 5 -0.4359 4.8348 372 -0.0902 1.0000
HP . 17 - 12 11.9578 4.8348 372 2.4733 0.1998
HP . 22 - 17 -1.1313 4.8348 372 -0.2340 1.0000
HP . 29 - 22 6.4609 4.8348 372 1.3363 0.9600
QP . 5 - (-1) -49.1686 4.8348 372 -10.1696 0.0000
QP . 12 - 5 2.1648 4.8348 372 0.4478 1.0000
QP . 17 - 12 17.1006 4.8348 372 3.5370 0.0073
QP . 22 - 17 -0.8781 4.8348 372 -0.1816 1.0000
QP . 29 - 22 1.5391 4.8348 372 0.3183 1.0000
. -1 QP - HP 2.2875 4.8348 372 0.4731 1.0000
. 5 QP - HP -5.7717 4.8348 372 -1.1938 0.9858
. 12 QP - HP -3.1709 4.8348 372 -0.6559 1.0000
. 17 QP - HP 1.9719 4.8348 372 0.4078 1.0000
. 22 QP - HP 2.2250 4.8348 372 0.4602 1.0000
. 29 QP - HP -2.6969 4.8348 372 -0.5578 1.0000

Fitovolumen

\[Fitovolumen \sim treat + meses + treat \times meses\]

Tabla ANOVA

ANOVA Efectos Quema, variable = Fitovolumen
Df Sum Sq Mean Sq F value Pr(>F)
treat 1 409567 409566.7 0.240 0.624
meses 5 484280716 96856143.2 56.803 0.000
treat:meses 5 547672 109534.4 0.064 0.997
Residuals 372 634309317 1705132.6 NA NA

Visualizando el modelo

Version Author Date
8d3328b ajpelu 2022-02-03

¿Es el modelo válido?

Version Author Date
8d3328b ajpelu 2022-02-03
Warning: Autocorrelated residuals detected (p = 0.006).
Warning: Variances differ between groups (Bartlett Test, p = 0.000).
Warning: Non-normality of residuals detected (p < .001).
OK: No outliers detected.

No, se detectan varios problemas:

  • No homogeneidad varianza,
  • Problemas de linealirad,
  • Correlaciones (problamente temporales) entre datos
  • No problemas con outlier

Por tanto, las conclusiones que se obtuvieran de este modelado no son válidas!!. Alternativas: Modelos GLMMs, Modelos GAMMs, … ver Zuur et al. (2013)

Tabla posthoc

Post-hoc ANOVA Efectos Quema, variable = Fitovolumen
treat meses contrast estimate SE df t.ratio p.value
HP . 5 - (-1) -3153.3055 326.4518 372 -9.6593 0.0000
HP . 12 - 5 69.5070 326.4518 372 0.2129 1.0000
HP . 17 - 12 269.1797 326.4518 372 0.8246 0.9998
HP . 22 - 17 11.9375 326.4518 372 0.0366 1.0000
HP . 29 - 22 180.9500 326.4518 372 0.5543 1.0000
QP . 5 - (-1) -3325.0494 326.4518 372 -10.1854 0.0000
QP . 12 - 5 72.1835 326.4518 372 0.2211 1.0000
QP . 17 - 12 262.1369 326.4518 372 0.8030 0.9998
QP . 22 - 17 125.5094 326.4518 372 0.3845 1.0000
QP . 29 - 22 27.3250 326.4518 372 0.0837 1.0000
. -1 QP - HP 67.2869 326.4518 372 0.2061 1.0000
. 5 QP - HP -104.4571 326.4518 372 -0.3200 1.0000
. 12 QP - HP -101.7806 326.4518 372 -0.3118 1.0000
. 17 QP - HP -108.8234 326.4518 372 -0.3334 1.0000
. 22 QP - HP 4.7484 326.4518 372 0.0145 1.0000
. 29 QP - HP -148.8766 326.4518 372 -0.4560 1.0000

Riqueza

\[Riqueza \sim treat + meses + treat \times meses\]

Tabla ANOVA

ANOVA Efectos Quema, variable = Riqueza
Df Sum Sq Mean Sq F value Pr(>F)
treat 1 502 501.878 52.899 0.000
meses 5 1822 364.467 38.416 0.000
treat:meses 5 69 13.846 1.459 0.202
Residuals 372 3529 9.487 NA NA

Visualizando el modelo

Version Author Date
8d3328b ajpelu 2022-02-03

¿Es el modelo válido?

Version Author Date
8d3328b ajpelu 2022-02-03
Warning: Autocorrelated residuals detected (p < .001).
Warning: Variances differ between groups (Bartlett Test, p = 0.000).
Warning: Non-normality of residuals detected (p < .001).
OK: No outliers detected.
# Distribution of Model Family

Predicted Distribution of Residuals

 Distribution Probability
       normal         53%
      tweedie         47%

Predicted Distribution of Response

               Distribution Probability
              beta-binomial         59%
          negative binomial         12%
 neg. binomial (zero-infl.)          9%

No, se detectan varios problemas:

  • No homogeneidad varianza,
  • Problemas de linealirad,
  • Correlaciones (problamente temporales) entre datos

Parace también que existe un problema con la distribución de probabilidad de los residuos (habría que especificar otro tipo de distribución: e.g. beta-binomial)

Por tanto, las conclusiones que se obtuvieran de este modelado no son válidas!!. Alternativas: Modelos GLMMs, Modelos GAMMs, … ver Zuur et al. (2013)

Tabla posthoc

Post-hoc Efectos Quema, variable = Riqueza
treat meses contrast estimate SE df t.ratio p.value
HP . 5 - (-1) 1.4062 0.77 372 1.8262 0.6794
HP . 12 - 5 -0.7188 0.77 372 -0.9334 0.9990
HP . 17 - 12 6.2813 0.77 372 8.1570 0.0000
HP . 22 - 17 -5.4062 0.77 372 -7.0207 0.0000
HP . 29 - 22 2.6875 0.77 372 3.4901 0.0086
QP . 5 - (-1) 0.8750 0.77 372 1.1363 0.9913
QP . 12 - 5 0.6875 0.77 372 0.8928 0.9994
QP . 17 - 12 4.5938 0.77 372 5.9656 0.0000
QP . 22 - 17 -5.4375 0.77 372 -7.0613 0.0000
QP . 29 - 22 1.6250 0.77 372 2.1103 0.4392
. -1 QP - HP -1.7500 0.77 372 -2.2726 0.3178
. 5 QP - HP -2.2813 0.77 372 -2.9625 0.0507
. 12 QP - HP -0.8750 0.77 372 -1.1363 0.9913
. 17 QP - HP -2.5625 0.77 372 -3.3277 0.0153
. 22 QP - HP -2.5938 0.77 372 -3.3683 0.0133
. 29 QP - HP -3.6563 0.77 372 -4.7481 0.0000

Diversidad

\[Shannon \sim treat + meses + treat \times meses\]

Tabla ANOVA

ANOVA Efectos Quema, variable = Diversidad
Df Sum Sq Mean Sq F value Pr(>F)
treat 1 1 1.296 5.023 0.026
meses 5 19 3.713 14.397 0.000
treat:meses 5 1 0.183 0.709 0.617
Residuals 372 96 0.258 NA NA

Visualizando el modelo

Version Author Date
8d3328b ajpelu 2022-02-03

¿Es el modelo válido?

Version Author Date
8d3328b ajpelu 2022-02-03
Warning: Autocorrelated residuals detected (p < .001).
OK: There is not clear evidence for different variances across groups (Bartlett Test, p = 0.939).
Warning: Non-normality of residuals detected (p < .001).
OK: No outliers detected.
# Distribution of Model Family

Predicted Distribution of Residuals

 Distribution Probability
       normal         62%
      tweedie         16%
         beta         12%

Predicted Distribution of Response

 Distribution Probability
      tweedie         47%
      weibull         25%
         beta         12%

No, se detectan varios problemas:

  • Problemas de linealirad,
  • Correlaciones (problamente temporales) entre datos

Por tanto, las conclusiones que se obtuvieran de este modelado no son válidas!!. Alternativas: Modelos GLMMs, Modelos GAMMs, … ver Zuur et al. (2013)

Tabla posthoc

Post-hoc Efectos Quema, variable = Diversidad
treat meses contrast estimate SE df t.ratio p.value
HP . 5 - (-1) 0.5124 0.127 372 4.0359 0.0011
HP . 12 - 5 -0.1828 0.127 372 -1.4397 0.9268
HP . 17 - 12 0.4215 0.127 372 3.3201 0.0157
HP . 22 - 17 -0.3269 0.127 372 -2.5744 0.1544
HP . 29 - 22 0.0749 0.127 372 0.5896 1.0000
QP . 5 - (-1) 0.2398 0.127 372 1.8889 0.6264
QP . 12 - 5 0.0446 0.127 372 0.3517 1.0000
QP . 17 - 12 0.4674 0.127 372 3.6817 0.0042
QP . 22 - 17 -0.4754 0.127 372 -3.7444 0.0033
QP . 29 - 22 0.0783 0.127 372 0.6166 1.0000
. -1 QP - HP -0.0147 0.127 372 -0.1155 1.0000
. 5 QP - HP -0.2872 0.127 372 -2.2624 0.3248
. 12 QP - HP -0.0598 0.127 372 -0.4710 1.0000
. 17 QP - HP -0.0139 0.127 372 -0.1094 1.0000
. 22 QP - HP -0.1624 0.127 372 -1.2794 0.9727
. 29 QP - HP -0.1590 0.127 372 -1.2523 0.9776

Modelo Efectos tras la quema

Quitamos el momento inicial

Cobertura vegetal

\[Cobertura \sim treat + meses + treat \times meses\]

Tabla ANOVA

ANOVA Efectos tras la Quema, variable = Cobertura
Df Sum Sq Mean Sq F value Pr(>F)
treat 1 177 177.257 0.772 0.380
meses 4 19328 4832.032 21.049 0.000
treat:meses 4 774 193.603 0.843 0.499
Residuals 310 71163 229.556 NA NA

Visualizando el modelo

Version Author Date
8d3328b ajpelu 2022-02-03

¿Es el modelo válido?

Version Author Date
8d3328b ajpelu 2022-02-03
Warning: Autocorrelated residuals detected (p < .001).
Warning: Variances differ between groups (Bartlett Test, p = 0.000).
Warning: Non-normality of residuals detected (p < .001).
OK: No outliers detected.
# Distribution of Model Family

Predicted Distribution of Residuals

 Distribution Probability
       normal         53%
      tweedie         47%

Predicted Distribution of Response

 Distribution Probability
      tweedie         50%
        gamma         38%
      weibull          9%

No, se detectan varios problemas:

  • No homogeneidad varianza,
  • Problemas de linealirad,
  • Correlaciones (problamente temporales) entre datos
  • Problemas de distribución de los residuos

Por tanto, las conclusiones que se obtuvieran de este modelado no son válidas!!. Alternativas: Modelos GLMMs, Modelos GAMMs, … ver Zuur et al. (2013)

Tabla posthoc

Post-hoc Efectos tras la Quema, variable = Cobertura
treat meses contrast estimate SE df t.ratio p.value
HP . 12 - 5 -0.4359 3.7878 310 -0.1151 1.0000
HP . 17 - 12 11.9578 3.7878 310 3.1569 0.0225
HP . 22 - 17 -1.1313 3.7878 310 -0.2987 1.0000
HP . 29 - 22 6.4609 3.7878 310 1.7057 0.7026
QP . 12 - 5 2.1648 3.7878 310 0.5715 1.0000
QP . 17 - 12 17.1006 3.7878 310 4.5147 0.0001
QP . 22 - 17 -0.8781 3.7878 310 -0.2318 1.0000
QP . 29 - 22 1.5391 3.7878 310 0.4063 1.0000
. 5 QP - HP -5.7717 3.7878 310 -1.5238 0.8329
. 12 QP - HP -3.1709 3.7878 310 -0.8371 0.9988
. 17 QP - HP 1.9719 3.7878 310 0.5206 1.0000
. 22 QP - HP 2.2250 3.7878 310 0.5874 1.0000
. 29 QP - HP -2.6969 3.7878 310 -0.7120 0.9998

Fitovolumen

\[Fitovolumen \sim treat + meses + treat \times meses\]

Tabla ANOVA

ANOVA Efectos tras la Quema, variable = Fitovolumen
Df Sum Sq Mean Sq F value Pr(>F)
treat 1 674735 674735.35 1.639 0.201
meses 4 12314211 3078552.87 7.478 0.000
treat:meses 4 210063 52515.76 0.128 0.972
Residuals 310 127618607 411672.92 NA NA

Visualizando el modelo

Version Author Date
8d3328b ajpelu 2022-02-03

¿Es el modelo válido?

Version Author Date
8d3328b ajpelu 2022-02-03
Warning: Autocorrelated residuals detected (p < .001).
Warning: Variances differ between groups (Bartlett Test, p = 0.000).
Warning: Non-normality of residuals detected (p < .001).
OK: No outliers detected.
# Distribution of Model Family

Predicted Distribution of Residuals

 Distribution Probability
       normal         41%
    lognormal         19%
            F         12%

Predicted Distribution of Response

               Distribution Probability
                  lognormal         72%
                          F         12%
 neg. binomial (zero-infl.)          6%

No, se detectan varios problemas:

  • No homogeneidad varianza,
  • Problemas de linealirad,
  • Correlaciones (problamente temporales) entre datos
  • No problemas con outlier

Por tanto, las conclusiones que se obtuvieran de este modelado no son válidas!!. Alternativas: Modelos GLMMs, Modelos GAMMs, … ver Zuur et al. (2013)

Tabla posthoc

Post-hoc Efectos tras la Quema, variable = Fitovolumen
treat meses contrast estimate SE df t.ratio p.value
HP . 12 - 5 69.5070 160.4044 310 0.4333 1.0000
HP . 17 - 12 269.1797 160.4044 310 1.6781 0.7242
HP . 22 - 17 11.9375 160.4044 310 0.0744 1.0000
HP . 29 - 22 180.9500 160.4044 310 1.1281 0.9801
QP . 12 - 5 72.1835 160.4044 310 0.4500 1.0000
QP . 17 - 12 262.1369 160.4044 310 1.6342 0.7574
QP . 22 - 17 125.5094 160.4044 310 0.7825 0.9994
QP . 29 - 22 27.3250 160.4044 310 0.1704 1.0000
. 5 QP - HP -104.4571 160.4044 310 -0.6512 0.9999
. 12 QP - HP -101.7806 160.4044 310 -0.6345 0.9999
. 17 QP - HP -108.8234 160.4044 310 -0.6784 0.9999
. 22 QP - HP 4.7484 160.4044 310 0.0296 1.0000
. 29 QP - HP -148.8766 160.4044 310 -0.9281 0.9966

Riqueza

\[Riqueza \sim treat + meses + treat \times meses\]

Tabla ANOVA

ANOVA Efectos tras la Quema, variable = Riqueza
Df Sum Sq Mean Sq F value Pr(>F)
treat 1 458 458.403 45.980 0.000
meses 4 1447 361.730 36.283 0.000
treat:meses 4 64 15.927 1.598 0.175
Residuals 310 3091 9.970 NA NA

Visualizando el modelo

Version Author Date
8d3328b ajpelu 2022-02-03

¿Es el modelo válido?

Version Author Date
8d3328b ajpelu 2022-02-03
Warning: Autocorrelated residuals detected (p < .001).
Warning: Variances differ between groups (Bartlett Test, p = 0.000).
Warning: Non-normality of residuals detected (p < .001).
OK: No outliers detected.
# Distribution of Model Family

Predicted Distribution of Residuals

               Distribution Probability
                     normal         53%
                    tweedie         44%
 neg. binomial (zero-infl.)          3%

Predicted Distribution of Response

         Distribution Probability
        beta-binomial         69%
    negative binomial          9%
 poisson (zero-infl.)          9%

No, se detectan varios problemas:

  • No homogeneidad varianza,
  • Problemas de linealirad,
  • Correlaciones (problamente temporales) entre datos

Parace también que existe un problema con la distribución de probabilidad de los residuos (habría que especificar otro tipo de distribución: e.g. beta-binomial)

Por tanto, las conclusiones que se obtuvieran de este modelado no son válidas!!. Alternativas: Modelos GLMMs, Modelos GAMMs, … ver Zuur et al. (2013)

Tabla posthoc

ANOVA Efectos tras la Quema, variable = Riqueza
treat meses contrast estimate SE df t.ratio p.value
HP . 12 - 5 -0.7188 0.7894 310 -0.9105 0.9972
HP . 17 - 12 6.2812 0.7894 310 7.9573 0.0000
HP . 22 - 17 -5.4062 0.7894 310 -6.8488 0.0000
HP . 29 - 22 2.6875 0.7894 310 3.4046 0.0097
QP . 12 - 5 0.6875 0.7894 310 0.8709 0.9982
QP . 17 - 12 4.5937 0.7894 310 5.8195 0.0000
QP . 22 - 17 -5.4375 0.7894 310 -6.8884 0.0000
QP . 29 - 22 1.6250 0.7894 310 2.0586 0.4147
. 5 QP - HP -2.2812 0.7894 310 -2.8900 0.0523
. 12 QP - HP -0.8750 0.7894 310 -1.1085 0.9828
. 17 QP - HP -2.5625 0.7894 310 -3.2463 0.0167
. 22 QP - HP -2.5937 0.7894 310 -3.2859 0.0146
. 29 QP - HP -3.6562 0.7894 310 -4.6319 0.0001

Diversidad

\[Shannon \sim treat + meses + treat \times meses\]

Tabla ANOVA

ANOVA Efectos tras la Quema, variable = Diversidad
Df Sum Sq Mean Sq F value Pr(>F)
treat 1 1 1.490 5.840 0.016
meses 4 8 2.032 7.963 0.000
treat:meses 4 1 0.179 0.703 0.591
Residuals 310 79 0.255 NA NA

Visualizando el modelo

Version Author Date
8d3328b ajpelu 2022-02-03

¿Es el modelo válido?

Version Author Date
8d3328b ajpelu 2022-02-03
Warning: Autocorrelated residuals detected (p < .001).
OK: There is not clear evidence for different variances across groups (Bartlett Test, p = 0.863).
Warning: Non-normality of residuals detected (p < .001).
OK: No outliers detected.
# Distribution of Model Family

Predicted Distribution of Residuals

         Distribution Probability
               normal         94%
            bernoulli          3%
 poisson (zero-infl.)          3%

Predicted Distribution of Response

 Distribution Probability
      weibull         84%
       normal          9%
         beta          3%

No, se detectan varios problemas:

  • Problemas de linealirad,
  • Correlaciones (problamente temporales) entre datos

Por tanto, las conclusiones que se obtuvieran de este modelado no son válidas!!. Alternativas: Modelos GLMMs, Modelos GAMMs, … ver Zuur et al. (2013)

Tabla posthoc

Post-hoc Efectos tras la Quema, variable = Diversidad
treat meses contrast estimate SE df t.ratio p.value
HP . 12 - 5 -0.1828 0.1263 310 -1.4475 0.8768
HP . 17 - 12 0.4215 0.1263 310 3.3381 0.0122
HP . 22 - 17 -0.3269 0.1263 310 -2.5884 0.1236
HP . 29 - 22 0.0749 0.1263 310 0.5928 1.0000
QP . 12 - 5 0.0446 0.1263 310 0.3536 1.0000
QP . 17 - 12 0.4674 0.1263 310 3.7017 0.0033
QP . 22 - 17 -0.4754 0.1263 310 -3.7647 0.0026
QP . 29 - 22 0.0783 0.1263 310 0.6199 1.0000
. 5 QP - HP -0.2872 0.1263 310 -2.2747 0.2670
. 12 QP - HP -0.0598 0.1263 310 -0.4736 1.0000
. 17 QP - HP -0.0139 0.1263 310 -0.1100 1.0000
. 22 QP - HP -0.1624 0.1263 310 -1.2863 0.9444
. 29 QP - HP -0.1590 0.1263 310 -1.2591 0.9525

Tasa de consumo

\[Consumo \sim treat + meses + treat \times meses\]

Tabla ANOVA

ANOVA Efectos tras la Quema, variable = Tasa Consumo
Df Sum Sq Mean Sq F value Pr(>F)
treat 1 6 5.980 35.126 0
meses 4 30 7.557 44.389 0
treat:meses 4 4 1.063 6.242 0
Residuals 310 53 0.170 NA NA

Visualizando el modelo

Version Author Date
0c68dda ajpelu 2022-02-04

¿Es el modelo válido?

Version Author Date
0c68dda ajpelu 2022-02-04
Warning: Autocorrelated residuals detected (p = 0.002).
Warning: Variances differ between groups (Bartlett Test, p = 0.000).
Warning: Non-normality of residuals detected (p < .001).
OK: No outliers detected.
# Distribution of Model Family

Predicted Distribution of Residuals

 Distribution Probability
       normal         53%
      tweedie         34%
         beta          9%

Predicted Distribution of Response

         Distribution Probability
              tweedie         88%
                 beta          6%
 poisson (zero-infl.)          6%

No, se detectan varios problemas:

  • No homogeneidad varianza,
  • Problemas de linealirad,
  • Correlaciones (problamente temporales) entre datos

Por tanto, las conclusiones que se obtuvieran de este modelado no son válidas!!. Alternativas: Modelos GLMMs, Modelos GAMMs, … ver Zuur et al. (2013)

Tabla posthoc

Post-hoc Efectos tras la Quema, variable = Tasa consumo
treat meses contrast estimate SE df t.ratio p.value
HP . 12 - 5 1.2113 0.1032 310 11.7427 0.0000
HP . 17 - 12 -0.7063 0.1032 310 -6.8469 0.0000
HP . 22 - 17 -0.2596 0.1032 310 -2.5169 0.1491
HP . 29 - 22 -0.0007 0.1032 310 -0.0069 1.0000
QP . 12 - 5 0.5609 0.1032 310 5.4377 0.0000
QP . 17 - 12 -0.4509 0.1032 310 -4.3713 0.0002
QP . 22 - 17 0.0404 0.1032 310 0.3912 1.0000
QP . 29 - 22 -0.1323 0.1032 310 -1.2822 0.9457
. 5 QP - HP 0.0000 0.1032 310 0.0000 1.0000
. 12 QP - HP -0.6504 0.1032 310 -6.3050 0.0000
. 17 QP - HP -0.3950 0.1032 310 -3.8294 0.0020
. 22 QP - HP -0.0950 0.1032 310 -0.9214 0.9968
. 29 QP - HP -0.2266 0.1032 310 -2.1967 0.3159

R version 4.0.2 (2020-06-22)
Platform: x86_64-apple-darwin17.0 (64-bit)
Running under: macOS Catalina 10.15.3

Matrix products: default
BLAS:   /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRblas.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRlapack.dylib

locale:
[1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
 [1] emmeans_1.5.4     plotrix_3.8-1     gtsummary_1.4.2   patchwork_1.1.1  
 [5] performance_0.8.0 broom_0.7.9       tidymv_3.2.1      ggpubr_0.4.0     
 [9] kableExtra_1.3.1  janitor_2.1.0     here_1.0.1        forcats_0.5.1    
[13] stringr_1.4.0     dplyr_1.0.6       purrr_0.3.4       readr_1.4.0      
[17] tidyr_1.1.3       tibble_3.1.2      ggplot2_3.3.5     tidyverse_1.3.1  
[21] workflowr_1.7.0  

loaded via a namespace (and not attached):
  [1] TH.data_1.0-10      colorspace_2.0-2    ggsignif_0.6.0     
  [4] ggridges_0.5.3      ellipsis_0.3.2      rio_0.5.16         
  [7] rprojroot_2.0.2     estimability_1.3    snakecase_0.11.0   
 [10] parameters_0.14.0   fs_1.5.0            rstudioapi_0.13    
 [13] farver_2.1.0        ggrepel_0.9.1       fansi_0.4.2        
 [16] mvtnorm_1.1-1       lubridate_1.7.10    xml2_1.3.2         
 [19] codetools_0.2-18    splines_4.0.2       robustbase_0.93-7  
 [22] knitr_1.31          jsonlite_1.7.2      gt_0.3.0           
 [25] dbplyr_2.1.1        effectsize_0.4.5    compiler_4.0.2     
 [28] httr_1.4.2          backports_1.2.1     assertthat_0.2.1   
 [31] Matrix_1.3-2        fastmap_1.1.0       cli_2.5.0          
 [34] later_1.1.0.1       htmltools_0.5.2     tools_4.0.2        
 [37] coda_0.19-4         gtable_0.3.0        glue_1.4.2         
 [40] Rcpp_1.0.7          carData_3.0-4       cellranger_1.1.0   
 [43] jquerylib_0.1.3     vctrs_0.3.8         nlme_3.1-152       
 [46] broom.helpers_1.4.0 insight_0.14.4      xfun_0.23          
 [49] ps_1.5.0            openxlsx_4.2.3      rvest_1.0.0        
 [52] lifecycle_1.0.1     rstatix_0.6.0       DEoptimR_1.0-8     
 [55] MASS_7.3-53         zoo_1.8-8           getPass_0.2-2      
 [58] scales_1.1.1.9000   hms_1.0.0           promises_1.2.0.1   
 [61] sandwich_3.0-0      qqplotr_0.0.5       yaml_2.2.1         
 [64] curl_4.3            gridExtra_2.3       see_0.6.4          
 [67] sass_0.3.1          stringi_1.7.4       bayestestR_0.9.0   
 [70] highr_0.8           randomForest_4.6-14 zip_2.1.1          
 [73] rlang_0.4.12        pkgconfig_2.0.3     evaluate_0.14      
 [76] lattice_0.20-41     labeling_0.4.2      processx_3.5.1     
 [79] tidyselect_1.1.1    ggsci_2.9           plyr_1.8.6         
 [82] magrittr_2.0.1      R6_2.5.1            generics_0.1.0     
 [85] multcomp_1.4-16     DBI_1.1.1           pillar_1.6.1       
 [88] haven_2.3.1         whisker_0.4         foreign_0.8-81     
 [91] withr_2.4.1         mgcv_1.8-33         survival_3.2-7     
 [94] abind_1.4-5         modelr_0.1.8        crayon_1.4.1       
 [97] car_3.0-10          utf8_1.1.4          rmarkdown_2.8      
[100] grid_4.0.2          readxl_1.3.1        data.table_1.14.0  
[103] callr_3.7.0         git2r_0.28.0        reprex_2.0.0       
[106] digest_0.6.27       webshot_0.5.2       xtable_1.8-4       
[109] httpuv_1.5.5        munsell_0.5.0       viridisLite_0.4.0  
[112] bslib_0.2.4