12  Weight [Nest]

❖ Data

❖ Description

Variable Description
Condition

Hypoxia condition: Normoxia (N) vs Intermittent Hypoxia (IH)

Avg_Weight

Average weight of Pups per Nest at P0 (g)

Variable Description
Condition

Hypoxia condition: Normoxia (N) vs Intermittent Hypoxia (IH)

Avg_Weight

Average weight of Pups per Nest at P0 (g)

❖ Correlations

12.1 Average Pup weight at P0 (based on nest weight)

12.1.1 Data Exploration

❖ Distribution:

Condition Mean SD Variance CoV IQR Min Max Skewness Kurtosis n
N 1.211 0.057 0.003 0.047 0.101 1.129 1.257 −1.594 2.648 4
IH 1.214 0.026 0.001 0.022 0.052 1.186 1.238 −0.913 −1.5 3
Condition Mean SD Variance CoV IQR Min Max Skewness Kurtosis n
N 1.211 0.057 0.003 0.047 0.101 1.129 1.257 −1.594 2.648 4
IH 1.214 0.026 0.001 0.022 0.052 1.186 1.238 −0.913 −1.5 3

12.1.2 Models & Diagnostics

Exploring some Generalized Linear (Mixed) model candidates:

❖ Model call:

```{r}
glmmTMB(formula = Avg_Weight ~ Condition, data = data, family = gaussian("identity"), 
    dispformula = ~Condition, REML = FALSE, ziformula = ~0)
```

❖ Performance:

performance::performance(mod)
AIC AICc BIC R2_conditional R2_marginal RMSE
-19.20 0.80 -19.42 2.53e-06 0.04
AIC AICc BIC R2_conditional R2_marginal RMSE
-19.20 0.80 -19.42 2.53e-06 0.04

❖ Residuals:

performance::check_model(
  mod, panel = FALSE,
  check = c("pp_check", "qq", "reqq", "linearity", "homogeneity")
)

❖ Predictions:

Simulating data from the model for pseudo “Posterior Predictive” plots.

♦ Simulated data vs observed data:

♦ Simulated statistics vs observed ones:

❖ Potential outliers:

No potential outliers detected by the model.

12.1.3 Effects Analysis

```{r}
glmmTMB(formula = Avg_Weight ~ Condition, data = data, family = gaussian("identity"), 
    dispformula = ~Condition, REML = FALSE, ziformula = ~0)
```

12.1.3.1 Coefficients

❖ All effects (Wald):

parameters::parameters(
  mod, component = "conditional", effects = "fixed",
  exponentiate = should_exp(mod), p_adjust = "none", summary = TRUE, digits = 3
)
Parameter Coefficient SE 95% CI z p
(Intercept) 1.213 0.014 (1.19, 1.24) 87.449 < .001
Condition1 -0.001 0.014 (-0.03, 0.03) -0.107 0.915
Model: Avg_Weight ~ Condition (7 Observations)
Parameter Coefficient SE 95% CI z p
(Intercept) 1.213 0.014 (1.19, 1.24) 87.449 < .001
Condition1 -0.001 0.014 (-0.03, 0.03) -0.107 0.915
Model: Avg_Weight ~ Condition (7 Observations)

❖ Main effects (Wald Chi-Square):

car::Anova(mod, type = 3)
term statistic df p.value
Condition 0.01 1 0.910
term statistic df p.value
Condition 0.01 1 0.910

❖ Main effects (Likelihood Ratio Test):

LRT(mod, pred = "Condition")
model df aic bic log_lik deviance chisq chi_df pr_chisq
mod_reduced 3 -21.19 -21.35 13.59 -27.19
mod_full 4 -19.20 -19.42 13.60 -27.20 0.01 1 0.910
model df aic bic log_lik deviance chisq chi_df pr_chisq
mod_reduced 3 -21.19 -21.35 13.59 -27.19
mod_full 4 -19.20 -19.42 13.60 -27.20 0.01 1 0.910
Important

Our LRT() method removes the predictor plus all its interactions

12.1.3.2 Marginal Effects

Marginal means & Contrasts for each predictor:

❖ Marginal Means:

emmeans(mod, specs = pred, type = "response")
Condition emmean SE df lower.CL upper.CL
N 1.211 0.025 3 1.132 1.29
IH 1.214 0.012 3 1.175 1.254
Condition emmean SE df lower.CL upper.CL
N 1.211 0.025 3 1.132 1.29
IH 1.214 0.012 3 1.175 1.254 
- Confidence level used: 0.95

❖ Contrasts:

emmeans(mod, specs = pred, type = "response") |> 
  contrast(method = "pairwise", adjust = "none", infer = TRUE)
contrast estimate SE df lower.CL upper.CL t.ratio p.value
N - IH −0.003 0.028 3 −0.091 0.085 −0.107 0.921
contrast estimate SE df lower.CL upper.CL t.ratio p.value
N - IH −0.003 0.028 3 −0.091 0.085 −0.107 0.921 
- Confidence level used: 0.95

❖ Boxplot: