10 Calbindin [P12]
❖ Data
❖ Description
| Variable | Description |
|---|---|
| Mouse |
Mouse unique identifier |
| Condition |
Hypoxia condition: Normoxia (N) vs Intermittent Hypoxia (IH) |
| Z |
Bregma coordinates (Ant, Med, Post) |
| N_CC |
Number of Purkinje cell bodies (per 413x10^(3) µm^(3)) |
| A_ML |
Area of the ML (10^(-4) µm^(2)) |
| A_PC_per_cell |
Purkinje dendrite area (10^(-4) µm^(2)) per Purkinje cell body |
| Vol_PC_per_cell |
Purkinje dendrite volume (10^(-4) µm^(3)) per Purkinje cell body |
| Variable | Description |
|---|---|
| Mouse |
Mouse unique identifier |
| Condition |
Hypoxia condition: Normoxia (N) vs Intermittent Hypoxia (IH) |
| Z |
Bregma coordinates (Ant, Med, Post) |
| N_CC |
Number of Purkinje cell bodies (per 413x10^(3) µm^(3)) |
| A_ML |
Area of the ML (10^(-4) µm^(2)) |
| A_PC_per_cell |
Purkinje dendrite area (10^(-4) µm^(2)) per Purkinje cell body |
| Vol_PC_per_cell |
Purkinje dendrite volume (10^(-4) µm^(3)) per Purkinje cell body |
❖ Correlations
10.1 Number of Purkinje cell bodies
10.1.1 Data Exploration
❖ Distribution:
| Condition | Mean | SD | Variance | CoV | IQR | Min | Max | Skewness | Kurtosis | n |
|---|---|---|---|---|---|---|---|---|---|---|
| N | 7.963 | 2.361 | 5.575 | 0.297 | 3 | 5 | 13 | 0.956 | 0.057 | 27 |
| IH | 8.467 | 1.552 | 2.41 | 0.183 | 2 | 6 | 11 | −0.523 | −0.579 | 15 |
| Condition | Mean | SD | Variance | CoV | IQR | Min | Max | Skewness | Kurtosis | n |
|---|---|---|---|---|---|---|---|---|---|---|
| N | 7.963 | 2.361 | 5.575 | 0.297 | 3 | 5 | 13 | 0.956 | 0.057 | 27 |
| IH | 8.467 | 1.552 | 2.41 | 0.183 | 2 | 6 | 11 | −0.523 | −0.579 | 15 |
| Condition | Mean | SD | Variance | CoV | IQR | Min | Max | Skewness | Kurtosis | n |
|---|---|---|---|---|---|---|---|---|---|---|
| N | 7.935 | 1.982 | 3.929 | 0.25 | 3 | 5 | 14 | 0.836 | 1.503 | 31 |
| IH | 8.353 | 2.262 | 5.118 | 0.271 | 3 | 4 | 14 | 0.493 | 1.492 | 17 |
| Condition | Mean | SD | Variance | CoV | IQR | Min | Max | Skewness | Kurtosis | n |
|---|---|---|---|---|---|---|---|---|---|---|
| N | 7.935 | 1.982 | 3.929 | 0.25 | 3 | 5 | 14 | 0.836 | 1.503 | 31 |
| IH | 8.353 | 2.262 | 5.118 | 0.271 | 3 | 4 | 14 | 0.493 | 1.492 | 17 |
| Condition | Mean | SD | Variance | CoV | IQR | Min | Max | Skewness | Kurtosis | n |
|---|---|---|---|---|---|---|---|---|---|---|
| N | 7.818 | 1.911 | 3.653 | 0.244 | 2.5 | 5 | 13 | 0.533 | 0.211 | 33 |
| IH | 9.148 | 1.955 | 3.823 | 0.214 | 4 | 6 | 12 | 0.043 | −1.277 | 27 |
| Condition | Mean | SD | Variance | CoV | IQR | Min | Max | Skewness | Kurtosis | n |
|---|---|---|---|---|---|---|---|---|---|---|
| N | 7.818 | 1.911 | 3.653 | 0.244 | 2.5 | 5 | 13 | 0.533 | 0.211 | 33 |
| IH | 9.148 | 1.955 | 3.823 | 0.214 | 4 | 6 | 12 | 0.043 | −1.277 | 27 |
10.1.2 Models & Diagnostics
Exploring some Generalized Linear (Mixed) model candidates:
❖ Model call:
```{r}
glmmTMB(formula = N_CC ~ Condition * Z + (1 | Mouse), data = data,
family = genpois("log"), REML = TRUE, ziformula = ~0, dispformula = ~1)
```❖ Performance:
performance::performance(mod)| AIC | AICc | BIC | R2_conditional | R2_marginal | ICC | RMSE | Sigma | Score_log | Score_spherical |
|---|---|---|---|---|---|---|---|---|---|
| 671.02 | 672.05 | 695.11 | 0.18 | 0.02 | 0.16 | 1.80 | 0.46 | -2.16 | 0.08 |
| AIC | AICc | BIC | R2_conditional | R2_marginal | ICC | RMSE | Sigma | Score_log | Score_spherical |
|---|---|---|---|---|---|---|---|---|---|
| 671.02 | 672.05 | 695.11 | 0.18 | 0.02 | 0.16 | 1.80 | 0.46 | -2.16 | 0.08 |
❖ Residuals:
performance::check_model(
mod, panel = FALSE,
check = c("pp_check", "qq", "reqq", "linearity", "homogeneity")
)
performance::check_overdispersion(mod)# Overdispersion test
dispersion ratio = 0.875
Pearson's Chi-Squared = 129.432
p-value = 0.862❖ 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 = N_CC ~ Condition * Z + (1 | Mouse), data = data,
family = nbinom2("log"), REML = TRUE, start = list(beta = c(I(mean(data$N_CC)),
rep(0, 5))), ziformula = ~0, dispformula = ~1)
```❖ Performance:
performance::performance(mod)| AIC | AICc | BIC | R2_conditional | R2_marginal | ICC | RMSE | Sigma | Score_log | Score_spherical |
|---|---|---|---|---|---|---|---|---|---|
| 1 | 0.32 | 1 | 1.86 | 4.29e+07 | -2.96 | 0.08 | |||
| AIC | AICc | BIC | R2_conditional | R2_marginal | ICC | RMSE | Sigma | Score_log | Score_spherical |
|---|---|---|---|---|---|---|---|---|---|
| 1 | 0.32 | 1 | 1.86 | 4.29e+07 | -2.96 | 0.08 | |||
❖ Residuals:
performance::check_model(
mod, panel = FALSE,
check = c("pp_check", "qq", "reqq", "linearity", "homogeneity")
)
performance::check_overdispersion(mod)# Overdispersion test
dispersion ratio = 0.431
Pearson's Chi-Squared = 63.832
p-value = 1❖ 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.❖ Model call:
```{r}
glmmTMB(formula = N_CC ~ Condition * Z + (1 | Mouse), data = data,
family = poisson("log"), REML = TRUE, ziformula = ~0, dispformula = ~1)
```❖ Performance:
performance::performance(mod)| AIC | AICc | BIC | R2_conditional | R2_marginal | ICC | RMSE | Sigma | Score_log | Score_spherical |
|---|---|---|---|---|---|---|---|---|---|
| 703.73 | 704.52 | 724.80 | 0.07 | 0.02 | 0.05 | 1.86 | 1 | -2.18 | 0.08 |
| AIC | AICc | BIC | R2_conditional | R2_marginal | ICC | RMSE | Sigma | Score_log | Score_spherical |
|---|---|---|---|---|---|---|---|---|---|
| 703.73 | 704.52 | 724.80 | 0.07 | 0.02 | 0.05 | 1.86 | 1 | -2.18 | 0.08 |
❖ Residuals:
performance::check_model(
mod, panel = FALSE,
check = c("pp_check", "qq", "reqq", "linearity", "homogeneity")
)
performance::check_overdispersion(mod)# Overdispersion test
dispersion ratio = 0.428
Pearson's Chi-Squared = 63.832
p-value = 1❖ 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.10.1.3 Effects Analysis
Chosen model: Genpois (‘log’)
```{r}
glmmTMB(formula = N_CC ~ Condition * Z + (1 | Mouse), data = data,
family = genpois("log"), REML = TRUE, ziformula = ~0, dispformula = ~1)
```10.1.3.1 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) | 8.138 | 0.304 | (7.56, 8.76) | 56.038 | < .001 |
| Condition1 | 0.971 | 0.036 | (0.90, 1.04) | -0.800 | 0.424 |
| Z1 | 1.008 | 0.033 | (0.95, 1.07) | 0.238 | 0.811 |
| Z2 | 0.977 | 0.029 | (0.92, 1.04) | -0.793 | 0.428 |
| Condition1 * Z1 | 1.001 | 0.033 | (0.94, 1.07) | 0.033 | 0.974 |
| Condition1 * Z2 | 1.022 | 0.030 | (0.96, 1.08) | 0.742 | 0.458 |
| Model: N_CC ~ Condition * Z (150 Observations) | |||||
| Parameter | Coefficient | SE | 95% CI | z | p |
|---|---|---|---|---|---|
| (Intercept) | 8.138 | 0.304 | (7.56, 8.76) | 56.038 | < .001 |
| Condition1 | 0.971 | 0.036 | (0.90, 1.04) | -0.800 | 0.424 |
| Z1 | 1.008 | 0.033 | (0.95, 1.07) | 0.238 | 0.811 |
| Z2 | 0.977 | 0.029 | (0.92, 1.04) | -0.793 | 0.428 |
| Condition1 * Z1 | 1.001 | 0.033 | (0.94, 1.07) | 0.033 | 0.974 |
| Condition1 * Z2 | 1.022 | 0.030 | (0.96, 1.08) | 0.742 | 0.458 |
| Model: N_CC ~ Condition * Z (150 Observations) | |||||
❖ Main effects (Wald Chi-Square):
car::Anova(mod, type = 3)| term | statistic | df | p.value |
|---|---|---|---|
| Condition | 0.64 | 1 | 0.420 |
| Z | 0.72 | 2 | 0.700 |
| Condition:Z | 0.92 | 2 | 0.630 |
| term | statistic | df | p.value |
|---|---|---|---|
| Condition | 0.64 | 1 | 0.420 |
| Z | 0.72 | 2 | 0.700 |
| Condition:Z | 0.92 | 2 | 0.630 |
❖ Main effects (Likelihood Ratio Test):
LRT(mod, pred = "Condition")| model | df | aic | bic | log_lik | deviance | chisq | chi_df | pr_chisq |
|---|---|---|---|---|---|---|---|---|
| mod_reduced | 5 | 635.64 | 650.69 | -312.82 | 625.64 | |||
| mod_full | 8 | 639.71 | 663.80 | -311.86 | 623.71 | 1.93 | 3 | 0.590 |
| model | df | aic | bic | log_lik | deviance | chisq | chi_df | pr_chisq |
|---|---|---|---|---|---|---|---|---|
| mod_reduced | 5 | 635.64 | 650.69 | -312.82 | 625.64 | |||
| mod_full | 8 | 639.71 | 663.80 | -311.86 | 623.71 | 1.93 | 3 | 0.590 |
Important
Our LRT() method removes the predictor plus all its interactions
10.1.3.2 Marginal Effects
Marginal means & Contrasts for each predictor:
❖ Marginal Means:
emmeans(mod, specs = pred, type = "response")| Condition | response | SE | df | lower.CL | upper.CL |
|---|---|---|---|---|---|
| N | 7.898 | 0.385 | 148 | 7.173 | 8.697 |
| IH | 8.384 | 0.475 | 148 | 7.496 | 9.378 |
| Condition | response | SE | df | lower.CL | upper.CL |
|---|---|---|---|---|---|
| N | 7.898 | 0.385 | 148 | 7.173 | 8.697 |
| IH | 8.384 | 0.475 | 148 | 7.496 | 9.378 |
- Results are averaged over the levels of: Z
- Confidence level used: 0.95
- Intervals are back-transformed from the log scale❖ Contrasts:
emmeans(mod, specs = pred, type = "response") |>
contrast(method = "pairwise", adjust = "none", infer = TRUE)| contrast | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 0.942 | 0.07 | 148 | 0.813 | 1.092 | 1 | −0.8 | 0.425 |
| contrast | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 0.942 | 0.07 | 148 | 0.813 | 1.092 | 1 | −0.8 | 0.425 |
- Results are averaged over the levels of: Z
- Confidence level used: 0.95
- Intervals are back-transformed from the log scale
- Tests are performed on the log scale❖ Boxplot:
❖ Marginal Means:
emmeans(mod, specs = pred, type = "response")| Z | response | SE | df | lower.CL | upper.CL |
|---|---|---|---|---|---|
| Ant | 8.201 | 0.419 | 148 | 7.414 | 9.072 |
| Med | 7.947 | 0.388 | 148 | 7.217 | 8.752 |
| Post | 8.268 | 0.364 | 148 | 7.579 | 9.019 |
| Z | response | SE | df | lower.CL | upper.CL |
|---|---|---|---|---|---|
| Ant | 8.201 | 0.419 | 148 | 7.414 | 9.072 |
| Med | 7.947 | 0.388 | 148 | 7.217 | 8.752 |
| Post | 8.268 | 0.364 | 148 | 7.579 | 9.019 |
- Results are averaged over the levels of: Condition
- Confidence level used: 0.95
- Intervals are back-transformed from the log scale❖ Contrasts:
emmeans(mod, specs = pred, type = "response") |>
contrast(method = "pairwise", adjust = "none", infer = TRUE)| contrast | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| Ant / Med | 1.032 | 0.058 | 148 | 0.924 | 1.153 | 1 | 0.561 | 0.576 |
| Ant / Post | 0.992 | 0.052 | 148 | 0.894 | 1.101 | 1 | −0.154 | 0.878 |
| Med / Post | 0.961 | 0.046 | 148 | 0.875 | 1.056 | 1 | −0.832 | 0.407 |
| contrast | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| Ant / Med | 1.032 | 0.058 | 148 | 0.924 | 1.153 | 1 | 0.561 | 0.576 |
| Ant / Post | 0.992 | 0.052 | 148 | 0.894 | 1.101 | 1 | −0.154 | 0.878 |
| Med / Post | 0.961 | 0.046 | 148 | 0.875 | 1.056 | 1 | −0.832 | 0.407 |
- Results are averaged over the levels of: Condition
- Confidence level used: 0.95
- Intervals are back-transformed from the log scale
- Tests are performed on the log scale❖ Boxplot:
❖ Marginal Means:
emmeans(mod, specs = emmeans_formula, type = "response")| Condition | response | SE | df | lower.CL | upper.CL |
|---|---|---|---|---|---|
| N | 7.969 | 0.508 | 148 | 7.025 | 9.039 |
| IH | 8.441 | 0.674 | 148 | 7.209 | 9.883 |
| Condition | response | SE | df | lower.CL | upper.CL |
|---|---|---|---|---|---|
| N | 7.969 | 0.508 | 148 | 7.025 | 9.039 |
| IH | 8.441 | 0.674 | 148 | 7.209 | 9.883 |
| Condition | response | SE | df | lower.CL | upper.CL |
|---|---|---|---|---|---|
| N | 7.886 | 0.476 | 148 | 7 | 8.885 |
| IH | 8.009 | 0.612 | 148 | 6.886 | 9.315 |
| Condition | response | SE | df | lower.CL | upper.CL |
|---|---|---|---|---|---|
| N | 7.886 | 0.476 | 148 | 7 | 8.885 |
| IH | 8.009 | 0.612 | 148 | 6.886 | 9.315 |
| Condition | response | SE | df | lower.CL | upper.CL |
|---|---|---|---|---|---|
| N | 7.841 | 0.467 | 148 | 6.97 | 8.82 |
| IH | 8.719 | 0.567 | 148 | 7.667 | 9.914 |
| Condition | response | SE | df | lower.CL | upper.CL |
|---|---|---|---|---|---|
| N | 7.841 | 0.467 | 148 | 6.97 | 8.82 |
| IH | 8.719 | 0.567 | 148 | 7.667 | 9.914 |
- Confidence level used: 0.95
- Intervals are back-transformed from the log scale❖ Contrasts:
emmeans(mod, specs = emmeans_formula, type = "response") |>
contrast(method = "pairwise", adjust = "none", infer = TRUE)| contrast | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 0.944 | 0.097 | 148 | 0.771 | 1.155 | 1 | −0.563 | 0.574 |
| contrast | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 0.944 | 0.097 | 148 | 0.771 | 1.155 | 1 | −0.563 | 0.574 |
| contrast | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 0.985 | 0.096 | 148 | 0.813 | 1.193 | 1 | −0.159 | 0.874 |
| contrast | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 0.985 | 0.096 | 148 | 0.813 | 1.193 | 1 | −0.159 | 0.874 |
| contrast | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 0.899 | 0.079 | 148 | 0.755 | 1.071 | 1 | −1.202 | 0.231 |
| contrast | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 0.899 | 0.079 | 148 | 0.755 | 1.071 | 1 | −1.202 | 0.231 |
- Confidence level used: 0.95
- Intervals are back-transformed from the log scale
- Tests are performed on the log scaleemmeans(mod, specs = emmeans_formula, type = "response") |>
contrast(interaction = "pairwise", by = NULL, adjust = "none", infer = T)| Condition | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 0.959 | 0.108 | 148 | 0.768 | 1.197 | 1 | −0.375 | 0.708 |
| Condition | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 0.959 | 0.108 | 148 | 0.768 | 1.197 | 1 | −0.375 | 0.708 |
| Condition | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 1.05 | 0.112 | 148 | 0.851 | 1.295 | 1 | 0.457 | 0.648 |
| Condition | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 1.05 | 0.112 | 148 | 0.851 | 1.295 | 1 | 0.457 | 0.648 |
| Condition | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 1.095 | 0.104 | 148 | 0.908 | 1.321 | 1 | 0.956 | 0.341 |
| Condition | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 1.095 | 0.104 | 148 | 0.908 | 1.321 | 1 | 0.956 | 0.341 |
- Confidence level used: 0.95
- Intervals are back-transformed from the log scale
- Tests are performed on the log scale❖ Boxplot:
10.2 Area of the ML
10.2.1 Data Exploration
❖ Distribution:
| Condition | Mean | SD | Variance | CoV | IQR | Min | Max | Skewness | Kurtosis | n |
|---|---|---|---|---|---|---|---|---|---|---|
| N | 196.676 | 46.254 | 2,139.45 | 0.235 | 65.741 | 74.138 | 316.416 | 0.11 | 1.833 | 27 |
| IH | 131.386 | 33.031 | 1,091.052 | 0.251 | 36.045 | 89.907 | 194.97 | 0.963 | −0.13 | 15 |
| Condition | Mean | SD | Variance | CoV | IQR | Min | Max | Skewness | Kurtosis | n |
|---|---|---|---|---|---|---|---|---|---|---|
| N | 196.676 | 46.254 | 2,139.45 | 0.235 | 65.741 | 74.138 | 316.416 | 0.11 | 1.833 | 27 |
| IH | 131.386 | 33.031 | 1,091.052 | 0.251 | 36.045 | 89.907 | 194.97 | 0.963 | −0.13 | 15 |
| Condition | Mean | SD | Variance | CoV | IQR | Min | Max | Skewness | Kurtosis | n |
|---|---|---|---|---|---|---|---|---|---|---|
| N | 175.21 | 40.098 | 1,607.841 | 0.229 | 55.706 | 111.411 | 282.624 | 0.974 | 0.679 | 31 |
| IH | 135.674 | 42.169 | 1,778.228 | 0.311 | 63.795 | 72.909 | 211.968 | 0.165 | −0.739 | 17 |
| Condition | Mean | SD | Variance | CoV | IQR | Min | Max | Skewness | Kurtosis | n |
|---|---|---|---|---|---|---|---|---|---|---|
| N | 175.21 | 40.098 | 1,607.841 | 0.229 | 55.706 | 111.411 | 282.624 | 0.974 | 0.679 | 31 |
| IH | 135.674 | 42.169 | 1,778.228 | 0.311 | 63.795 | 72.909 | 211.968 | 0.165 | −0.739 | 17 |
| Condition | Mean | SD | Variance | CoV | IQR | Min | Max | Skewness | Kurtosis | n |
|---|---|---|---|---|---|---|---|---|---|---|
| N | 204.881 | 46.349 | 2,148.231 | 0.226 | 62.157 | 132.096 | 308.838 | 0.494 | −0.152 | 33 |
| IH | 204.747 | 66.127 | 4,372.741 | 0.323 | 105.882 | 76.8 | 322.56 | −0.183 | −0.659 | 27 |
| Condition | Mean | SD | Variance | CoV | IQR | Min | Max | Skewness | Kurtosis | n |
|---|---|---|---|---|---|---|---|---|---|---|
| N | 204.881 | 46.349 | 2,148.231 | 0.226 | 62.157 | 132.096 | 308.838 | 0.494 | −0.152 | 33 |
| IH | 204.747 | 66.127 | 4,372.741 | 0.323 | 105.882 | 76.8 | 322.56 | −0.183 | −0.659 | 27 |
10.2.2 Models & Diagnostics
Exploring some Generalized Linear (Mixed) model candidates:
❖ Model call:
```{r}
glmmTMB(formula = A_ML ~ Condition * Z + (1 | Mouse), data = data,
family = Gamma("log"), REML = TRUE, ziformula = ~0, dispformula = ~1)
```❖ Performance:
performance::performance(mod)| AIC | AICc | BIC | R2_conditional | R2_marginal | ICC | RMSE | Sigma |
|---|---|---|---|---|---|---|---|
| 1582.63 | 1583.65 | 1606.71 | 0.59 | 0.17 | 0.51 | 37.82 | 0.22 |
| AIC | AICc | BIC | R2_conditional | R2_marginal | ICC | RMSE | Sigma |
|---|---|---|---|---|---|---|---|
| 1582.63 | 1583.65 | 1606.71 | 0.59 | 0.17 | 0.51 | 37.82 | 0.22 |
❖ 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 = A_ML ~ Condition * Z + (1 | Mouse), data = data,
family = gaussian("log"), REML = TRUE, ziformula = ~0, dispformula = ~1)
```❖ Performance:
performance::performance(mod)| AIC | AICc | BIC | R2_conditional | R2_marginal | ICC | RMSE | Sigma |
|---|---|---|---|---|---|---|---|
| 1596.85 | 1597.87 | 1620.93 | 3.97e-05 | 1.22e-05 | 2.75e-05 | 37.82 | 39.72 |
| AIC | AICc | BIC | R2_conditional | R2_marginal | ICC | RMSE | Sigma |
|---|---|---|---|---|---|---|---|
| 1596.85 | 1597.87 | 1620.93 | 3.97e-05 | 1.22e-05 | 2.75e-05 | 37.82 | 39.72 |
❖ 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:
10.2.3 Effects Analysis
Chosen model: Gamma (‘log’)
```{r}
glmmTMB(formula = A_ML ~ Condition * Z + (1 | Mouse), data = data,
family = Gamma("log"), REML = TRUE, ziformula = ~0, dispformula = ~1)
```10.2.3.1 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) | 171.679 | 11.832 | (149.99, 196.51) | 74.661 | < .001 |
| Condition1 | 1.117 | 0.077 | (0.98, 1.28) | 1.599 | 0.110 |
| Z1 | 1.011 | 0.031 | (0.95, 1.07) | 0.343 | 0.732 |
| Z2 | 0.879 | 0.025 | (0.83, 0.93) | -4.586 | < .001 |
| Condition1 * Z1 | 1.003 | 0.031 | (0.94, 1.07) | 0.100 | 0.921 |
| Condition1 * Z2 | 1.041 | 0.029 | (0.99, 1.10) | 1.437 | 0.151 |
| Model: A_ML ~ Condition * Z (150 Observations) | |||||
| Parameter | Coefficient | SE | 95% CI | z | p |
|---|---|---|---|---|---|
| (Intercept) | 171.679 | 11.832 | (149.99, 196.51) | 74.661 | < .001 |
| Condition1 | 1.117 | 0.077 | (0.98, 1.28) | 1.599 | 0.110 |
| Z1 | 1.011 | 0.031 | (0.95, 1.07) | 0.343 | 0.732 |
| Z2 | 0.879 | 0.025 | (0.83, 0.93) | -4.586 | < .001 |
| Condition1 * Z1 | 1.003 | 0.031 | (0.94, 1.07) | 0.100 | 0.921 |
| Condition1 * Z2 | 1.041 | 0.029 | (0.99, 1.10) | 1.437 | 0.151 |
| Model: A_ML ~ Condition * Z (150 Observations) | |||||
❖ Main effects (Wald Chi-Square):
car::Anova(mod, type = 3)| term | statistic | df | p.value |
|---|---|---|---|
| Condition | 2.56 | 1 | 0.110 |
| Z | 29.91 | 2 | <0.001 *** |
| Condition:Z | 3.48 | 2 | 0.180 |
| term | statistic | df | p.value |
|---|---|---|---|
| Condition | 2.56 | 1 | 0.110 |
| Z | 29.91 | 2 | <0.001 *** |
| Condition:Z | 3.48 | 2 | 0.180 |
❖ Main effects (Likelihood Ratio Test):
LRT(mod, pred = "Condition")| model | df | aic | bic | log_lik | deviance | chisq | chi_df | pr_chisq |
|---|---|---|---|---|---|---|---|---|
| mod_reduced | 5 | 1553.34 | 1568.39 | -771.67 | 1543.34 | |||
| mod_full | 8 | 1553.34 | 1577.42 | -768.67 | 1537.34 | 6.00 | 3 | 0.110 |
| model | df | aic | bic | log_lik | deviance | chisq | chi_df | pr_chisq |
|---|---|---|---|---|---|---|---|---|
| mod_reduced | 5 | 1553.34 | 1568.39 | -771.67 | 1543.34 | |||
| mod_full | 8 | 1553.34 | 1577.42 | -768.67 | 1537.34 | 6.00 | 3 | 0.110 |
Important
Our LRT() method removes the predictor plus all its interactions
10.2.3.2 Marginal Effects
Marginal means & Contrasts for each predictor:
❖ Marginal Means:
emmeans(mod, specs = pred, type = "response")| Condition | response | SE | df | lower.CL | upper.CL |
|---|---|---|---|---|---|
| N | 191.682 | 17.647 | 148 | 159.797 | 229.928 |
| IH | 153.763 | 15.774 | 148 | 125.549 | 188.318 |
| Condition | response | SE | df | lower.CL | upper.CL |
|---|---|---|---|---|---|
| N | 191.682 | 17.647 | 148 | 159.797 | 229.928 |
| IH | 153.763 | 15.774 | 148 | 125.549 | 188.318 |
- Results are averaged over the levels of: Z
- Confidence level used: 0.95
- Intervals are back-transformed from the log scale❖ Contrasts:
emmeans(mod, specs = pred, type = "response") |>
contrast(method = "pairwise", adjust = "none", infer = TRUE)| contrast | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 1.247 | 0.172 | 148 | 0.949 | 1.637 | 1 | 1.599 | 0.112 |
| contrast | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 1.247 | 0.172 | 148 | 0.949 | 1.637 | 1 | 1.599 | 0.112 |
- Results are averaged over the levels of: Z
- Confidence level used: 0.95
- Intervals are back-transformed from the log scale
- Tests are performed on the log scale❖ Boxplot:
❖ Marginal Means:
emmeans(mod, specs = pred, type = "response")| Z | response | SE | df | lower.CL | upper.CL |
|---|---|---|---|---|---|
| Ant | 173.521 | 13.316 | 148 | 149.104 | 201.936 |
| Med | 150.966 | 11.297 | 148 | 130.214 | 175.025 |
| Post | 193.16 | 13.966 | 148 | 167.442 | 222.829 |
| Z | response | SE | df | lower.CL | upper.CL |
|---|---|---|---|---|---|
| Ant | 173.521 | 13.316 | 148 | 149.104 | 201.936 |
| Med | 150.966 | 11.297 | 148 | 130.214 | 175.025 |
| Post | 193.16 | 13.966 | 148 | 167.442 | 222.829 |
- Results are averaged over the levels of: Condition
- Confidence level used: 0.95
- Intervals are back-transformed from the log scale❖ Contrasts:
emmeans(mod, specs = pred, type = "response") |>
contrast(method = "pairwise", adjust = "none", infer = TRUE)| contrast | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| Ant / Med | 1.149 | 0.061 | 148 | 1.035 | 1.276 | 1 | 2.634 | 0.009 ** |
| Ant / Post | 0.898 | 0.046 | 148 | 0.813 | 0.993 | 1 | −2.112 | 0.036 * |
| Med / Post | 0.782 | 0.035 | 148 | 0.715 | 0.854 | 1 | −5.469 | <0.001 *** |
| contrast | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| Ant / Med | 1.149 | 0.061 | 148 | 1.035 | 1.276 | 1 | 2.634 | 0.009 ** |
| Ant / Post | 0.898 | 0.046 | 148 | 0.813 | 0.993 | 1 | −2.112 | 0.036 * |
| Med / Post | 0.782 | 0.035 | 148 | 0.715 | 0.854 | 1 | −5.469 | <0.001 *** |
- Results are averaged over the levels of: Condition
- Confidence level used: 0.95
- Intervals are back-transformed from the log scale
- Tests are performed on the log scale❖ Boxplot:
❖ Marginal Means:
emmeans(mod, specs = emmeans_formula, type = "response")| Condition | response | SE | df | lower.CL | upper.CL |
|---|---|---|---|---|---|
| N | 194.342 | 19.329 | 148 | 159.664 | 236.551 |
| IH | 154.931 | 18.117 | 148 | 122.965 | 195.206 |
| Condition | response | SE | df | lower.CL | upper.CL |
|---|---|---|---|---|---|
| N | 194.342 | 19.329 | 148 | 159.664 | 236.551 |
| IH | 154.931 | 18.117 | 148 | 122.965 | 195.206 |
| Condition | response | SE | df | lower.CL | upper.CL |
|---|---|---|---|---|---|
| N | 175.485 | 17.158 | 148 | 144.653 | 212.889 |
| IH | 129.873 | 14.716 | 148 | 103.819 | 162.465 |
| Condition | response | SE | df | lower.CL | upper.CL |
|---|---|---|---|---|---|
| N | 175.485 | 17.158 | 148 | 144.653 | 212.889 |
| IH | 129.873 | 14.716 | 148 | 103.819 | 162.465 |
| Condition | response | SE | df | lower.CL | upper.CL |
|---|---|---|---|---|---|
| N | 206.507 | 20.039 | 148 | 170.474 | 250.157 |
| IH | 180.676 | 19.376 | 148 | 146.173 | 223.324 |
| Condition | response | SE | df | lower.CL | upper.CL |
|---|---|---|---|---|---|
| N | 206.507 | 20.039 | 148 | 170.474 | 250.157 |
| IH | 180.676 | 19.376 | 148 | 146.173 | 223.324 |
- Confidence level used: 0.95
- Intervals are back-transformed from the log scale❖ Contrasts:
emmeans(mod, specs = emmeans_formula, type = "response") |>
contrast(method = "pairwise", adjust = "none", infer = TRUE)| contrast | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 1.254 | 0.193 | 148 | 0.926 | 1.699 | 1 | 1.476 | 0.142 |
| contrast | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 1.254 | 0.193 | 148 | 0.926 | 1.699 | 1 | 1.476 | 0.142 |
| contrast | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 1.351 | 0.202 | 148 | 1.005 | 1.816 | 1 | 2.011 | 0.046 * |
| contrast | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 1.351 | 0.202 | 148 | 1.005 | 1.816 | 1 | 2.011 | 0.046 * |
| contrast | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 1.143 | 0.165 | 148 | 0.859 | 1.521 | 1 | 0.924 | 0.357 |
| contrast | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 1.143 | 0.165 | 148 | 0.859 | 1.521 | 1 | 0.924 | 0.357 |
- Confidence level used: 0.95
- Intervals are back-transformed from the log scale
- Tests are performed on the log scaleemmeans(mod, specs = emmeans_formula, type = "response") |>
contrast(interaction = "pairwise", by = NULL, adjust = "none", infer = T)| Condition | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 0.928 | 0.098 | 148 | 0.753 | 1.144 | 1 | −0.703 | 0.483 |
| Condition | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 0.928 | 0.098 | 148 | 0.753 | 1.144 | 1 | −0.703 | 0.483 |
| Condition | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 1.097 | 0.112 | 148 | 0.897 | 1.342 | 1 | 0.914 | 0.362 |
| Condition | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 1.097 | 0.112 | 148 | 0.897 | 1.342 | 1 | 0.914 | 0.362 |
| Condition | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 1.182 | 0.107 | 148 | 0.989 | 1.413 | 1 | 1.856 | 0.065 |
| Condition | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 1.182 | 0.107 | 148 | 0.989 | 1.413 | 1 | 1.856 | 0.065 |
- Confidence level used: 0.95
- Intervals are back-transformed from the log scale
- Tests are performed on the log scale❖ Boxplot:
10.3 Purkinje dendrite Area per Purkinje cell body
10.3.1 Data Exploration
❖ Distribution:
| Condition | Mean | SD | Variance | CoV | IQR | Min | Max | Skewness | Kurtosis | n |
|---|---|---|---|---|---|---|---|---|---|---|
| N | 0.427 | 0.171 | 0.029 | 0.401 | 0.245 | 0.187 | 1.04 | 1.685 | 5.225 | 27 |
| IH | 0.274 | 0.085 | 0.007 | 0.311 | 0.117 | 0.164 | 0.464 | 0.7 | 0.059 | 15 |
| Condition | Mean | SD | Variance | CoV | IQR | Min | Max | Skewness | Kurtosis | n |
|---|---|---|---|---|---|---|---|---|---|---|
| N | 0.427 | 0.171 | 0.029 | 0.401 | 0.245 | 0.187 | 1.04 | 1.685 | 5.225 | 27 |
| IH | 0.274 | 0.085 | 0.007 | 0.311 | 0.117 | 0.164 | 0.464 | 0.7 | 0.059 | 15 |
| Condition | Mean | SD | Variance | CoV | IQR | Min | Max | Skewness | Kurtosis | n |
|---|---|---|---|---|---|---|---|---|---|---|
| N | 0.335 | 0.112 | 0.013 | 0.334 | 0.132 | 0.138 | 0.617 | 0.912 | 0.701 | 31 |
| IH | 0.254 | 0.081 | 0.007 | 0.318 | 0.112 | 0.148 | 0.411 | 0.628 | −0.427 | 17 |
| Condition | Mean | SD | Variance | CoV | IQR | Min | Max | Skewness | Kurtosis | n |
|---|---|---|---|---|---|---|---|---|---|---|
| N | 0.335 | 0.112 | 0.013 | 0.334 | 0.132 | 0.138 | 0.617 | 0.912 | 0.701 | 31 |
| IH | 0.254 | 0.081 | 0.007 | 0.318 | 0.112 | 0.148 | 0.411 | 0.628 | −0.427 | 17 |
| Condition | Mean | SD | Variance | CoV | IQR | Min | Max | Skewness | Kurtosis | n |
|---|---|---|---|---|---|---|---|---|---|---|
| N | 0.367 | 0.123 | 0.015 | 0.335 | 0.183 | 0.136 | 0.648 | 0.541 | −0.251 | 32 |
| IH | 0.353 | 0.175 | 0.031 | 0.496 | 0.17 | 0.163 | 0.822 | 1.488 | 1.74 | 26 |
| Condition | Mean | SD | Variance | CoV | IQR | Min | Max | Skewness | Kurtosis | n |
|---|---|---|---|---|---|---|---|---|---|---|
| N | 0.367 | 0.123 | 0.015 | 0.335 | 0.183 | 0.136 | 0.648 | 0.541 | −0.251 | 32 |
| IH | 0.353 | 0.175 | 0.031 | 0.496 | 0.17 | 0.163 | 0.822 | 1.488 | 1.74 | 26 |
10.3.2 Models & Diagnostics
Exploring some Generalized Linear (Mixed) model candidates:
❖ Model call:
```{r}
glmmTMB(formula = A_PC_per_cell ~ Condition * Z + (1 | Mouse),
data = data, family = Gamma("log"), REML = TRUE, ziformula = ~0,
dispformula = ~1)
```❖ Performance:
performance::performance(mod)| AIC | AICc | BIC | R2_conditional | R2_marginal | ICC | RMSE | Sigma |
|---|---|---|---|---|---|---|---|
| -180.41 | -179.38 | -156.43 | 0.26 | 0.14 | 0.14 | 0.12 | 0.34 |
| AIC | AICc | BIC | R2_conditional | R2_marginal | ICC | RMSE | Sigma |
|---|---|---|---|---|---|---|---|
| -180.41 | -179.38 | -156.43 | 0.26 | 0.14 | 0.14 | 0.12 | 0.34 |
❖ 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 = A_PC_per_cell ~ Condition * Z + (1 | Mouse),
data = data, family = gaussian("log"), REML = TRUE, ziformula = ~0,
dispformula = ~1)
```❖ Performance:
performance::performance(mod)| AIC | AICc | BIC | R2_conditional | R2_marginal | ICC | RMSE | Sigma |
|---|---|---|---|---|---|---|---|
| -137.71 | -136.67 | -113.73 | 0.67 | 0.43 | 0.43 | 0.13 | 0.13 |
| AIC | AICc | BIC | R2_conditional | R2_marginal | ICC | RMSE | Sigma |
|---|---|---|---|---|---|---|---|
| -137.71 | -136.67 | -113.73 | 0.67 | 0.43 | 0.43 | 0.13 | 0.13 |
❖ 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:
10.3.3 Effects Analysis
Chosen model: Gamma (‘log’)
```{r}
glmmTMB(formula = A_PC_per_cell ~ Condition * Z + (1 | Mouse),
data = data, family = Gamma("log"), REML = TRUE, ziformula = ~0,
dispformula = ~1)
```10.3.3.1 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) | 0.331 | 0.017 | (0.30, 0.37) | -21.596 | < .001 |
| Condition1 | 1.132 | 0.058 | (1.02, 1.25) | 2.430 | 0.015 * |
| Z1 | 1.049 | 0.049 | (0.96, 1.15) | 1.026 | 0.305 |
| Z2 | 0.901 | 0.040 | (0.83, 0.98) | -2.369 | 0.018 * |
| Condition1 * Z1 | 1.097 | 0.051 | (1.00, 1.20) | 1.983 | 0.047 * |
| Condition1 * Z2 | 0.984 | 0.044 | (0.90, 1.07) | -0.355 | 0.722 |
| Model: A_PC_per_cell ~ Condition * Z (148 Observations) | |||||
| Parameter | Coefficient | SE | 95% CI | z | p |
|---|---|---|---|---|---|
| (Intercept) | 0.331 | 0.017 | (0.30, 0.37) | -21.596 | < .001 |
| Condition1 | 1.132 | 0.058 | (1.02, 1.25) | 2.430 | 0.015 * |
| Z1 | 1.049 | 0.049 | (0.96, 1.15) | 1.026 | 0.305 |
| Z2 | 0.901 | 0.040 | (0.83, 0.98) | -2.369 | 0.018 * |
| Condition1 * Z1 | 1.097 | 0.051 | (1.00, 1.20) | 1.983 | 0.047 * |
| Condition1 * Z2 | 0.984 | 0.044 | (0.90, 1.07) | -0.355 | 0.722 |
| Model: A_PC_per_cell ~ Condition * Z (148 Observations) | |||||
❖ Main effects (Wald Chi-Square):
car::Anova(mod, type = 3)| term | statistic | df | p.value |
|---|---|---|---|
| Condition | 5.91 | 1 | 0.020 * |
| Z | 5.73 | 2 | 0.060 |
| Condition:Z | 4.73 | 2 | 0.090 |
| term | statistic | df | p.value |
|---|---|---|---|
| Condition | 5.91 | 1 | 0.020 * |
| Z | 5.73 | 2 | 0.060 |
| Condition:Z | 4.73 | 2 | 0.090 |
❖ Main effects (Likelihood Ratio Test):
LRT(mod, pred = "Condition")| model | df | aic | bic | log_lik | deviance | chisq | chi_df | pr_chisq |
|---|---|---|---|---|---|---|---|---|
| mod_reduced | 5 | -204.41 | -189.43 | 107.21 | -214.41 | |||
| mod_full | 8 | -207.55 | -183.57 | 111.77 | -223.55 | 9.14 | 3 | 0.030 * |
| model | df | aic | bic | log_lik | deviance | chisq | chi_df | pr_chisq |
|---|---|---|---|---|---|---|---|---|
| mod_reduced | 5 | -204.41 | -189.43 | 107.21 | -214.41 | |||
| mod_full | 8 | -207.55 | -183.57 | 111.77 | -223.55 | 9.14 | 3 | 0.030 * |
Important
Our LRT() method removes the predictor plus all its interactions
10.3.3.2 Marginal Effects
Marginal means & Contrasts for each predictor:
❖ Marginal Means:
emmeans(mod, specs = pred, type = "response")| Condition | response | SE | df | lower.CL | upper.CL |
|---|---|---|---|---|---|
| N | 0.375 | 0.025 | 146 | 0.328 | 0.427 |
| IH | 0.292 | 0.023 | 146 | 0.25 | 0.341 |
| Condition | response | SE | df | lower.CL | upper.CL |
|---|---|---|---|---|---|
| N | 0.375 | 0.025 | 146 | 0.328 | 0.427 |
| IH | 0.292 | 0.023 | 146 | 0.25 | 0.341 |
- Results are averaged over the levels of: Z
- Confidence level used: 0.95
- Intervals are back-transformed from the log scale❖ Contrasts:
emmeans(mod, specs = pred, type = "response") |>
contrast(method = "pairwise", adjust = "none", infer = TRUE)| contrast | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 1.282 | 0.131 | 146 | 1.048 | 1.57 | 1 | 2.43 | 0.016 * |
| contrast | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 1.282 | 0.131 | 146 | 1.048 | 1.57 | 1 | 2.43 | 0.016 * |
- Results are averaged over the levels of: Z
- Confidence level used: 0.95
- Intervals are back-transformed from the log scale
- Tests are performed on the log scale❖ Boxplot:
❖ Marginal Means:
emmeans(mod, specs = pred, type = "response")| Z | response | SE | df | lower.CL | upper.CL |
|---|---|---|---|---|---|
| Ant | 0.347 | 0.025 | 146 | 0.301 | 0.4 |
| Med | 0.298 | 0.02 | 146 | 0.26 | 0.341 |
| Post | 0.35 | 0.022 | 146 | 0.309 | 0.396 |
| Z | response | SE | df | lower.CL | upper.CL |
|---|---|---|---|---|---|
| Ant | 0.347 | 0.025 | 146 | 0.301 | 0.4 |
| Med | 0.298 | 0.02 | 146 | 0.26 | 0.341 |
| Post | 0.35 | 0.022 | 146 | 0.309 | 0.396 |
- Results are averaged over the levels of: Condition
- Confidence level used: 0.95
- Intervals are back-transformed from the log scale❖ Contrasts:
emmeans(mod, specs = pred, type = "response") |>
contrast(method = "pairwise", adjust = "none", infer = TRUE)| contrast | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| Ant / Med | 1.165 | 0.093 | 146 | 0.994 | 1.365 | 1 | 1.905 | 0.059 |
| Ant / Post | 0.991 | 0.078 | 146 | 0.849 | 1.157 | 1 | −0.112 | 0.911 |
| Med / Post | 0.851 | 0.063 | 146 | 0.736 | 0.984 | 1 | −2.19 | 0.030 * |
| contrast | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| Ant / Med | 1.165 | 0.093 | 146 | 0.994 | 1.365 | 1 | 1.905 | 0.059 |
| Ant / Post | 0.991 | 0.078 | 146 | 0.849 | 1.157 | 1 | −0.112 | 0.911 |
| Med / Post | 0.851 | 0.063 | 146 | 0.736 | 0.984 | 1 | −2.19 | 0.030 * |
- Results are averaged over the levels of: Condition
- Confidence level used: 0.95
- Intervals are back-transformed from the log scale
- Tests are performed on the log scale❖ Boxplot:
❖ Marginal Means:
emmeans(mod, specs = emmeans_formula, type = "response")| Condition | response | SE | df | lower.CL | upper.CL |
|---|---|---|---|---|---|
| N | 0.431 | 0.038 | 146 | 0.362 | 0.513 |
| IH | 0.28 | 0.032 | 146 | 0.223 | 0.35 |
| Condition | response | SE | df | lower.CL | upper.CL |
|---|---|---|---|---|---|
| N | 0.431 | 0.038 | 146 | 0.362 | 0.513 |
| IH | 0.28 | 0.032 | 146 | 0.223 | 0.35 |
| Condition | response | SE | df | lower.CL | upper.CL |
|---|---|---|---|---|---|
| N | 0.332 | 0.028 | 146 | 0.281 | 0.392 |
| IH | 0.267 | 0.029 | 146 | 0.215 | 0.332 |
| Condition | response | SE | df | lower.CL | upper.CL |
|---|---|---|---|---|---|
| N | 0.332 | 0.028 | 146 | 0.281 | 0.392 |
| IH | 0.267 | 0.029 | 146 | 0.215 | 0.332 |
| Condition | response | SE | df | lower.CL | upper.CL |
|---|---|---|---|---|---|
| N | 0.367 | 0.03 | 146 | 0.312 | 0.432 |
| IH | 0.334 | 0.032 | 146 | 0.277 | 0.402 |
| Condition | response | SE | df | lower.CL | upper.CL |
|---|---|---|---|---|---|
| N | 0.367 | 0.03 | 146 | 0.312 | 0.432 |
| IH | 0.334 | 0.032 | 146 | 0.277 | 0.402 |
- Confidence level used: 0.95
- Intervals are back-transformed from the log scale❖ Contrasts:
emmeans(mod, specs = emmeans_formula, type = "response") |>
contrast(method = "pairwise", adjust = "none", infer = TRUE)| contrast | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 1.542 | 0.221 | 146 | 1.161 | 2.047 | 1 | 3.019 | 0.003 ** |
| contrast | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 1.542 | 0.221 | 146 | 1.161 | 2.047 | 1 | 3.019 | 0.003 ** |
| contrast | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 1.242 | 0.171 | 146 | 0.946 | 1.632 | 1 | 1.573 | 0.118 |
| contrast | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 1.242 | 0.171 | 146 | 0.946 | 1.632 | 1 | 1.573 | 0.118 |
| contrast | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 1.101 | 0.138 | 146 | 0.859 | 1.411 | 1 | 0.765 | 0.446 |
| contrast | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 1.101 | 0.138 | 146 | 0.859 | 1.411 | 1 | 0.765 | 0.446 |
- Confidence level used: 0.95
- Intervals are back-transformed from the log scale
- Tests are performed on the log scaleemmeans(mod, specs = emmeans_formula, type = "response") |>
contrast(interaction = "pairwise", by = NULL, adjust = "none", infer = T)| Condition | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 1.241 | 0.199 | 146 | 0.904 | 1.705 | 1 | 1.345 | 0.181 |
| Condition | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 1.241 | 0.199 | 146 | 0.904 | 1.705 | 1 | 1.345 | 0.181 |
| Condition | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 1.401 | 0.217 | 146 | 1.031 | 1.904 | 1 | 2.17 | 0.032 * |
| Condition | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 1.401 | 0.217 | 146 | 1.031 | 1.904 | 1 | 2.17 | 0.032 * |
| Condition | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 1.129 | 0.168 | 146 | 0.841 | 1.513 | 1 | 0.814 | 0.417 |
| Condition | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 1.129 | 0.168 | 146 | 0.841 | 1.513 | 1 | 0.814 | 0.417 |
- Confidence level used: 0.95
- Intervals are back-transformed from the log scale
- Tests are performed on the log scale❖ Boxplot:
10.4 Purkinje dendrite Volume per Purkinje cell body
10.4.1 Data Exploration
❖ Distribution:
| Condition | Mean | SD | Variance | CoV | IQR | Min | Max | Skewness | Kurtosis | n |
|---|---|---|---|---|---|---|---|---|---|---|
| N | 0.247 | 0.103 | 0.011 | 0.416 | 0.127 | 0.091 | 0.499 | 0.859 | 0.924 | 27 |
| IH | 0.19 | 0.049 | 0.002 | 0.255 | 0.07 | 0.125 | 0.275 | 0.467 | −0.691 | 15 |
| Condition | Mean | SD | Variance | CoV | IQR | Min | Max | Skewness | Kurtosis | n |
|---|---|---|---|---|---|---|---|---|---|---|
| N | 0.247 | 0.103 | 0.011 | 0.416 | 0.127 | 0.091 | 0.499 | 0.859 | 0.924 | 27 |
| IH | 0.19 | 0.049 | 0.002 | 0.255 | 0.07 | 0.125 | 0.275 | 0.467 | −0.691 | 15 |
| Condition | Mean | SD | Variance | CoV | IQR | Min | Max | Skewness | Kurtosis | n |
|---|---|---|---|---|---|---|---|---|---|---|
| N | 0.195 | 0.061 | 0.004 | 0.313 | 0.089 | 0.071 | 0.34 | 0.265 | 0.18 | 31 |
| IH | 0.147 | 0.056 | 0.003 | 0.385 | 0.085 | 0.079 | 0.251 | 0.712 | −0.568 | 17 |
| Condition | Mean | SD | Variance | CoV | IQR | Min | Max | Skewness | Kurtosis | n |
|---|---|---|---|---|---|---|---|---|---|---|
| N | 0.195 | 0.061 | 0.004 | 0.313 | 0.089 | 0.071 | 0.34 | 0.265 | 0.18 | 31 |
| IH | 0.147 | 0.056 | 0.003 | 0.385 | 0.085 | 0.079 | 0.251 | 0.712 | −0.568 | 17 |
| Condition | Mean | SD | Variance | CoV | IQR | Min | Max | Skewness | Kurtosis | n |
|---|---|---|---|---|---|---|---|---|---|---|
| N | 0.217 | 0.086 | 0.007 | 0.398 | 0.134 | 0.112 | 0.485 | 1.083 | 1.595 | 33 |
| IH | 0.186 | 0.083 | 0.007 | 0.444 | 0.09 | 0.068 | 0.419 | 1.209 | 1.931 | 26 |
| Condition | Mean | SD | Variance | CoV | IQR | Min | Max | Skewness | Kurtosis | n |
|---|---|---|---|---|---|---|---|---|---|---|
| N | 0.217 | 0.086 | 0.007 | 0.398 | 0.134 | 0.112 | 0.485 | 1.083 | 1.595 | 33 |
| IH | 0.186 | 0.083 | 0.007 | 0.444 | 0.09 | 0.068 | 0.419 | 1.209 | 1.931 | 26 |
10.4.2 Models & Diagnostics
Exploring some Generalized Linear (Mixed) model candidates:
❖ Model call:
```{r}
glmmTMB(formula = Vol_PC_per_cell ~ Condition * Z + (1 | Mouse),
data = data, family = Gamma("log"), REML = TRUE, ziformula = ~0,
dispformula = ~1)
```❖ Performance:
performance::performance(mod)| AIC | AICc | BIC | R2_conditional | R2_marginal | ICC | RMSE | Sigma |
|---|---|---|---|---|---|---|---|
| -330.31 | -329.29 | -306.28 | 0.22 | 0.12 | 0.12 | 0.07 | 0.36 |
| AIC | AICc | BIC | R2_conditional | R2_marginal | ICC | RMSE | Sigma |
|---|---|---|---|---|---|---|---|
| -330.31 | -329.29 | -306.28 | 0.22 | 0.12 | 0.12 | 0.07 | 0.36 |
❖ 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 = Vol_PC_per_cell ~ Condition * Z + (1 | Mouse),
data = data, family = gaussian("log"), REML = TRUE, ziformula = ~0,
dispformula = ~1)
```❖ Performance:
performance::performance(mod)| AIC | AICc | BIC | R2_conditional | R2_marginal | ICC | RMSE | Sigma |
|---|---|---|---|---|---|---|---|
| -299.32 | -298.29 | -275.29 | 0.83 | 0.57 | 0.60 | 0.07 | 0.08 |
| AIC | AICc | BIC | R2_conditional | R2_marginal | ICC | RMSE | Sigma |
|---|---|---|---|---|---|---|---|
| -299.32 | -298.29 | -275.29 | 0.83 | 0.57 | 0.60 | 0.07 | 0.08 |
❖ 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:
10.4.3 Effects Analysis
Chosen model: Gamma (‘log’)
```{r}
glmmTMB(formula = Vol_PC_per_cell ~ Condition * Z + (1 | Mouse),
data = data, family = Gamma("log"), REML = TRUE, ziformula = ~0,
dispformula = ~1)
```10.4.3.1 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) | 0.194 | 0.010 | (0.18, 0.21) | -32.459 | < .001 |
| Condition1 | 1.121 | 0.057 | (1.02, 1.24) | 2.260 | 0.024 * |
| Z1 | 1.096 | 0.053 | (1.00, 1.21) | 1.889 | 0.059 |
| Z2 | 0.895 | 0.042 | (0.82, 0.98) | -2.362 | 0.018 * |
| Condition1 * Z1 | 1.049 | 0.052 | (0.95, 1.16) | 0.959 | 0.338 |
| Condition1 * Z2 | 0.991 | 0.047 | (0.90, 1.09) | -0.189 | 0.850 |
| Model: Vol_PC_per_cell ~ Condition * Z (149 Observations) | |||||
| Parameter | Coefficient | SE | 95% CI | z | p |
|---|---|---|---|---|---|
| (Intercept) | 0.194 | 0.010 | (0.18, 0.21) | -32.459 | < .001 |
| Condition1 | 1.121 | 0.057 | (1.02, 1.24) | 2.260 | 0.024 * |
| Z1 | 1.096 | 0.053 | (1.00, 1.21) | 1.889 | 0.059 |
| Z2 | 0.895 | 0.042 | (0.82, 0.98) | -2.362 | 0.018 * |
| Condition1 * Z1 | 1.049 | 0.052 | (0.95, 1.16) | 0.959 | 0.338 |
| Condition1 * Z2 | 0.991 | 0.047 | (0.90, 1.09) | -0.189 | 0.850 |
| Model: Vol_PC_per_cell ~ Condition * Z (149 Observations) | |||||
❖ Main effects (Wald Chi-Square):
car::Anova(mod, type = 3)| term | statistic | df | p.value |
|---|---|---|---|
| Condition | 5.11 | 1 | 0.020 * |
| Z | 5.95 | 2 | 0.050 * |
| Condition:Z | 1.17 | 2 | 0.560 |
| term | statistic | df | p.value |
|---|---|---|---|
| Condition | 5.11 | 1 | 0.020 * |
| Z | 5.95 | 2 | 0.050 * |
| Condition:Z | 1.17 | 2 | 0.560 |
❖ Main effects (Likelihood Ratio Test):
LRT(mod, pred = "Condition")| model | df | aic | bic | log_lik | deviance | chisq | chi_df | pr_chisq |
|---|---|---|---|---|---|---|---|---|
| mod_reduced | 5 | -357.24 | -342.22 | 183.62 | -367.24 | |||
| mod_full | 8 | -357.12 | -333.09 | 186.56 | -373.12 | 5.88 | 3 | 0.120 |
| model | df | aic | bic | log_lik | deviance | chisq | chi_df | pr_chisq |
|---|---|---|---|---|---|---|---|---|
| mod_reduced | 5 | -357.24 | -342.22 | 183.62 | -367.24 | |||
| mod_full | 8 | -357.12 | -333.09 | 186.56 | -373.12 | 5.88 | 3 | 0.120 |
Important
Our LRT() method removes the predictor plus all its interactions
10.4.3.2 Marginal Effects
Marginal means & Contrasts for each predictor:
❖ Marginal Means:
emmeans(mod, specs = pred, type = "response")| Condition | response | SE | df | lower.CL | upper.CL |
|---|---|---|---|---|---|
| N | 0.217 | 0.014 | 147 | 0.191 | 0.247 |
| IH | 0.173 | 0.013 | 147 | 0.148 | 0.201 |
| Condition | response | SE | df | lower.CL | upper.CL |
|---|---|---|---|---|---|
| N | 0.217 | 0.014 | 147 | 0.191 | 0.247 |
| IH | 0.173 | 0.013 | 147 | 0.148 | 0.201 |
- Results are averaged over the levels of: Z
- Confidence level used: 0.95
- Intervals are back-transformed from the log scale❖ Contrasts:
emmeans(mod, specs = pred, type = "response") |>
contrast(method = "pairwise", adjust = "none", infer = TRUE)| contrast | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 1.257 | 0.127 | 147 | 1.029 | 1.535 | 1 | 2.26 | 0.025 * |
| contrast | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 1.257 | 0.127 | 147 | 1.029 | 1.535 | 1 | 2.26 | 0.025 * |
- Results are averaged over the levels of: Z
- Confidence level used: 0.95
- Intervals are back-transformed from the log scale
- Tests are performed on the log scale❖ Boxplot:
❖ Marginal Means:
emmeans(mod, specs = pred, type = "response")| Z | response | SE | df | lower.CL | upper.CL |
|---|---|---|---|---|---|
| Ant | 0.212 | 0.015 | 147 | 0.184 | 0.245 |
| Med | 0.174 | 0.012 | 147 | 0.151 | 0.199 |
| Post | 0.198 | 0.012 | 147 | 0.175 | 0.224 |
| Z | response | SE | df | lower.CL | upper.CL |
|---|---|---|---|---|---|
| Ant | 0.212 | 0.015 | 147 | 0.184 | 0.245 |
| Med | 0.174 | 0.012 | 147 | 0.151 | 0.199 |
| Post | 0.198 | 0.012 | 147 | 0.175 | 0.224 |
- Results are averaged over the levels of: Condition
- Confidence level used: 0.95
- Intervals are back-transformed from the log scale❖ Contrasts:
emmeans(mod, specs = pred, type = "response") |>
contrast(method = "pairwise", adjust = "none", infer = TRUE)| contrast | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| Ant / Med | 1.225 | 0.104 | 147 | 1.035 | 1.449 | 1 | 2.377 | 0.019 * |
| Ant / Post | 1.075 | 0.085 | 147 | 0.92 | 1.257 | 1 | 0.919 | 0.359 |
| Med / Post | 0.878 | 0.067 | 147 | 0.756 | 1.02 | 1 | −1.711 | 0.089 |
| contrast | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| Ant / Med | 1.225 | 0.104 | 147 | 1.035 | 1.449 | 1 | 2.377 | 0.019 * |
| Ant / Post | 1.075 | 0.085 | 147 | 0.92 | 1.257 | 1 | 0.919 | 0.359 |
| Med / Post | 0.878 | 0.067 | 147 | 0.756 | 1.02 | 1 | −1.711 | 0.089 |
- Results are averaged over the levels of: Condition
- Confidence level used: 0.95
- Intervals are back-transformed from the log scale
- Tests are performed on the log scale❖ Boxplot:
❖ Marginal Means:
emmeans(mod, specs = emmeans_formula, type = "response")| Condition | response | SE | df | lower.CL | upper.CL |
|---|---|---|---|---|---|
| N | 0.25 | 0.022 | 147 | 0.209 | 0.298 |
| IH | 0.181 | 0.021 | 147 | 0.144 | 0.227 |
| Condition | response | SE | df | lower.CL | upper.CL |
|---|---|---|---|---|---|
| N | 0.25 | 0.022 | 147 | 0.209 | 0.298 |
| IH | 0.181 | 0.021 | 147 | 0.144 | 0.227 |
| Condition | response | SE | df | lower.CL | upper.CL |
|---|---|---|---|---|---|
| N | 0.193 | 0.016 | 147 | 0.163 | 0.228 |
| IH | 0.156 | 0.017 | 147 | 0.125 | 0.195 |
| Condition | response | SE | df | lower.CL | upper.CL |
|---|---|---|---|---|---|
| N | 0.193 | 0.016 | 147 | 0.163 | 0.228 |
| IH | 0.156 | 0.017 | 147 | 0.125 | 0.195 |
| Condition | response | SE | df | lower.CL | upper.CL |
|---|---|---|---|---|---|
| N | 0.213 | 0.018 | 147 | 0.181 | 0.251 |
| IH | 0.183 | 0.017 | 147 | 0.152 | 0.22 |
| Condition | response | SE | df | lower.CL | upper.CL |
|---|---|---|---|---|---|
| N | 0.213 | 0.018 | 147 | 0.181 | 0.251 |
| IH | 0.183 | 0.017 | 147 | 0.152 | 0.22 |
- Confidence level used: 0.95
- Intervals are back-transformed from the log scale❖ Contrasts:
emmeans(mod, specs = emmeans_formula, type = "response") |>
contrast(method = "pairwise", adjust = "none", infer = TRUE)| contrast | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 1.382 | 0.203 | 147 | 1.035 | 1.847 | 1 | 2.209 | 0.029 * |
| contrast | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 1.382 | 0.203 | 147 | 1.035 | 1.847 | 1 | 2.209 | 0.029 * |
| contrast | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 1.235 | 0.174 | 147 | 0.934 | 1.632 | 1 | 1.494 | 0.137 |
| contrast | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 1.235 | 0.174 | 147 | 0.934 | 1.632 | 1 | 1.494 | 0.137 |
| contrast | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 1.164 | 0.145 | 147 | 0.91 | 1.488 | 1 | 1.219 | 0.225 |
| contrast | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 1.164 | 0.145 | 147 | 0.91 | 1.488 | 1 | 1.219 | 0.225 |
- Confidence level used: 0.95
- Intervals are back-transformed from the log scale
- Tests are performed on the log scaleemmeans(mod, specs = emmeans_formula, type = "response") |>
contrast(interaction = "pairwise", by = NULL, adjust = "none", infer = T)| Condition | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 1.12 | 0.195 | 147 | 0.793 | 1.58 | 1 | 0.648 | 0.518 |
| Condition | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 1.12 | 0.195 | 147 | 0.793 | 1.58 | 1 | 0.648 | 0.518 |
| Condition | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 1.188 | 0.189 | 147 | 0.868 | 1.626 | 1 | 1.084 | 0.280 |
| Condition | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 1.188 | 0.189 | 147 | 0.868 | 1.626 | 1 | 1.084 | 0.280 |
| Condition | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 1.061 | 0.16 | 147 | 0.787 | 1.43 | 1 | 0.392 | 0.696 |
| Condition | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 1.061 | 0.16 | 147 | 0.787 | 1.43 | 1 | 0.392 | 0.696 |
- Confidence level used: 0.95
- Intervals are back-transformed from the log scale
- Tests are performed on the log scale❖ Boxplot:
