15  Pups

❖ Data

❖ Description

Variable Description
Mouse

Mouse unique identifier

Stage

Developmental stage

Condition

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

Time_RR

Latency to right (s)

Time_GR

Latency to fall (s)

Variable Description
Mouse

Mouse unique identifier

Stage

Developmental stage

Condition

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

Time_RR

Latency to right (s)

Time_GR

Latency to fall (s)

❖ Correlations

15.1 Grasping Reflex

15.1.1 Data Exploration

❖ Distribution:

Condition Mean SD Variance CoV IQR Min Max Skewness Kurtosis n
N 0.122 0.094 0.009 0.771 0 0.1 0.5 4.243 18 18
IH 0.1 0 0 0 0 0.1 0.1 NaN NaN 15
Condition Mean SD Variance CoV IQR Min Max Skewness Kurtosis n
N 0.122 0.094 0.009 0.771 0 0.1 0.5 4.243 18 18
IH 0.1 0 0 0 0 0.1 0.1 NaN NaN 15
Condition Mean SD Variance CoV IQR Min Max Skewness Kurtosis n
N 0.1 0 0 0 0 0.1 0.1 NaN NaN 18
IH 0.1 0 0 0 0 0.1 0.1 NaN NaN 15
Condition Mean SD Variance CoV IQR Min Max Skewness Kurtosis n
N 0.1 0 0 0 0 0.1 0.1 NaN NaN 18
IH 0.1 0 0 0 0 0.1 0.1 NaN NaN 15
Condition Mean SD Variance CoV IQR Min Max Skewness Kurtosis n
N 0.1 0 0 0 0 0.1 0.1 NaN NaN 18
IH 0.1 0 0 0 0 0.1 0.1 NaN NaN 15
Condition Mean SD Variance CoV IQR Min Max Skewness Kurtosis n
N 0.1 0 0 0 0 0.1 0.1 NaN NaN 18
IH 0.1 0 0 0 0 0.1 0.1 NaN NaN 15
Condition Mean SD Variance CoV IQR Min Max Skewness Kurtosis n
N 0.728 0.987 0.975 1.357 1.025 0.1 3 1.418 0.66 18
IH 0.76 1.649 2.718 2.169 0.4 0.1 6.5 3.437 12.411 15
Condition Mean SD Variance CoV IQR Min Max Skewness Kurtosis n
N 0.728 0.987 0.975 1.357 1.025 0.1 3 1.418 0.66 18
IH 0.76 1.649 2.718 2.169 0.4 0.1 6.5 3.437 12.411 15
Condition Mean SD Variance CoV IQR Min Max Skewness Kurtosis n
N 1.536 1.62 2.625 1.055 1.913 0.1 5 1.281 0.622 18
IH 1.057 1.067 1.139 1.01 1.9 0.1 3.5 0.794 0.012 15
Condition Mean SD Variance CoV IQR Min Max Skewness Kurtosis n
N 1.536 1.62 2.625 1.055 1.913 0.1 5 1.281 0.622 18
IH 1.057 1.067 1.139 1.01 1.9 0.1 3.5 0.794 0.012 15
Condition Mean SD Variance CoV IQR Min Max Skewness Kurtosis n
N 1.675 1.437 2.065 0.858 2.163 0.1 5.5 1.05 1.474 18
IH 1.667 1.538 2.367 0.923 2.9 0.1 4.5 0.487 −1.106 15
Condition Mean SD Variance CoV IQR Min Max Skewness Kurtosis n
N 1.675 1.437 2.065 0.858 2.163 0.1 5.5 1.05 1.474 18
IH 1.667 1.538 2.367 0.923 2.9 0.1 4.5 0.487 −1.106 15
Condition Mean SD Variance CoV IQR Min Max Skewness Kurtosis n
N 3.306 1.986 3.945 0.601 3 0.5 7 0.419 −0.79 18
IH 1.197 1.461 2.136 1.221 1.65 0.1 4.5 1.345 0.908 15
Condition Mean SD Variance CoV IQR Min Max Skewness Kurtosis n
N 3.306 1.986 3.945 0.601 3 0.5 7 0.419 −0.79 18
IH 1.197 1.461 2.136 1.221 1.65 0.1 4.5 1.345 0.908 15
Condition Mean SD Variance CoV IQR Min Max Skewness Kurtosis n
N 5.083 1.574 2.478 0.31 2.5 2 7.5 −0.211 −0.415 18
IH 2.193 2.415 5.831 1.101 4.4 0.1 7 1.035 −0.328 15
Condition Mean SD Variance CoV IQR Min Max Skewness Kurtosis n
N 5.083 1.574 2.478 0.31 2.5 2 7.5 −0.211 −0.415 18
IH 2.193 2.415 5.831 1.101 4.4 0.1 7 1.035 −0.328 15
Condition Mean SD Variance CoV IQR Min Max Skewness Kurtosis n
N 10 5.641 31.824 0.564 10.5 4 20 0.705 −0.971 18
IH 3.503 3.454 11.928 0.986 4.75 0.1 13.5 1.765 4.416 15
Condition Mean SD Variance CoV IQR Min Max Skewness Kurtosis n
N 10 5.641 31.824 0.564 10.5 4 20 0.705 −0.971 18
IH 3.503 3.454 11.928 0.986 4.75 0.1 13.5 1.765 4.416 15
Condition Mean SD Variance CoV IQR Min Max Skewness Kurtosis n
N 13.806 8.186 67.004 0.593 10 3 40 1.854 5.711 18
IH 3.517 1.744 3.04 0.496 2.5 1 7 0.649 −0.212 15
Condition Mean SD Variance CoV IQR Min Max Skewness Kurtosis n
N 13.806 8.186 67.004 0.593 10 3 40 1.854 5.711 18
IH 3.517 1.744 3.04 0.496 2.5 1 7 0.649 −0.212 15

❖ Evolution:

15.1.2 Models & Diagnostics

Exploring some Generalized Linear (Mixed) model candidates:

❖ Model call:

```{r}
glmmTMB(formula = Time_GR ~ Condition * Stage + ar1(Stage + 0 | 
    Mouse), data = data, family = Gamma("identity"), REML = TRUE, 
    start = list(beta = c(I(mean(data$Time_GR)), rep(0, 19))), 
    ziformula = ~0, dispformula = ~1)
```

❖ Performance:

performance::performance(mod)
AIC AICc BIC R2_conditional R2_marginal RMSE Sigma
704.33 707.94 791.71 0.94 2.64 0.88
AIC AICc BIC R2_conditional R2_marginal RMSE Sigma
704.33 707.94 791.71 0.94 2.64 0.88

❖ 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:

❖ Model call:

```{r}
glmmTMB(formula = Time_GR ~ Condition * Stage + ar1(Stage + 0 | 
    Mouse), data = data, family = gaussian("identity"), REML = TRUE, 
    start = list(beta = c(I(mean(data$Time_GR)), rep(0, 19))), 
    ziformula = ~0, dispformula = ~1)
```

❖ Performance:

performance::performance(mod)
AIC AICc BIC R2_conditional R2_marginal ICC RMSE Sigma
1624.23 1627.84 1711.61 0.65 0.65 0 2.43 2.61
AIC AICc BIC R2_conditional R2_marginal ICC RMSE Sigma
1624.23 1627.84 1711.61 0.65 0.65 0 2.43 2.61

❖ 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:

15.1.3 Effects Analysis

```{r}
glmmTMB(formula = Time_GR ~ Condition * Stage + ar1(Stage + 0 | 
    Mouse), data = data, family = Gamma("identity"), REML = TRUE, 
    start = list(beta = c(I(mean(data$Time_GR)), rep(0, 19))), 
    ziformula = ~0, dispformula = ~1)
```

15.1.3.1 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) 2.532 0.200 (2.14, 2.92) 12.670 < .001
Condition1 1.113 0.200 (0.72, 1.50) 5.569 < .001
Stage1 -2.421 0.200 (-2.81, -2.03) -12.079 < .001
Stage2 -2.432 0.200 (-2.83, -2.04) -12.141 < .001
Stage3 -2.432 0.200 (-2.83, -2.04) -12.141 < .001
Stage4 -1.789 0.224 (-2.23, -1.35) -7.970 < .001
Stage5 -1.236 0.267 (-1.76, -0.71) -4.625 < .001
Stage6 -0.862 0.304 (-1.46, -0.27) -2.838 0.005 **
Stage7 -0.281 0.384 (-1.03, 0.47) -0.732 0.464
Stage8 1.106 0.556 (0.02, 2.20) 1.989 0.047 *
Stage9 4.219 1.008 (2.24, 6.20) 4.185 < .001
Condition1 * Stage1 -1.102 0.200 (-1.49, -0.71) -5.497 < .001
Condition1 * Stage2 -1.113 0.200 (-1.51, -0.72) -5.556 < .001
Condition1 * Stage3 -1.113 0.200 (-1.51, -0.72) -5.556 < .001
Condition1 * Stage4 -1.129 0.224 (-1.57, -0.69) -5.032 < .001
Condition1 * Stage5 -0.873 0.267 (-1.40, -0.35) -3.268 0.001 ***
Condition1 * Stage6 -1.109 0.304 (-1.70, -0.51) -3.652 < .001
Condition1 * Stage7 -0.059 0.384 (-0.81, 0.69) -0.153 0.879
Condition1 * Stage8 0.332 0.556 (-0.76, 1.42) 0.597 0.550
Condition1 * Stage9 2.135 1.008 (0.16, 4.11) 2.118 0.034 *
Model: Time_GR ~ Condition * Stage (330 Observations)
Parameter Coefficient SE 95% CI z p
(Intercept) 2.532 0.200 (2.14, 2.92) 12.670 < .001
Condition1 1.113 0.200 (0.72, 1.50) 5.569 < .001
Stage1 -2.421 0.200 (-2.81, -2.03) -12.079 < .001
Stage2 -2.432 0.200 (-2.83, -2.04) -12.141 < .001
Stage3 -2.432 0.200 (-2.83, -2.04) -12.141 < .001
Stage4 -1.789 0.224 (-2.23, -1.35) -7.970 < .001
Stage5 -1.236 0.267 (-1.76, -0.71) -4.625 < .001
Stage6 -0.862 0.304 (-1.46, -0.27) -2.838 0.005 **
Stage7 -0.281 0.384 (-1.03, 0.47) -0.732 0.464
Stage8 1.106 0.556 (0.02, 2.20) 1.989 0.047 *
Stage9 4.219 1.008 (2.24, 6.20) 4.185 < .001
Condition1 * Stage1 -1.102 0.200 (-1.49, -0.71) -5.497 < .001
Condition1 * Stage2 -1.113 0.200 (-1.51, -0.72) -5.556 < .001
Condition1 * Stage3 -1.113 0.200 (-1.51, -0.72) -5.556 < .001
Condition1 * Stage4 -1.129 0.224 (-1.57, -0.69) -5.032 < .001
Condition1 * Stage5 -0.873 0.267 (-1.40, -0.35) -3.268 0.001 ***
Condition1 * Stage6 -1.109 0.304 (-1.70, -0.51) -3.652 < .001
Condition1 * Stage7 -0.059 0.384 (-0.81, 0.69) -0.153 0.879
Condition1 * Stage8 0.332 0.556 (-0.76, 1.42) 0.597 0.550
Condition1 * Stage9 2.135 1.008 (0.16, 4.11) 2.118 0.034 *
Model: Time_GR ~ Condition * Stage (330 Observations)

❖ Main effects (Wald Chi-Square):

car::Anova(mod, type = 3)
term statistic df p.value
Condition 31.01 1 <0.001 ***
Stage 245.24 9 <0.001 ***
Condition:Stage 36.83 9 <0.001 ***
term statistic df p.value
Condition 31.01 1 <0.001 ***
Stage 245.24 9 <0.001 ***
Condition:Stage 36.83 9 <0.001 ***

15.1.3.2 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 3.646 0.376 327 2.905 4.386
IH 1.419 0.134 327 1.155 1.684
Condition emmean SE df lower.CL upper.CL
N 3.646 0.376 327 2.905 4.386
IH 1.419 0.134 327 1.155 1.684 
- Results are averaged over the levels of: Stage
- Confidence level used: 0.95

❖ Contrasts:

emmeans(mod, specs = pred, type = "response") |> 
  contrast(method = "consec", adjust = "none", infer = TRUE)
contrast estimate SE df lower.CL upper.CL t.ratio p.value
IH - N −2.226 0.4 327 −3.013 −1.44 −5.569 <0.001 ***
contrast estimate SE df lower.CL upper.CL t.ratio p.value
IH - N −2.226 0.4 327 −3.013 −1.44 −5.569 <0.001 *** 
- Results are averaged over the levels of: Stage
- Confidence level used: 0.95

❖ Boxplot:

❖ Marginal Means:

emmeans(mod, specs = pred, type = "response")
Stage emmean SE df lower.CL upper.CL
P2 0.111 0.017 327 0.078 0.144
P3 0.1 0.015 327 0.07 0.13
P4 0.1 0.015 327 0.07 0.13
P5 0.744 0.114 327 0.52 0.968
P6 1.296 0.198 327 0.906 1.687
P7 1.671 0.256 327 1.168 2.174
P8 2.251 0.367 327 1.53 2.973
P9 3.638 0.58 327 2.497 4.779
P10 6.752 1.105 327 4.578 8.925
P11 8.661 1.478 327 5.753 11.569
Stage emmean SE df lower.CL upper.CL
P2 0.111 0.017 327 0.078 0.144
P3 0.1 0.015 327 0.07 0.13
P4 0.1 0.015 327 0.07 0.13
P5 0.744 0.114 327 0.52 0.968
P6 1.296 0.198 327 0.906 1.687
P7 1.671 0.256 327 1.168 2.174
P8 2.251 0.367 327 1.53 2.973
P9 3.638 0.58 327 2.497 4.779
P10 6.752 1.105 327 4.578 8.925
P11 8.661 1.478 327 5.753 11.569 
- Results are averaged over the levels of: Condition
- Confidence level used: 0.95

❖ Contrasts:

emmeans(mod, specs = pred, type = "response") |> 
  contrast(method = "consec", adjust = "none", infer = TRUE)
contrast estimate SE df lower.CL upper.CL t.ratio p.value
P3 - P2 −0.011 0.023 327 −0.056 0.034 −0.487 0.627
P4 - P3 0 0.022 327 −0.043 0.043 0 0.999
P5 - P4 0.644 0.115 327 0.418 0.87 5.595 <0.001 ***
P6 - P5 0.553 0.229 327 0.102 1.003 2.414 0.016 *
P7 - P6 0.374 0.324 327 −0.262 1.011 1.157 0.248
P8 - P7 0.58 0.447 327 −0.299 1.46 1.298 0.195
P9 - P8 1.387 0.686 327 0.037 2.737 2.022 0.044 *
P10 - P9 3.113 1.248 327 0.659 5.568 2.495 0.013 *
P11 - P10 1.909 1.846 327 −1.721 5.54 1.035 0.302
contrast estimate SE df lower.CL upper.CL t.ratio p.value
P3 - P2 −0.011 0.023 327 −0.056 0.034 −0.487 0.627
P4 - P3 0 0.022 327 −0.043 0.043 0 0.999
P5 - P4 0.644 0.115 327 0.418 0.87 5.595 <0.001 ***
P6 - P5 0.553 0.229 327 0.102 1.003 2.414 0.016 *
P7 - P6 0.374 0.324 327 −0.262 1.011 1.157 0.248
P8 - P7 0.58 0.447 327 −0.299 1.46 1.298 0.195
P9 - P8 1.387 0.686 327 0.037 2.737 2.022 0.044 *
P10 - P9 3.113 1.248 327 0.659 5.568 2.495 0.013 *
P11 - P10 1.909 1.846 327 −1.721 5.54 1.035 0.302 
- Results are averaged over the levels of: Condition
- Confidence level used: 0.95

❖ Boxplot:

❖ Marginal Means:

emmeans(mod, specs = emmeans_formula, type = "response")
Condition emmean SE df lower.CL upper.CL
N 0.122 0.025 327 0.073 0.172
IH 0.1 0.023 327 0.056 0.144
Condition emmean SE df lower.CL upper.CL
N 0.122 0.025 327 0.073 0.172
IH 0.1 0.023 327 0.056 0.144
Condition emmean SE df lower.CL upper.CL
N 0.1 0.021 327 0.059 0.141
IH 0.1 0.023 327 0.056 0.144
Condition emmean SE df lower.CL upper.CL
N 0.1 0.021 327 0.059 0.141
IH 0.1 0.023 327 0.056 0.144
Condition emmean SE df lower.CL upper.CL
N 0.1 0.021 327 0.059 0.141
IH 0.1 0.023 327 0.056 0.144
Condition emmean SE df lower.CL upper.CL
N 0.1 0.021 327 0.059 0.141
IH 0.1 0.023 327 0.056 0.144
Condition emmean SE df lower.CL upper.CL
N 0.728 0.15 327 0.432 1.023
IH 0.76 0.172 327 0.422 1.098
Condition emmean SE df lower.CL upper.CL
N 0.728 0.15 327 0.432 1.023
IH 0.76 0.172 327 0.422 1.098
Condition emmean SE df lower.CL upper.CL
N 1.536 0.317 327 0.913 2.159
IH 1.057 0.239 327 0.587 1.526
Condition emmean SE df lower.CL upper.CL
N 1.536 0.317 327 0.913 2.159
IH 1.057 0.239 327 0.587 1.526
Condition emmean SE df lower.CL upper.CL
N 1.675 0.346 327 0.995 2.355
IH 1.667 0.377 327 0.926 2.408
Condition emmean SE df lower.CL upper.CL
N 1.675 0.346 327 0.995 2.355
IH 1.667 0.377 327 0.926 2.408
Condition emmean SE df lower.CL upper.CL
N 3.306 0.682 327 1.964 4.647
IH 1.197 0.27 327 0.665 1.729
Condition emmean SE df lower.CL upper.CL
N 3.306 0.682 327 1.964 4.647
IH 1.197 0.27 327 0.665 1.729
Condition emmean SE df lower.CL upper.CL
N 5.083 1.049 327 3.02 7.146
IH 2.193 0.496 327 1.218 3.168
Condition emmean SE df lower.CL upper.CL
N 5.083 1.049 327 3.02 7.146
IH 2.193 0.496 327 1.218 3.168
Condition emmean SE df lower.CL upper.CL
N 10 2.063 327 5.942 14.058
IH 3.503 0.792 327 1.946 5.061
Condition emmean SE df lower.CL upper.CL
N 10 2.063 327 5.942 14.058
IH 3.503 0.792 327 1.946 5.061
Condition emmean SE df lower.CL upper.CL
N 13.806 2.848 327 8.203 19.408
IH 3.517 0.795 327 1.953 5.08
Condition emmean SE df lower.CL upper.CL
N 13.806 2.848 327 8.203 19.408
IH 3.517 0.795 327 1.953 5.08 
- Confidence level used: 0.95

❖ Contrasts:

emmeans(mod, specs = emmeans_formula, type = "response") |> 
  contrast(method = "pairwise", adjust = "none", infer = TRUE)
contrast estimate SE df lower.CL upper.CL t.ratio p.value
N - IH 0.022 0.034 327 −0.044 0.089 0.656 0.512
contrast estimate SE df lower.CL upper.CL t.ratio p.value
N - IH 0.022 0.034 327 −0.044 0.089 0.656 0.512
contrast estimate SE df lower.CL upper.CL t.ratio p.value
N - IH 0 0.031 327 −0.06 0.06 0 0.999
contrast estimate SE df lower.CL upper.CL t.ratio p.value
N - IH 0 0.031 327 −0.06 0.06 0 0.999
contrast estimate SE df lower.CL upper.CL t.ratio p.value
N - IH 0 0.031 327 −0.06 0.06 0 0.999
contrast estimate SE df lower.CL upper.CL t.ratio p.value
N - IH 0 0.031 327 −0.06 0.06 0 0.999
contrast estimate SE df lower.CL upper.CL t.ratio p.value
N - IH −0.032 0.228 327 −0.481 0.417 −0.141 0.888
contrast estimate SE df lower.CL upper.CL t.ratio p.value
N - IH −0.032 0.228 327 −0.481 0.417 −0.141 0.888
contrast estimate SE df lower.CL upper.CL t.ratio p.value
N - IH 0.479 0.397 327 −0.301 1.26 1.208 0.228
contrast estimate SE df lower.CL upper.CL t.ratio p.value
N - IH 0.479 0.397 327 −0.301 1.26 1.208 0.228
contrast estimate SE df lower.CL upper.CL t.ratio p.value
N - IH 0.008 0.511 327 −0.997 1.014 0.016 0.987
contrast estimate SE df lower.CL upper.CL t.ratio p.value
N - IH 0.008 0.511 327 −0.997 1.014 0.016 0.987
contrast estimate SE df lower.CL upper.CL t.ratio p.value
N - IH 2.109 0.734 327 0.666 3.552 2.875 0.004 **
contrast estimate SE df lower.CL upper.CL t.ratio p.value
N - IH 2.109 0.734 327 0.666 3.552 2.875 0.004 **
contrast estimate SE df lower.CL upper.CL t.ratio p.value
N - IH 2.89 1.16 327 0.608 5.172 2.492 0.013 *
contrast estimate SE df lower.CL upper.CL t.ratio p.value
N - IH 2.89 1.16 327 0.608 5.172 2.492 0.013 *
contrast estimate SE df lower.CL upper.CL t.ratio p.value
N - IH 6.497 2.21 327 2.15 10.843 2.94 0.004 **
contrast estimate SE df lower.CL upper.CL t.ratio p.value
N - IH 6.497 2.21 327 2.15 10.843 2.94 0.004 **
contrast estimate SE df lower.CL upper.CL t.ratio p.value
N - IH 10.289 2.957 327 4.472 16.105 3.48 <0.001 ***
contrast estimate SE df lower.CL upper.CL t.ratio p.value
N - IH 10.289 2.957 327 4.472 16.105 3.48 <0.001 *** 
- Confidence level used: 0.95

❖ Temporal plot:

15.2 Righting Reflex

15.2.1 Data Exploration

❖ Distribution:

Condition Mean SD Variance CoV IQR Min Max Skewness Kurtosis n
N 53.611 13.877 192.575 0.259 5.5 9.5 60 −2.438 5.73 18
IH 50 15.706 246.679 0.314 23.5 12.5 60 −1.304 0.601 15
Condition Mean SD Variance CoV IQR Min Max Skewness Kurtosis n
N 53.611 13.877 192.575 0.259 5.5 9.5 60 −2.438 5.73 18
IH 50 15.706 246.679 0.314 23.5 12.5 60 −1.304 0.601 15
Condition Mean SD Variance CoV IQR Min Max Skewness Kurtosis n
N 55.056 9.613 92.408 0.175 5 33 60 −1.544 0.601 18
IH 56.787 8.561 73.283 0.151 0 32.8 60 −2.496 5.081 15
Condition Mean SD Variance CoV IQR Min Max Skewness Kurtosis n
N 55.056 9.613 92.408 0.175 5 33 60 −1.544 0.601 18
IH 56.787 8.561 73.283 0.151 0 32.8 60 −2.496 5.081 15
Condition Mean SD Variance CoV IQR Min Max Skewness Kurtosis n
N 53.944 10.379 107.732 0.192 15.75 32.5 60 −1.302 −0.037 18
IH 55.633 8.301 68.91 0.149 8 34.5 60 −1.812 2.258 15
Condition Mean SD Variance CoV IQR Min Max Skewness Kurtosis n
N 53.944 10.379 107.732 0.192 15.75 32.5 60 −1.302 −0.037 18
IH 55.633 8.301 68.91 0.149 8 34.5 60 −1.812 2.258 15
Condition Mean SD Variance CoV IQR Min Max Skewness Kurtosis n
N 31.676 20.452 418.273 0.646 39.25 2.86 60 −0.132 −1.363 18
IH 42.533 23.041 530.874 0.542 40 3.5 60 −0.873 −0.998 15
Condition Mean SD Variance CoV IQR Min Max Skewness Kurtosis n
N 31.676 20.452 418.273 0.646 39.25 2.86 60 −0.132 −1.363 18
IH 42.533 23.041 530.874 0.542 40 3.5 60 −0.873 −0.998 15
Condition Mean SD Variance CoV IQR Min Max Skewness Kurtosis n
N 9.311 10.066 101.333 1.081 10.194 1.565 33.25 1.655 1.807 18
IH 35.867 24.268 588.945 0.677 53 3.5 60 −0.243 −1.868 15
Condition Mean SD Variance CoV IQR Min Max Skewness Kurtosis n
N 9.311 10.066 101.333 1.081 10.194 1.565 33.25 1.655 1.807 18
IH 35.867 24.268 588.945 0.677 53 3.5 60 −0.243 −1.868 15
Condition Mean SD Variance CoV IQR Min Max Skewness Kurtosis n
N 4.912 7.945 63.119 1.617 1.938 1 34.25 3.391 12.161 18
IH 37.703 24.98 623.996 0.663 57 2.35 60 −0.523 −1.553 15
Condition Mean SD Variance CoV IQR Min Max Skewness Kurtosis n
N 4.912 7.945 63.119 1.617 1.938 1 34.25 3.391 12.161 18
IH 37.703 24.98 623.996 0.663 57 2.35 60 −0.523 −1.553 15
Condition Mean SD Variance CoV IQR Min Max Skewness Kurtosis n
N 4.504 10.157 103.165 2.255 1.269 1.015 45 4.173 17.577 18
IH 8.567 9.058 82.047 1.057 8.855 1.875 34 1.91 3.654 15
Condition Mean SD Variance CoV IQR Min Max Skewness Kurtosis n
N 4.504 10.157 103.165 2.255 1.269 1.015 45 4.173 17.577 18
IH 8.567 9.058 82.047 1.057 8.855 1.875 34 1.91 3.654 15
Condition Mean SD Variance CoV IQR Min Max Skewness Kurtosis n
N 2.129 1.92 3.687 0.902 1.027 0.875 9.25 3.36 12.363 18
IH 4.979 7.128 50.803 1.432 1.84 1.565 29.33 3.284 11.287 15
Condition Mean SD Variance CoV IQR Min Max Skewness Kurtosis n
N 2.129 1.92 3.687 0.902 1.027 0.875 9.25 3.36 12.363 18
IH 4.979 7.128 50.803 1.432 1.84 1.565 29.33 3.284 11.287 15
Condition Mean SD Variance CoV IQR Min Max Skewness Kurtosis n
N 1.296 0.448 0.2 0.345 0.538 0.83 2.78 2.248 6.842 18
IH 2.537 1.233 1.52 0.486 1.5 1.165 5.725 1.471 1.971 15
Condition Mean SD Variance CoV IQR Min Max Skewness Kurtosis n
N 1.296 0.448 0.2 0.345 0.538 0.83 2.78 2.248 6.842 18
IH 2.537 1.233 1.52 0.486 1.5 1.165 5.725 1.471 1.971 15
Condition Mean SD Variance CoV IQR Min Max Skewness Kurtosis n
N 1.471 0.715 0.511 0.486 1.216 0.79 3.245 1.082 0.463 18
IH 2.617 3.366 11.332 1.287 1.29 0.855 14.55 3.624 13.612 15
Condition Mean SD Variance CoV IQR Min Max Skewness Kurtosis n
N 1.471 0.715 0.511 0.486 1.216 0.79 3.245 1.082 0.463 18
IH 2.617 3.366 11.332 1.287 1.29 0.855 14.55 3.624 13.612 15

❖ Evolution:

15.2.2 Models & Diagnostics

Exploring some Generalized Linear (Mixed) model candidates:

❖ Model call:

```{r}
glmmTMB(formula = Time_RR ~ Condition * Stage + ar1(Stage + 0 | 
    Mouse), data = data, family = gaussian("identity"), REML = TRUE, 
    start = list(beta = c(I(mean(data$Time_RR)), rep(0, 19))), 
    ziformula = ~0, dispformula = ~1)
```

❖ Performance:

performance::performance(mod)
AIC AICc BIC R2_conditional R2_marginal ICC RMSE Sigma
2543.66 2547.27 2631.04 0.93 0.93 0 3.23 6.17
AIC AICc BIC R2_conditional R2_marginal ICC RMSE Sigma
2543.66 2547.27 2631.04 0.93 0.93 0 3.23 6.17

❖ 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:

❖ Model call:

```{r}
glmmTMB(formula = Time_RR ~ Condition * Stage + ar1(Stage + 0 | 
    Mouse), data = data, family = Gamma("log"), control = glmmTMBControl(optimizer = optim, 
    optArgs = list(method = "BFGS")), REML = TRUE, start = list(beta = c(I(mean(data$Time_RR)), 
    rep(0, 19))), ziformula = ~0, dispformula = ~1)
```

❖ Performance:

performance::performance(mod)
AIC AICc BIC R2_conditional R2_marginal ICC RMSE Sigma
2248.85 2252.46 2336.23 1.00 1.00 0 0.01 0.02
AIC AICc BIC R2_conditional R2_marginal ICC RMSE Sigma
2248.85 2252.46 2336.23 1.00 1.00 0 0.01 0.02

❖ 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:

15.2.3 Effects Analysis

```{r}
glmmTMB(formula = Time_RR ~ Condition * Stage + ar1(Stage + 0 | 
    Mouse), data = data, family = gaussian("identity"), REML = TRUE, 
    start = list(beta = c(I(mean(data$Time_RR)), rep(0, 19))), 
    ziformula = ~0, dispformula = ~1)
```

15.2.3.1 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) 25.757 0.996 (23.80, 27.71) 25.857 < .001
Condition1 -3.966 0.996 (-5.92, -2.01) -3.981 < .001
Stage1 26.049 2.075 (21.98, 30.12) 12.556 < .001
Stage2 30.164 1.992 (26.26, 34.07) 15.144 < .001
Stage3 29.032 1.954 (25.20, 32.86) 14.860 < .001
Stage4 11.348 1.937 (7.55, 15.14) 5.859 < .001
Stage5 -3.168 1.930 (-6.95, 0.62) -1.641 0.101
Stage6 -4.449 1.930 (-8.23, -0.67) -2.305 0.021 *
Stage7 -19.221 1.937 (-23.02, -15.42) -9.924 < .001
Stage8 -22.203 1.954 (-26.03, -18.37) -11.365 < .001
Stage9 -23.840 1.992 (-27.74, -19.94) -11.969 < .001
Condition1 * Stage1 5.771 2.075 (1.71, 9.84) 2.782 0.005 **
Condition1 * Stage2 3.100 1.992 (-0.80, 7.00) 1.556 0.120
Condition1 * Stage3 3.121 1.954 (-0.71, 6.95) 1.598 0.110
Condition1 * Stage4 -1.463 1.937 (-5.26, 2.33) -0.755 0.450
Condition1 * Stage5 -9.312 1.930 (-13.10, -5.53) -4.824 < .001
Condition1 * Stage6 -12.430 1.930 (-16.21, -8.65) -6.439 < .001
Condition1 * Stage7 1.934 1.937 (-1.86, 5.73) 0.999 0.318
Condition1 * Stage8 2.541 1.954 (-1.29, 6.37) 1.301 0.193
Condition1 * Stage9 3.345 1.992 (-0.56, 7.25) 1.679 0.093
Model: Time_RR ~ Condition * Stage (330 Observations)
Parameter Coefficient SE 95% CI z p
(Intercept) 25.757 0.996 (23.80, 27.71) 25.857 < .001
Condition1 -3.966 0.996 (-5.92, -2.01) -3.981 < .001
Stage1 26.049 2.075 (21.98, 30.12) 12.556 < .001
Stage2 30.164 1.992 (26.26, 34.07) 15.144 < .001
Stage3 29.032 1.954 (25.20, 32.86) 14.860 < .001
Stage4 11.348 1.937 (7.55, 15.14) 5.859 < .001
Stage5 -3.168 1.930 (-6.95, 0.62) -1.641 0.101
Stage6 -4.449 1.930 (-8.23, -0.67) -2.305 0.021 *
Stage7 -19.221 1.937 (-23.02, -15.42) -9.924 < .001
Stage8 -22.203 1.954 (-26.03, -18.37) -11.365 < .001
Stage9 -23.840 1.992 (-27.74, -19.94) -11.969 < .001
Condition1 * Stage1 5.771 2.075 (1.71, 9.84) 2.782 0.005 **
Condition1 * Stage2 3.100 1.992 (-0.80, 7.00) 1.556 0.120
Condition1 * Stage3 3.121 1.954 (-0.71, 6.95) 1.598 0.110
Condition1 * Stage4 -1.463 1.937 (-5.26, 2.33) -0.755 0.450
Condition1 * Stage5 -9.312 1.930 (-13.10, -5.53) -4.824 < .001
Condition1 * Stage6 -12.430 1.930 (-16.21, -8.65) -6.439 < .001
Condition1 * Stage7 1.934 1.937 (-1.86, 5.73) 0.999 0.318
Condition1 * Stage8 2.541 1.954 (-1.29, 6.37) 1.301 0.193
Condition1 * Stage9 3.345 1.992 (-0.56, 7.25) 1.679 0.093
Model: Time_RR ~ Condition * Stage (330 Observations)

❖ Main effects (Wald Chi-Square):

car::Anova(mod, type = 3)
term statistic df p.value
Condition 15.85 1 <0.001 ***
Stage 575.21 9 <0.001 ***
Condition:Stage 61.41 9 <0.001 ***
term statistic df p.value
Condition 15.85 1 <0.001 ***
Stage 575.21 9 <0.001 ***
Condition:Stage 61.41 9 <0.001 ***

❖ Main effects (Likelihood Ratio Test):

LRT(mod, pred = "Condition")
model df aic bic log_lik deviance chisq chi_df pr_chisq
mod_reduced 13 2647.81 2697.20 -1310.90 2621.81
mod_full 23 2600.01 2687.39 -1277.00 2554.01 67.80 10 <0.001 ***
model df aic bic log_lik deviance chisq chi_df pr_chisq
mod_reduced 13 2647.81 2697.20 -1310.90 2621.81
mod_full 23 2600.01 2687.39 -1277.00 2554.01 67.80 10 <0.001 ***
Important

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

15.2.3.2 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 21.791 1.343 327 19.149 24.433
IH 29.722 1.471 327 26.828 32.617
Condition emmean SE df lower.CL upper.CL
N 21.791 1.343 327 19.149 24.433
IH 29.722 1.471 327 26.828 32.617 
- Results are averaged over the levels of: Stage
- Confidence level used: 0.95

❖ Contrasts:

emmeans(mod, specs = pred, type = "response") |> 
  contrast(method = "consec", adjust = "none", infer = TRUE)
contrast estimate SE df lower.CL upper.CL t.ratio p.value
IH - N 7.931 1.992 327 4.012 11.851 3.981 <0.001 ***
contrast estimate SE df lower.CL upper.CL t.ratio p.value
IH - N 7.931 1.992 327 4.012 11.851 3.981 <0.001 *** 
- Results are averaged over the levels of: Stage
- Confidence level used: 0.95

❖ Boxplot:

❖ Marginal Means:

emmeans(mod, specs = pred, type = "response")
Stage emmean SE df lower.CL upper.CL
P2 51.806 2.215 327 47.448 56.163
P3 55.921 2.215 327 51.564 60.278
P4 54.789 2.215 327 50.432 59.146
P5 37.104 2.215 327 32.747 41.462
P6 22.589 2.215 327 18.232 26.946
P7 21.308 2.215 327 16.951 25.665
P8 6.536 2.215 327 2.179 10.893
P9 3.554 2.215 327 −0.803 7.911
P10 1.916 2.215 327 −2.441 6.274
P11 2.044 2.215 327 −2.313 6.401
Stage emmean SE df lower.CL upper.CL
P2 51.806 2.215 327 47.448 56.163
P3 55.921 2.215 327 51.564 60.278
P4 54.789 2.215 327 50.432 59.146
P5 37.104 2.215 327 32.747 41.462
P6 22.589 2.215 327 18.232 26.946
P7 21.308 2.215 327 16.951 25.665
P8 6.536 2.215 327 2.179 10.893
P9 3.554 2.215 327 −0.803 7.911
P10 1.916 2.215 327 −2.441 6.274
P11 2.044 2.215 327 −2.313 6.401 
- Results are averaged over the levels of: Condition
- Confidence level used: 0.95

❖ Contrasts:

emmeans(mod, specs = pred, type = "response") |> 
  contrast(method = "consec", adjust = "none", infer = TRUE)
contrast estimate SE df lower.CL upper.CL t.ratio p.value
P3 - P2 4.116 2.538 327 −0.877 9.108 1.622 0.106
P4 - P3 −1.132 2.538 327 −6.124 3.86 −0.446 0.656
P5 - P4 −17.684 2.538 327 −22.677 −12.692 −6.969 <0.001 ***
P6 - P5 −14.516 2.538 327 −19.508 −9.523 −5.72 <0.001 ***
P7 - P6 −1.281 2.538 327 −6.273 3.711 −0.505 0.614
P8 - P7 −14.772 2.538 327 −19.764 −9.78 −5.821 <0.001 ***
P9 - P8 −2.982 2.538 327 −7.974 2.011 −1.175 0.241
P10 - P9 −1.638 2.538 327 −6.63 3.355 −0.645 0.519
P11 - P10 0.127 2.538 327 −4.865 5.119 0.05 0.960
contrast estimate SE df lower.CL upper.CL t.ratio p.value
P3 - P2 4.116 2.538 327 −0.877 9.108 1.622 0.106
P4 - P3 −1.132 2.538 327 −6.124 3.86 −0.446 0.656
P5 - P4 −17.684 2.538 327 −22.677 −12.692 −6.969 <0.001 ***
P6 - P5 −14.516 2.538 327 −19.508 −9.523 −5.72 <0.001 ***
P7 - P6 −1.281 2.538 327 −6.273 3.711 −0.505 0.614
P8 - P7 −14.772 2.538 327 −19.764 −9.78 −5.821 <0.001 ***
P9 - P8 −2.982 2.538 327 −7.974 2.011 −1.175 0.241
P10 - P9 −1.638 2.538 327 −6.63 3.355 −0.645 0.519
P11 - P10 0.127 2.538 327 −4.865 5.119 0.05 0.960 
- Results are averaged over the levels of: Condition
- Confidence level used: 0.95

❖ Boxplot:

❖ Marginal Means:

emmeans(mod, specs = emmeans_formula, type = "response")
Condition emmean SE df lower.CL upper.CL
N 53.611 2.986 327 47.736 59.486
IH 50 3.272 327 43.564 56.436
Condition emmean SE df lower.CL upper.CL
N 53.611 2.986 327 47.736 59.486
IH 50 3.272 327 43.564 56.436
Condition emmean SE df lower.CL upper.CL
N 55.056 2.986 327 49.18 60.931
IH 56.787 3.272 327 50.351 63.223
Condition emmean SE df lower.CL upper.CL
N 55.056 2.986 327 49.18 60.931
IH 56.787 3.272 327 50.351 63.223
Condition emmean SE df lower.CL upper.CL
N 53.944 2.986 327 48.069 59.82
IH 55.633 3.272 327 49.197 62.069
Condition emmean SE df lower.CL upper.CL
N 53.944 2.986 327 48.069 59.82
IH 55.633 3.272 327 49.197 62.069
Condition emmean SE df lower.CL upper.CL
N 31.676 2.986 327 25.8 37.551
IH 42.533 3.272 327 36.097 48.969
Condition emmean SE df lower.CL upper.CL
N 31.676 2.986 327 25.8 37.551
IH 42.533 3.272 327 36.097 48.969
Condition emmean SE df lower.CL upper.CL
N 9.311 2.986 327 3.436 15.186
IH 35.867 3.272 327 29.431 42.303
Condition emmean SE df lower.CL upper.CL
N 9.311 2.986 327 3.436 15.186
IH 35.867 3.272 327 29.431 42.303
Condition emmean SE df lower.CL upper.CL
N 4.912 2.986 327 −0.963 10.787
IH 37.703 3.272 327 31.267 44.139
Condition emmean SE df lower.CL upper.CL
N 4.912 2.986 327 −0.963 10.787
IH 37.703 3.272 327 31.267 44.139
Condition emmean SE df lower.CL upper.CL
N 4.504 2.986 327 −1.371 10.379
IH 8.567 3.272 327 2.131 15.003
Condition emmean SE df lower.CL upper.CL
N 4.504 2.986 327 −1.371 10.379
IH 8.567 3.272 327 2.131 15.003
Condition emmean SE df lower.CL upper.CL
N 2.129 2.986 327 −3.746 8.005
IH 4.979 3.272 327 −1.457 11.415
Condition emmean SE df lower.CL upper.CL
N 2.129 2.986 327 −3.746 8.005
IH 4.979 3.272 327 −1.457 11.415
Condition emmean SE df lower.CL upper.CL
N 1.296 2.986 327 −4.58 7.171
IH 2.537 3.272 327 −3.899 8.973
Condition emmean SE df lower.CL upper.CL
N 1.296 2.986 327 −4.58 7.171
IH 2.537 3.272 327 −3.899 8.973
Condition emmean SE df lower.CL upper.CL
N 1.471 2.986 327 −4.404 7.346
IH 2.617 3.272 327 −3.819 9.053
Condition emmean SE df lower.CL upper.CL
N 1.471 2.986 327 −4.404 7.346
IH 2.617 3.272 327 −3.819 9.053 
- Confidence level used: 0.95

❖ Contrasts:

emmeans(mod, specs = emmeans_formula, type = "response") |> 
  contrast(method = "pairwise", adjust = "none", infer = TRUE)
contrast estimate SE df lower.CL upper.CL t.ratio p.value
N - IH 3.611 4.43 327 −5.103 12.325 0.815 0.416
contrast estimate SE df lower.CL upper.CL t.ratio p.value
N - IH 3.611 4.43 327 −5.103 12.325 0.815 0.416
contrast estimate SE df lower.CL upper.CL t.ratio p.value
N - IH −1.731 4.43 327 −10.445 6.983 −0.391 0.696
contrast estimate SE df lower.CL upper.CL t.ratio p.value
N - IH −1.731 4.43 327 −10.445 6.983 −0.391 0.696
contrast estimate SE df lower.CL upper.CL t.ratio p.value
N - IH −1.689 4.43 327 −10.403 7.025 −0.381 0.703
contrast estimate SE df lower.CL upper.CL t.ratio p.value
N - IH −1.689 4.43 327 −10.403 7.025 −0.381 0.703
contrast estimate SE df lower.CL upper.CL t.ratio p.value
N - IH −10.858 4.43 327 −19.572 −2.144 −2.451 0.015 *
contrast estimate SE df lower.CL upper.CL t.ratio p.value
N - IH −10.858 4.43 327 −19.572 −2.144 −2.451 0.015 *
contrast estimate SE df lower.CL upper.CL t.ratio p.value
N - IH −26.556 4.43 327 −35.27 −17.841 −5.995 <0.001 ***
contrast estimate SE df lower.CL upper.CL t.ratio p.value
N - IH −26.556 4.43 327 −35.27 −17.841 −5.995 <0.001 ***
contrast estimate SE df lower.CL upper.CL t.ratio p.value
N - IH −32.791 4.43 327 −41.506 −24.077 −7.403 <0.001 ***
contrast estimate SE df lower.CL upper.CL t.ratio p.value
N - IH −32.791 4.43 327 −41.506 −24.077 −7.403 <0.001 ***
contrast estimate SE df lower.CL upper.CL t.ratio p.value
N - IH −4.063 4.43 327 −12.778 4.651 −0.917 0.360
contrast estimate SE df lower.CL upper.CL t.ratio p.value
N - IH −4.063 4.43 327 −12.778 4.651 −0.917 0.360
contrast estimate SE df lower.CL upper.CL t.ratio p.value
N - IH −2.849 4.43 327 −11.563 5.865 −0.643 0.521
contrast estimate SE df lower.CL upper.CL t.ratio p.value
N - IH −2.849 4.43 327 −11.563 5.865 −0.643 0.521
contrast estimate SE df lower.CL upper.CL t.ratio p.value
N - IH −1.242 4.43 327 −9.956 7.472 −0.28 0.779
contrast estimate SE df lower.CL upper.CL t.ratio p.value
N - IH −1.242 4.43 327 −9.956 7.472 −0.28 0.779
contrast estimate SE df lower.CL upper.CL t.ratio p.value
N - IH −1.146 4.43 327 −9.86 7.568 −0.259 0.796
contrast estimate SE df lower.CL upper.CL t.ratio p.value
N - IH −1.146 4.43 327 −9.86 7.568 −0.259 0.796 
- Confidence level used: 0.95

❖ Temporal plot: