11 Calbindin [P21]
❖ 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
11.1 Number of Purkinje cell bodies
11.1.1 Data Exploration
❖ Distribution:
| Condition | Mean | SD | Variance | CoV | IQR | Min | Max | Skewness | Kurtosis | n |
|---|---|---|---|---|---|---|---|---|---|---|
| N | 8.727 | 1.902 | 3.618 | 0.218 | 3 | 5 | 11 | −1.015 | −0.044 | 11 |
| IH | 8 | 1.549 | 2.4 | 0.194 | 1 | 6 | 12 | 1.775 | 4.618 | 11 |
| Condition | Mean | SD | Variance | CoV | IQR | Min | Max | Skewness | Kurtosis | n |
|---|---|---|---|---|---|---|---|---|---|---|
| N | 8.727 | 1.902 | 3.618 | 0.218 | 3 | 5 | 11 | −1.015 | −0.044 | 11 |
| IH | 8 | 1.549 | 2.4 | 0.194 | 1 | 6 | 12 | 1.775 | 4.618 | 11 |
| Condition | Mean | SD | Variance | CoV | IQR | Min | Max | Skewness | Kurtosis | n |
|---|---|---|---|---|---|---|---|---|---|---|
| N | 8.529 | 1.231 | 1.515 | 0.144 | 2 | 6 | 10 | −0.532 | −0.617 | 17 |
| IH | 7.895 | 1.883 | 3.544 | 0.238 | 2 | 4 | 13 | 0.895 | 2.756 | 19 |
| Condition | Mean | SD | Variance | CoV | IQR | Min | Max | Skewness | Kurtosis | n |
|---|---|---|---|---|---|---|---|---|---|---|
| N | 8.529 | 1.231 | 1.515 | 0.144 | 2 | 6 | 10 | −0.532 | −0.617 | 17 |
| IH | 7.895 | 1.883 | 3.544 | 0.238 | 2 | 4 | 13 | 0.895 | 2.756 | 19 |
| Condition | Mean | SD | Variance | CoV | IQR | Min | Max | Skewness | Kurtosis | n |
|---|---|---|---|---|---|---|---|---|---|---|
| N | 8.7 | 1.337 | 1.789 | 0.154 | 1.25 | 8 | 12 | 2.076 | 4.059 | 10 |
| IH | 8.111 | 1.453 | 2.111 | 0.179 | 2 | 7 | 11 | 1.329 | 0.746 | 9 |
| Condition | Mean | SD | Variance | CoV | IQR | Min | Max | Skewness | Kurtosis | n |
|---|---|---|---|---|---|---|---|---|---|---|
| N | 8.7 | 1.337 | 1.789 | 0.154 | 1.25 | 8 | 12 | 2.076 | 4.059 | 10 |
| IH | 8.111 | 1.453 | 2.111 | 0.179 | 2 | 7 | 11 | 1.329 | 0.746 | 9 |
11.1.2 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 |
|---|---|---|---|---|---|---|---|---|---|
| 335.41 | 337.53 | 354.16 | 0.06 | 0.03 | 0.03 | 1.51 | 0.34 | -2.12 | 0.11 |
| AIC | AICc | BIC | R2_conditional | R2_marginal | ICC | RMSE | Sigma | Score_log | Score_spherical |
|---|---|---|---|---|---|---|---|---|---|
| 335.41 | 337.53 | 354.16 | 0.06 | 0.03 | 0.03 | 1.51 | 0.34 | -2.12 | 0.11 |
❖ Residuals:
performance::check_model(
mod, panel = FALSE,
check = c("pp_check", "qq", "reqq", "linearity", "homogeneity")
)
performance::check_overdispersion(mod)# Overdispersion test
dispersion ratio = 0.840
Pearson's Chi-Squared = 62.978
p-value = 0.838❖ 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 = poisson("log"), REML = TRUE, ziformula = ~0, dispformula = ~1)
```❖ Performance:
performance::performance(mod)| AIC | AICc | BIC | R2_conditional | R2_marginal | RMSE | Sigma | Score_log | Score_spherical |
|---|---|---|---|---|---|---|---|---|
| 365.75 | 367.37 | 382.16 | 0.01 | 1.53 | 1 | -2.12 | 0.11 | |
| AIC | AICc | BIC | R2_conditional | R2_marginal | RMSE | Sigma | Score_log | Score_spherical |
|---|---|---|---|---|---|---|---|---|
| 365.75 | 367.37 | 382.16 | 0.01 | 1.53 | 1 | -2.12 | 0.11 | |
❖ Residuals:
performance::check_model(
mod, panel = FALSE,
check = c("pp_check", "qq", "reqq", "linearity", "homogeneity")
)
performance::check_overdispersion(mod)# Overdispersion test
dispersion ratio = 0.289
Pearson's Chi-Squared = 22.000
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 = 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 | RMSE | Sigma | Score_log | Score_spherical |
|---|---|---|---|---|---|---|---|---|
| 367.75 | 369.87 | 386.50 | 1 | 1.53 | 3.34e+07 | -3.03 | 0.11 | |
| AIC | AICc | BIC | R2_conditional | R2_marginal | RMSE | Sigma | Score_log | Score_spherical |
|---|---|---|---|---|---|---|---|---|
| 367.75 | 369.87 | 386.50 | 1 | 1.53 | 3.34e+07 | -3.03 | 0.11 | |
❖ Residuals:
performance::check_model(
mod, panel = FALSE,
check = c("pp_check", "qq", "reqq", "linearity", "homogeneity")
)
performance::check_overdispersion(mod)# Overdispersion test
dispersion ratio = 0.293
Pearson's Chi-Squared = 22.000
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.11.1.3 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)
```11.1.3.1 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) | 8.288 | 0.234 | (7.84, 8.76) | 74.875 | < .001 |
| Condition1 | 1.035 | 0.029 | (0.98, 1.09) | 1.219 | 0.223 |
| Z1 | 1.005 | 0.034 | (0.94, 1.07) | 0.158 | 0.874 |
| Z2 | 0.989 | 0.030 | (0.93, 1.05) | -0.375 | 0.708 |
| Condition1 * Z1 | 1.012 | 0.034 | (0.95, 1.08) | 0.349 | 0.727 |
| Condition1 * Z2 | 0.990 | 0.030 | (0.93, 1.05) | -0.329 | 0.742 |
| Model: N_CC ~ Condition * Z (77 Observations) | |||||
| Parameter | Coefficient | SE | 95% CI | z | p |
|---|---|---|---|---|---|
| (Intercept) | 8.288 | 0.234 | (7.84, 8.76) | 74.875 | < .001 |
| Condition1 | 1.035 | 0.029 | (0.98, 1.09) | 1.219 | 0.223 |
| Z1 | 1.005 | 0.034 | (0.94, 1.07) | 0.158 | 0.874 |
| Z2 | 0.989 | 0.030 | (0.93, 1.05) | -0.375 | 0.708 |
| Condition1 * Z1 | 1.012 | 0.034 | (0.95, 1.08) | 0.349 | 0.727 |
| Condition1 * Z2 | 0.990 | 0.030 | (0.93, 1.05) | -0.329 | 0.742 |
| Model: N_CC ~ Condition * Z (77 Observations) | |||||
❖ Main effects (Wald Chi-Square):
car::Anova(mod, type = 3)| term | statistic | df | p.value |
|---|---|---|---|
| Condition | 1.49 | 1 | 0.220 |
| Z | 0.14 | 2 | 0.930 |
| Condition:Z | 0.16 | 2 | 0.920 |
| term | statistic | df | p.value |
|---|---|---|---|
| Condition | 1.49 | 1 | 0.220 |
| Z | 0.14 | 2 | 0.930 |
| Condition:Z | 0.16 | 2 | 0.920 |
❖ Main effects (Likelihood Ratio Test):
LRT(mod, pred = "Condition")| model | df | aic | bic | log_lik | deviance | chisq | chi_df | pr_chisq |
|---|---|---|---|---|---|---|---|---|
| mod_reduced | 5 | 299.45 | 311.17 | -144.72 | 289.45 | |||
| mod_full | 8 | 303.57 | 322.32 | -143.78 | 287.57 | 1.88 | 3 | 0.600 |
| model | df | aic | bic | log_lik | deviance | chisq | chi_df | pr_chisq |
|---|---|---|---|---|---|---|---|---|
| mod_reduced | 5 | 299.45 | 311.17 | -144.72 | 289.45 | |||
| mod_full | 8 | 303.57 | 322.32 | -143.78 | 287.57 | 1.88 | 3 | 0.600 |
Important
Our LRT() method removes the predictor plus all its interactions
11.1.3.2 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 | 8.575 | 0.334 | 75 | 7.934 | 9.267 |
| IH | 8.01 | 0.324 | 75 | 7.39 | 8.682 |
| Condition | response | SE | df | lower.CL | upper.CL |
|---|---|---|---|---|---|
| N | 8.575 | 0.334 | 75 | 7.934 | 9.267 |
| IH | 8.01 | 0.324 | 75 | 7.39 | 8.682 |
- 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 | 1.071 | 0.06 | 75 | 0.958 | 1.197 | 1 | 1.219 | 0.227 |
| contrast | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 1.071 | 0.06 | 75 | 0.958 | 1.197 | 1 | 1.219 | 0.227 |
- 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 | 8.332 | 0.375 | 75 | 7.618 | 9.113 |
| Med | 8.194 | 0.301 | 75 | 7.616 | 8.817 |
| Post | 8.337 | 0.402 | 75 | 7.574 | 9.177 |
| Z | response | SE | df | lower.CL | upper.CL |
|---|---|---|---|---|---|
| Ant | 8.332 | 0.375 | 75 | 7.618 | 9.113 |
| Med | 8.194 | 0.301 | 75 | 7.616 | 8.817 |
| Post | 8.337 | 0.402 | 75 | 7.574 | 9.177 |
- 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 | 1.017 | 0.054 | 75 | 0.914 | 1.131 | 1 | 0.311 | 0.756 |
| Ant / Post | 0.999 | 0.062 | 75 | 0.883 | 1.131 | 1 | −0.01 | 0.992 |
| Med / Post | 0.983 | 0.055 | 75 | 0.879 | 1.1 | 1 | −0.306 | 0.760 |
| contrast | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| Ant / Med | 1.017 | 0.054 | 75 | 0.914 | 1.131 | 1 | 0.311 | 0.756 |
| Ant / Post | 0.999 | 0.062 | 75 | 0.883 | 1.131 | 1 | −0.01 | 0.992 |
| Med / Post | 0.983 | 0.055 | 75 | 0.879 | 1.1 | 1 | −0.306 | 0.760 |
- 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 | 8.723 | 0.542 | 75 | 7.708 | 9.873 |
| IH | 7.958 | 0.516 | 75 | 6.994 | 9.056 |
| Condition | response | SE | df | lower.CL | upper.CL |
|---|---|---|---|---|---|
| N | 8.723 | 0.542 | 75 | 7.708 | 9.873 |
| IH | 7.958 | 0.516 | 75 | 6.994 | 9.056 |
| Condition | response | SE | df | lower.CL | upper.CL |
|---|---|---|---|---|---|
| N | 8.394 | 0.444 | 75 | 7.556 | 9.326 |
| IH | 7.999 | 0.406 | 75 | 7.229 | 8.851 |
| Condition | response | SE | df | lower.CL | upper.CL |
|---|---|---|---|---|---|
| N | 8.394 | 0.444 | 75 | 7.556 | 9.326 |
| IH | 7.999 | 0.406 | 75 | 7.229 | 8.851 |
| Condition | response | SE | df | lower.CL | upper.CL |
|---|---|---|---|---|---|
| N | 8.61 | 0.563 | 75 | 7.559 | 9.807 |
| IH | 8.073 | 0.57 | 75 | 7.014 | 9.292 |
| Condition | response | SE | df | lower.CL | upper.CL |
|---|---|---|---|---|---|
| N | 8.61 | 0.563 | 75 | 7.559 | 9.807 |
| IH | 8.073 | 0.57 | 75 | 7.014 | 9.292 |
- 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 | 1.096 | 0.098 | 75 | 0.917 | 1.311 | 1 | 1.023 | 0.310 |
| contrast | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 1.096 | 0.098 | 75 | 0.917 | 1.311 | 1 | 1.023 | 0.310 |
| contrast | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 1.049 | 0.077 | 75 | 0.907 | 1.214 | 1 | 0.66 | 0.511 |
| contrast | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 1.049 | 0.077 | 75 | 0.907 | 1.214 | 1 | 0.66 | 0.511 |
| contrast | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 1.067 | 0.102 | 75 | 0.881 | 1.292 | 1 | 0.67 | 0.505 |
| contrast | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 1.067 | 0.102 | 75 | 0.881 | 1.292 | 1 | 0.67 | 0.505 |
- 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 | 1.045 | 0.112 | 75 | 0.844 | 1.293 | 1 | 0.406 | 0.686 |
| Condition | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 1.045 | 0.112 | 75 | 0.844 | 1.293 | 1 | 0.406 | 0.686 |
| Condition | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 1.028 | 0.128 | 75 | 0.802 | 1.318 | 1 | 0.22 | 0.827 |
| Condition | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 1.028 | 0.128 | 75 | 0.802 | 1.318 | 1 | 0.22 | 0.827 |
| Condition | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 0.984 | 0.111 | 75 | 0.786 | 1.232 | 1 | −0.143 | 0.886 |
| Condition | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 0.984 | 0.111 | 75 | 0.786 | 1.232 | 1 | −0.143 | 0.886 |
- Confidence level used: 0.95
- Intervals are back-transformed from the log scale
- Tests are performed on the log scale❖ Boxplot:
11.2 Area of the ML
11.2.1 Data Exploration
❖ Distribution:
| Condition | Mean | SD | Variance | CoV | IQR | Min | Max | Skewness | Kurtosis | n |
|---|---|---|---|---|---|---|---|---|---|---|
| N | 286.515 | 35.489 | 1,259.44 | 0.124 | 68.608 | 226.714 | 328.704 | −0.721 | −0.947 | 11 |
| IH | 252.165 | 56.721 | 3,217.25 | 0.225 | 82.33 | 167.117 | 346.522 | −0.207 | −0.679 | 11 |
| Condition | Mean | SD | Variance | CoV | IQR | Min | Max | Skewness | Kurtosis | n |
|---|---|---|---|---|---|---|---|---|---|---|
| N | 286.515 | 35.489 | 1,259.44 | 0.124 | 68.608 | 226.714 | 328.704 | −0.721 | −0.947 | 11 |
| IH | 252.165 | 56.721 | 3,217.25 | 0.225 | 82.33 | 167.117 | 346.522 | −0.207 | −0.679 | 11 |
| Condition | Mean | SD | Variance | CoV | IQR | Min | Max | Skewness | Kurtosis | n |
|---|---|---|---|---|---|---|---|---|---|---|
| N | 285.829 | 34.54 | 1,193.022 | 0.121 | 46.08 | 196.198 | 333.824 | −0.89 | 1.427 | 17 |
| IH | 263.976 | 40.209 | 1,616.748 | 0.152 | 68.608 | 212.378 | 335.053 | 0.512 | −1.101 | 19 |
| Condition | Mean | SD | Variance | CoV | IQR | Min | Max | Skewness | Kurtosis | n |
|---|---|---|---|---|---|---|---|---|---|---|
| N | 285.829 | 34.54 | 1,193.022 | 0.121 | 46.08 | 196.198 | 333.824 | −0.89 | 1.427 | 17 |
| IH | 263.976 | 40.209 | 1,616.748 | 0.152 | 68.608 | 212.378 | 335.053 | 0.512 | −1.101 | 19 |
| Condition | Mean | SD | Variance | CoV | IQR | Min | Max | Skewness | Kurtosis | n |
|---|---|---|---|---|---|---|---|---|---|---|
| N | 283.894 | 35.514 | 1,261.235 | 0.125 | 34.867 | 196.813 | 317.235 | −1.831 | 3.962 | 10 |
| IH | 280.986 | 24.764 | 613.249 | 0.088 | 31.949 | 235.725 | 319.078 | −0.178 | 0.554 | 9 |
| Condition | Mean | SD | Variance | CoV | IQR | Min | Max | Skewness | Kurtosis | n |
|---|---|---|---|---|---|---|---|---|---|---|
| N | 283.894 | 35.514 | 1,261.235 | 0.125 | 34.867 | 196.813 | 317.235 | −1.831 | 3.962 | 10 |
| IH | 280.986 | 24.764 | 613.249 | 0.088 | 31.949 | 235.725 | 319.078 | −0.178 | 0.554 | 9 |
11.2.2 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 | RMSE | Sigma |
|---|---|---|---|---|---|---|
| 835.21 | 837.33 | 853.96 | 0.09 | 37.66 | 0.15 | |
| AIC | AICc | BIC | R2_conditional | R2_marginal | RMSE | Sigma |
|---|---|---|---|---|---|---|
| 835.21 | 837.33 | 853.96 | 0.09 | 37.66 | 0.15 | |
❖ 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 | RMSE | Sigma |
|---|---|---|---|---|---|---|
| 829.55 | 831.67 | 848.30 | 1.48e-06 | 37.66 | 39.22 | |
| AIC | AICc | BIC | R2_conditional | R2_marginal | RMSE | Sigma |
|---|---|---|---|---|---|---|
| 829.55 | 831.67 | 848.30 | 1.48e-06 | 37.66 | 39.22 | |
❖ 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:
11.2.3 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)
```11.2.3.1 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) | 275.248 | 4.878 | (265.85, 284.98) | 316.955 | < .001 |
| Condition1 | 1.037 | 0.018 | (1.00, 1.07) | 2.046 | 0.041 * |
| Z1 | 0.977 | 0.025 | (0.93, 1.03) | -0.928 | 0.353 |
| Z2 | 0.998 | 0.023 | (0.95, 1.04) | -0.090 | 0.929 |
| Condition1 * Z1 | 1.028 | 0.026 | (0.98, 1.08) | 1.079 | 0.280 |
| Condition1 * Z2 | 1.004 | 0.023 | (0.96, 1.05) | 0.154 | 0.878 |
| Model: A_ML ~ Condition * Z (77 Observations) | |||||
| Parameter | Coefficient | SE | 95% CI | z | p |
|---|---|---|---|---|---|
| (Intercept) | 275.248 | 4.878 | (265.85, 284.98) | 316.955 | < .001 |
| Condition1 | 1.037 | 0.018 | (1.00, 1.07) | 2.046 | 0.041 * |
| Z1 | 0.977 | 0.025 | (0.93, 1.03) | -0.928 | 0.353 |
| Z2 | 0.998 | 0.023 | (0.95, 1.04) | -0.090 | 0.929 |
| Condition1 * Z1 | 1.028 | 0.026 | (0.98, 1.08) | 1.079 | 0.280 |
| Condition1 * Z2 | 1.004 | 0.023 | (0.96, 1.05) | 0.154 | 0.878 |
| Model: A_ML ~ Condition * Z (77 Observations) | |||||
❖ Main effects (Wald Chi-Square):
car::Anova(mod, type = 3)| term | statistic | df | p.value |
|---|---|---|---|
| Condition | 4.18 | 1 | 0.040 * |
| Z | 1.11 | 2 | 0.570 |
| Condition:Z | 1.57 | 2 | 0.460 |
| term | statistic | df | p.value |
|---|---|---|---|
| Condition | 4.18 | 1 | 0.040 * |
| Z | 1.11 | 2 | 0.570 |
| Condition:Z | 1.57 | 2 | 0.460 |
❖ Main effects (Likelihood Ratio Test):
LRT(mod, pred = "Condition")| model | df | aic | bic | log_lik | deviance | chisq | chi_df | pr_chisq |
|---|---|---|---|---|---|---|---|---|
| mod_reduced | 5 | 800.10 | 811.82 | -395.05 | 790.10 | |||
| mod_full | 8 | 799.58 | 818.33 | -391.79 | 783.58 | 6.51 | 3 | 0.090 |
| model | df | aic | bic | log_lik | deviance | chisq | chi_df | pr_chisq |
|---|---|---|---|---|---|---|---|---|
| mod_reduced | 5 | 800.10 | 811.82 | -395.05 | 790.10 | |||
| mod_full | 8 | 799.58 | 818.33 | -391.79 | 783.58 | 6.51 | 3 | 0.090 |
Important
Our LRT() method removes the predictor plus all its interactions
11.2.3.2 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 | 285.41 | 7.119 | 75 | 271.575 | 299.95 |
| IH | 265.447 | 6.686 | 75 | 252.457 | 279.106 |
| Condition | response | SE | df | lower.CL | upper.CL |
|---|---|---|---|---|---|
| N | 285.41 | 7.119 | 75 | 271.575 | 299.95 |
| IH | 265.447 | 6.686 | 75 | 252.457 | 279.106 |
- 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 | 1.075 | 0.038 | 75 | 1.002 | 1.154 | 1 | 2.046 | 0.044 * |
| contrast | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 1.075 | 0.038 | 75 | 1.002 | 1.154 | 1 | 2.046 | 0.044 * |
- 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 | 268.792 | 8.581 | 75 | 252.23 | 286.441 |
| Med | 274.685 | 6.866 | 75 | 261.343 | 288.709 |
| Post | 282.436 | 9.716 | 75 | 263.73 | 302.469 |
| Z | response | SE | df | lower.CL | upper.CL |
|---|---|---|---|---|---|
| Ant | 268.792 | 8.581 | 75 | 252.23 | 286.441 |
| Med | 274.685 | 6.866 | 75 | 261.343 | 288.709 |
| Post | 282.436 | 9.716 | 75 | 263.73 | 302.469 |
- 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 | 0.979 | 0.04 | 75 | 0.903 | 1.061 | 1 | −0.535 | 0.594 |
| Ant / Post | 0.952 | 0.045 | 75 | 0.867 | 1.045 | 1 | −1.055 | 0.295 |
| Med / Post | 0.973 | 0.041 | 75 | 0.894 | 1.059 | 1 | −0.654 | 0.515 |
| contrast | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| Ant / Med | 0.979 | 0.04 | 75 | 0.903 | 1.061 | 1 | −0.535 | 0.594 |
| Ant / Post | 0.952 | 0.045 | 75 | 0.867 | 1.045 | 1 | −1.055 | 0.295 |
| Med / Post | 0.973 | 0.041 | 75 | 0.894 | 1.059 | 1 | −0.654 | 0.515 |
- 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 | 286.515 | 12.935 | 75 | 261.871 | 313.478 |
| IH | 252.165 | 11.385 | 75 | 230.475 | 275.895 |
| Condition | response | SE | df | lower.CL | upper.CL |
|---|---|---|---|---|---|
| N | 286.515 | 12.935 | 75 | 261.871 | 313.478 |
| IH | 252.165 | 11.385 | 75 | 230.475 | 275.895 |
| Condition | response | SE | df | lower.CL | upper.CL |
|---|---|---|---|---|---|
| N | 285.829 | 10.38 | 75 | 265.88 | 307.274 |
| IH | 263.976 | 9.068 | 75 | 246.516 | 282.674 |
| Condition | response | SE | df | lower.CL | upper.CL |
|---|---|---|---|---|---|
| N | 285.829 | 10.38 | 75 | 265.88 | 307.274 |
| IH | 263.976 | 9.068 | 75 | 246.516 | 282.674 |
| Condition | response | SE | df | lower.CL | upper.CL |
|---|---|---|---|---|---|
| N | 283.894 | 13.443 | 75 | 258.339 | 311.977 |
| IH | 280.986 | 14.025 | 75 | 254.391 | 310.36 |
| Condition | response | SE | df | lower.CL | upper.CL |
|---|---|---|---|---|---|
| N | 283.894 | 13.443 | 75 | 258.339 | 311.977 |
| IH | 280.986 | 14.025 | 75 | 254.391 | 310.36 |
- 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 | 1.136 | 0.073 | 75 | 1.001 | 1.29 | 1 | 2 | 0.049 * |
| contrast | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 1.136 | 0.073 | 75 | 1.001 | 1.29 | 1 | 2 | 0.049 * |
| contrast | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 1.083 | 0.054 | 75 | 0.98 | 1.196 | 1 | 1.591 | 0.116 |
| contrast | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 1.083 | 0.054 | 75 | 0.98 | 1.196 | 1 | 1.591 | 0.116 |
| contrast | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 1.01 | 0.07 | 75 | 0.881 | 1.159 | 1 | 0.15 | 0.881 |
| contrast | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 1.01 | 0.07 | 75 | 0.881 | 1.159 | 1 | 0.15 | 0.881 |
- 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 | 1.049 | 0.085 | 75 | 0.893 | 1.233 | 1 | 0.594 | 0.554 |
| Condition | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 1.049 | 0.085 | 75 | 0.893 | 1.233 | 1 | 0.594 | 0.554 |
| Condition | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 1.125 | 0.106 | 75 | 0.933 | 1.356 | 1 | 1.251 | 0.215 |
| Condition | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 1.125 | 0.106 | 75 | 0.933 | 1.356 | 1 | 1.251 | 0.215 |
| Condition | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 1.072 | 0.091 | 75 | 0.905 | 1.27 | 1 | 0.814 | 0.418 |
| Condition | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 1.072 | 0.091 | 75 | 0.905 | 1.27 | 1 | 0.814 | 0.418 |
- Confidence level used: 0.95
- Intervals are back-transformed from the log scale
- Tests are performed on the log scale❖ Boxplot:
11.3 Purkinje dendrite Area per Purkinje cell body
11.3.1 Data Exploration
❖ Distribution:
| Condition | Mean | SD | Variance | CoV | IQR | Min | Max | Skewness | Kurtosis | n |
|---|---|---|---|---|---|---|---|---|---|---|
| N | 0.547 | 0.15 | 0.023 | 0.275 | 0.094 | 0.306 | 0.908 | 1.36 | 4.445 | 10 |
| IH | 0.551 | 0.152 | 0.023 | 0.276 | 0.281 | 0.299 | 0.752 | −0.61 | −0.757 | 11 |
| Condition | Mean | SD | Variance | CoV | IQR | Min | Max | Skewness | Kurtosis | n |
|---|---|---|---|---|---|---|---|---|---|---|
| N | 0.547 | 0.15 | 0.023 | 0.275 | 0.094 | 0.306 | 0.908 | 1.36 | 4.445 | 10 |
| IH | 0.551 | 0.152 | 0.023 | 0.276 | 0.281 | 0.299 | 0.752 | −0.61 | −0.757 | 11 |
| Condition | Mean | SD | Variance | CoV | IQR | Min | Max | Skewness | Kurtosis | n |
|---|---|---|---|---|---|---|---|---|---|---|
| N | 0.565 | 0.134 | 0.018 | 0.237 | 0.183 | 0.328 | 0.861 | 0.27 | 0.336 | 17 |
| IH | 0.556 | 0.167 | 0.028 | 0.3 | 0.23 | 0.3 | 0.901 | 0.321 | −0.365 | 18 |
| Condition | Mean | SD | Variance | CoV | IQR | Min | Max | Skewness | Kurtosis | n |
|---|---|---|---|---|---|---|---|---|---|---|
| N | 0.565 | 0.134 | 0.018 | 0.237 | 0.183 | 0.328 | 0.861 | 0.27 | 0.336 | 17 |
| IH | 0.556 | 0.167 | 0.028 | 0.3 | 0.23 | 0.3 | 0.901 | 0.321 | −0.365 | 18 |
| Condition | Mean | SD | Variance | CoV | IQR | Min | Max | Skewness | Kurtosis | n |
|---|---|---|---|---|---|---|---|---|---|---|
| N | 0.448 | 0.084 | 0.007 | 0.187 | 0.124 | 0.302 | 0.56 | −0.35 | −0.746 | 10 |
| IH | 0.529 | 0.176 | 0.031 | 0.333 | 0.289 | 0.255 | 0.809 | −0.025 | −0.541 | 9 |
| Condition | Mean | SD | Variance | CoV | IQR | Min | Max | Skewness | Kurtosis | n |
|---|---|---|---|---|---|---|---|---|---|---|
| N | 0.448 | 0.084 | 0.007 | 0.187 | 0.124 | 0.302 | 0.56 | −0.35 | −0.746 | 10 |
| IH | 0.529 | 0.176 | 0.031 | 0.333 | 0.289 | 0.255 | 0.809 | −0.025 | −0.541 | 9 |
11.3.2 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 | RMSE | Sigma |
|---|---|---|---|---|---|---|
| -38.10 | -35.92 | -19.56 | 0.07 | 0.14 | 0.28 | |
| AIC | AICc | BIC | R2_conditional | R2_marginal | RMSE | Sigma |
|---|---|---|---|---|---|---|
| -38.10 | -35.92 | -19.56 | 0.07 | 0.14 | 0.28 | |
❖ 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 | RMSE | Sigma |
|---|---|---|---|---|---|---|
| -36.24 | -34.06 | -17.70 | 0.20 | 0.14 | 0.15 | |
| AIC | AICc | BIC | R2_conditional | R2_marginal | RMSE | Sigma |
|---|---|---|---|---|---|---|
| -36.24 | -34.06 | -17.70 | 0.20 | 0.14 | 0.15 | |
❖ 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:
11.3.3 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)
```11.3.3.1 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) | 0.531 | 0.018 | (0.50, 0.57) | -19.010 | < .001 |
| Condition1 | 0.974 | 0.032 | (0.91, 1.04) | -0.798 | 0.425 |
| Z1 | 1.033 | 0.050 | (0.94, 1.14) | 0.677 | 0.498 |
| Z2 | 1.056 | 0.045 | (0.97, 1.15) | 1.263 | 0.207 |
| Condition1 * Z1 | 1.023 | 0.049 | (0.93, 1.12) | 0.468 | 0.639 |
| Condition1 * Z2 | 1.035 | 0.044 | (0.95, 1.13) | 0.802 | 0.423 |
| Model: A_PC_per_cell ~ Condition * Z (75 Observations) | |||||
| Parameter | Coefficient | SE | 95% CI | z | p |
|---|---|---|---|---|---|
| (Intercept) | 0.531 | 0.018 | (0.50, 0.57) | -19.010 | < .001 |
| Condition1 | 0.974 | 0.032 | (0.91, 1.04) | -0.798 | 0.425 |
| Z1 | 1.033 | 0.050 | (0.94, 1.14) | 0.677 | 0.498 |
| Z2 | 1.056 | 0.045 | (0.97, 1.15) | 1.263 | 0.207 |
| Condition1 * Z1 | 1.023 | 0.049 | (0.93, 1.12) | 0.468 | 0.639 |
| Condition1 * Z2 | 1.035 | 0.044 | (0.95, 1.13) | 0.802 | 0.423 |
| Model: A_PC_per_cell ~ Condition * Z (75 Observations) | |||||
❖ Main effects (Wald Chi-Square):
car::Anova(mod, type = 3)| term | statistic | df | p.value |
|---|---|---|---|
| Condition | 0.64 | 1 | 0.420 |
| Z | 3.33 | 2 | 0.190 |
| Condition:Z | 1.41 | 2 | 0.490 |
| term | statistic | df | p.value |
|---|---|---|---|
| Condition | 0.64 | 1 | 0.420 |
| Z | 3.33 | 2 | 0.190 |
| Condition:Z | 1.41 | 2 | 0.490 |
❖ Main effects (Likelihood Ratio Test):
LRT(mod, pred = "Condition")| model | df | aic | bic | log_lik | deviance | chisq | chi_df | pr_chisq |
|---|---|---|---|---|---|---|---|---|
| mod_reduced | 5 | -70.29 | -58.70 | 40.14 | -80.29 | |||
| mod_full | 8 | -66.17 | -47.63 | 41.08 | -82.17 | 1.88 | 3 | 0.600 |
| model | df | aic | bic | log_lik | deviance | chisq | chi_df | pr_chisq |
|---|---|---|---|---|---|---|---|---|
| mod_reduced | 5 | -70.29 | -58.70 | 40.14 | -80.29 | |||
| mod_full | 8 | -66.17 | -47.63 | 41.08 | -82.17 | 1.88 | 3 | 0.600 |
Important
Our LRT() method removes the predictor plus all its interactions
11.3.3.2 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 | 0.517 | 0.024 | 73 | 0.471 | 0.568 |
| IH | 0.545 | 0.026 | 73 | 0.497 | 0.599 |
| Condition | response | SE | df | lower.CL | upper.CL |
|---|---|---|---|---|---|
| N | 0.517 | 0.024 | 73 | 0.471 | 0.568 |
| IH | 0.545 | 0.026 | 73 | 0.497 | 0.599 |
- 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 | 0.948 | 0.063 | 73 | 0.83 | 1.083 | 1 | −0.798 | 0.427 |
| contrast | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 0.948 | 0.063 | 73 | 0.83 | 1.083 | 1 | −0.798 | 0.427 |
- 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 | 0.549 | 0.033 | 73 | 0.486 | 0.619 |
| Med | 0.561 | 0.026 | 73 | 0.511 | 0.616 |
| Post | 0.487 | 0.031 | 73 | 0.429 | 0.553 |
| Z | response | SE | df | lower.CL | upper.CL |
|---|---|---|---|---|---|
| Ant | 0.549 | 0.033 | 73 | 0.486 | 0.619 |
| Med | 0.561 | 0.026 | 73 | 0.511 | 0.616 |
| Post | 0.487 | 0.031 | 73 | 0.429 | 0.553 |
- 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 | 0.979 | 0.075 | 73 | 0.84 | 1.141 | 1 | −0.28 | 0.780 |
| Ant / Post | 1.127 | 0.099 | 73 | 0.946 | 1.344 | 1 | 1.359 | 0.178 |
| Med / Post | 1.152 | 0.091 | 73 | 0.983 | 1.349 | 1 | 1.781 | 0.079 |
| contrast | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| Ant / Med | 0.979 | 0.075 | 73 | 0.84 | 1.141 | 1 | −0.28 | 0.780 |
| Ant / Post | 1.127 | 0.099 | 73 | 0.946 | 1.344 | 1 | 1.359 | 0.178 |
| Med / Post | 1.152 | 0.091 | 73 | 0.983 | 1.349 | 1 | 1.781 | 0.079 |
- 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 | 0.547 | 0.048 | 73 | 0.459 | 0.651 |
| IH | 0.551 | 0.046 | 73 | 0.466 | 0.651 |
| Condition | response | SE | df | lower.CL | upper.CL |
|---|---|---|---|---|---|
| N | 0.547 | 0.048 | 73 | 0.459 | 0.651 |
| IH | 0.551 | 0.046 | 73 | 0.466 | 0.651 |
| Condition | response | SE | df | lower.CL | upper.CL |
|---|---|---|---|---|---|
| N | 0.565 | 0.038 | 73 | 0.494 | 0.646 |
| IH | 0.556 | 0.036 | 73 | 0.488 | 0.634 |
| Condition | response | SE | df | lower.CL | upper.CL |
|---|---|---|---|---|---|
| N | 0.565 | 0.038 | 73 | 0.494 | 0.646 |
| IH | 0.556 | 0.036 | 73 | 0.488 | 0.634 |
| Condition | response | SE | df | lower.CL | upper.CL |
|---|---|---|---|---|---|
| N | 0.448 | 0.039 | 73 | 0.376 | 0.534 |
| IH | 0.529 | 0.049 | 73 | 0.44 | 0.637 |
| Condition | response | SE | df | lower.CL | upper.CL |
|---|---|---|---|---|---|
| N | 0.448 | 0.039 | 73 | 0.376 | 0.534 |
| IH | 0.529 | 0.049 | 73 | 0.44 | 0.637 |
- 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 | 0.992 | 0.12 | 73 | 0.779 | 1.264 | 1 | −0.065 | 0.949 |
| contrast | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 0.992 | 0.12 | 73 | 0.779 | 1.264 | 1 | −0.065 | 0.949 |
| contrast | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 1.016 | 0.095 | 73 | 0.842 | 1.225 | 1 | 0.167 | 0.867 |
| contrast | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 1.016 | 0.095 | 73 | 0.842 | 1.225 | 1 | 0.167 | 0.867 |
| contrast | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 0.846 | 0.108 | 73 | 0.656 | 1.091 | 1 | −1.31 | 0.194 |
| contrast | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 0.846 | 0.108 | 73 | 0.656 | 1.091 | 1 | −1.31 | 0.194 |
- 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 | 0.977 | 0.15 | 73 | 0.719 | 1.326 | 1 | −0.154 | 0.878 |
| Condition | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 0.977 | 0.15 | 73 | 0.719 | 1.326 | 1 | −0.154 | 0.878 |
| Condition | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 1.173 | 0.207 | 73 | 0.826 | 1.666 | 1 | 0.905 | 0.368 |
| Condition | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 1.173 | 0.207 | 73 | 0.826 | 1.666 | 1 | 0.905 | 0.368 |
| Condition | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 1.201 | 0.19 | 73 | 0.876 | 1.647 | 1 | 1.155 | 0.252 |
| Condition | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 1.201 | 0.19 | 73 | 0.876 | 1.647 | 1 | 1.155 | 0.252 |
- Confidence level used: 0.95
- Intervals are back-transformed from the log scale
- Tests are performed on the log scale❖ Boxplot:
11.4 Purkinje dendrite Volume per Purkinje cell body
11.4.1 Data Exploration
❖ Distribution:
| Condition | Mean | SD | Variance | CoV | IQR | Min | Max | Skewness | Kurtosis | n |
|---|---|---|---|---|---|---|---|---|---|---|
| N | 0.333 | 0.119 | 0.014 | 0.358 | 0.121 | 0.181 | 0.624 | 1.662 | 4.012 | 10 |
| IH | 0.374 | 0.12 | 0.014 | 0.321 | 0.17 | 0.179 | 0.546 | −0.318 | −0.805 | 11 |
| Condition | Mean | SD | Variance | CoV | IQR | Min | Max | Skewness | Kurtosis | n |
|---|---|---|---|---|---|---|---|---|---|---|
| N | 0.333 | 0.119 | 0.014 | 0.358 | 0.121 | 0.181 | 0.624 | 1.662 | 4.012 | 10 |
| IH | 0.374 | 0.12 | 0.014 | 0.321 | 0.17 | 0.179 | 0.546 | −0.318 | −0.805 | 11 |
| Condition | Mean | SD | Variance | CoV | IQR | Min | Max | Skewness | Kurtosis | n |
|---|---|---|---|---|---|---|---|---|---|---|
| N | 0.317 | 0.075 | 0.006 | 0.236 | 0.123 | 0.197 | 0.47 | 0.249 | −0.486 | 17 |
| IH | 0.349 | 0.13 | 0.017 | 0.374 | 0.169 | 0.139 | 0.579 | 0.232 | −0.603 | 19 |
| Condition | Mean | SD | Variance | CoV | IQR | Min | Max | Skewness | Kurtosis | n |
|---|---|---|---|---|---|---|---|---|---|---|
| N | 0.317 | 0.075 | 0.006 | 0.236 | 0.123 | 0.197 | 0.47 | 0.249 | −0.486 | 17 |
| IH | 0.349 | 0.13 | 0.017 | 0.374 | 0.169 | 0.139 | 0.579 | 0.232 | −0.603 | 19 |
| Condition | Mean | SD | Variance | CoV | IQR | Min | Max | Skewness | Kurtosis | n |
|---|---|---|---|---|---|---|---|---|---|---|
| N | 0.245 | 0.043 | 0.002 | 0.177 | 0.061 | 0.159 | 0.305 | −0.833 | 0.399 | 10 |
| IH | 0.343 | 0.14 | 0.02 | 0.408 | 0.216 | 0.126 | 0.578 | 0.021 | −0.151 | 9 |
| Condition | Mean | SD | Variance | CoV | IQR | Min | Max | Skewness | Kurtosis | n |
|---|---|---|---|---|---|---|---|---|---|---|
| N | 0.245 | 0.043 | 0.002 | 0.177 | 0.061 | 0.159 | 0.305 | −0.833 | 0.399 | 10 |
| IH | 0.343 | 0.14 | 0.02 | 0.408 | 0.216 | 0.126 | 0.578 | 0.021 | −0.151 | 9 |
11.4.2 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 |
|---|---|---|---|---|---|---|---|
| -91.58 | -89.43 | -72.93 | 0.13 | 0.12 | 4.58e-03 | 0.10 | 0.33 |
| AIC | AICc | BIC | R2_conditional | R2_marginal | ICC | RMSE | Sigma |
|---|---|---|---|---|---|---|---|
| -91.58 | -89.43 | -72.93 | 0.13 | 0.12 | 4.58e-03 | 0.10 | 0.33 |
❖ 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 |
|---|---|---|---|---|---|---|---|
| -85.14 | -82.99 | -66.49 | 0.61 | 0.53 | 0.19 | 0.10 | 0.11 |
| AIC | AICc | BIC | R2_conditional | R2_marginal | ICC | RMSE | Sigma |
|---|---|---|---|---|---|---|---|
| -85.14 | -82.99 | -66.49 | 0.61 | 0.53 | 0.19 | 0.10 | 0.11 |
❖ 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:
11.4.3 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)
```11.4.3.1 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) | 0.324 | 0.013 | (0.30, 0.35) | -27.636 | < .001 |
| Condition1 | 0.912 | 0.037 | (0.84, 0.99) | -2.249 | 0.025 * |
| Z1 | 1.090 | 0.063 | (0.97, 1.22) | 1.492 | 0.136 |
| Z2 | 1.026 | 0.052 | (0.93, 1.13) | 0.512 | 0.609 |
| Condition1 * Z1 | 1.035 | 0.060 | (0.92, 1.16) | 0.594 | 0.552 |
| Condition1 * Z2 | 1.044 | 0.053 | (0.94, 1.15) | 0.847 | 0.397 |
| Model: Vol_PC_per_cell ~ Condition * Z (76 Observations) | |||||
| Parameter | Coefficient | SE | 95% CI | z | p |
|---|---|---|---|---|---|
| (Intercept) | 0.324 | 0.013 | (0.30, 0.35) | -27.636 | < .001 |
| Condition1 | 0.912 | 0.037 | (0.84, 0.99) | -2.249 | 0.025 * |
| Z1 | 1.090 | 0.063 | (0.97, 1.22) | 1.492 | 0.136 |
| Z2 | 1.026 | 0.052 | (0.93, 1.13) | 0.512 | 0.609 |
| Condition1 * Z1 | 1.035 | 0.060 | (0.92, 1.16) | 0.594 | 0.552 |
| Condition1 * Z2 | 1.044 | 0.053 | (0.94, 1.15) | 0.847 | 0.397 |
| Model: Vol_PC_per_cell ~ Condition * Z (76 Observations) | |||||
❖ Main effects (Wald Chi-Square):
car::Anova(mod, type = 3)| term | statistic | df | p.value |
|---|---|---|---|
| Condition | 5.06 | 1 | 0.020 * |
| Z | 3.75 | 2 | 0.150 |
| Condition:Z | 1.78 | 2 | 0.410 |
| term | statistic | df | p.value |
|---|---|---|---|
| Condition | 5.06 | 1 | 0.020 * |
| Z | 3.75 | 2 | 0.150 |
| Condition:Z | 1.78 | 2 | 0.410 |
❖ Main effects (Likelihood Ratio Test):
LRT(mod, pred = "Condition")| model | df | aic | bic | log_lik | deviance | chisq | chi_df | pr_chisq |
|---|---|---|---|---|---|---|---|---|
| mod_reduced | 5 | -117.44 | -105.79 | 63.72 | -127.44 | |||
| mod_full | 8 | -117.56 | -98.92 | 66.78 | -133.56 | 6.12 | 3 | 0.110 |
| model | df | aic | bic | log_lik | deviance | chisq | chi_df | pr_chisq |
|---|---|---|---|---|---|---|---|---|
| mod_reduced | 5 | -117.44 | -105.79 | 63.72 | -127.44 | |||
| mod_full | 8 | -117.56 | -98.92 | 66.78 | -133.56 | 6.12 | 3 | 0.110 |
Important
Our LRT() method removes the predictor plus all its interactions
11.4.3.2 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 | 0.296 | 0.017 | 74 | 0.264 | 0.332 |
| IH | 0.355 | 0.02 | 74 | 0.317 | 0.398 |
| Condition | response | SE | df | lower.CL | upper.CL |
|---|---|---|---|---|---|
| N | 0.296 | 0.017 | 74 | 0.264 | 0.332 |
| IH | 0.355 | 0.02 | 74 | 0.317 | 0.398 |
- 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 | 0.832 | 0.068 | 74 | 0.708 | 0.979 | 1 | −2.249 | 0.027 * |
| contrast | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 0.832 | 0.068 | 74 | 0.708 | 0.979 | 1 | −2.249 | 0.027 * |
- 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 | 0.353 | 0.026 | 74 | 0.305 | 0.408 |
| Med | 0.333 | 0.019 | 74 | 0.297 | 0.372 |
| Post | 0.29 | 0.022 | 74 | 0.249 | 0.337 |
| Z | response | SE | df | lower.CL | upper.CL |
|---|---|---|---|---|---|
| Ant | 0.353 | 0.026 | 74 | 0.305 | 0.408 |
| Med | 0.333 | 0.019 | 74 | 0.297 | 0.372 |
| Post | 0.29 | 0.022 | 74 | 0.249 | 0.337 |
- 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 | 1.062 | 0.097 | 74 | 0.885 | 1.273 | 1 | 0.654 | 0.515 |
| Ant / Post | 1.219 | 0.128 | 74 | 0.989 | 1.503 | 1 | 1.884 | 0.063 |
| Med / Post | 1.148 | 0.108 | 74 | 0.951 | 1.386 | 1 | 1.463 | 0.148 |
| contrast | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| Ant / Med | 1.062 | 0.097 | 74 | 0.885 | 1.273 | 1 | 0.654 | 0.515 |
| Ant / Post | 1.219 | 0.128 | 74 | 0.989 | 1.503 | 1 | 1.884 | 0.063 |
| Med / Post | 1.148 | 0.108 | 74 | 0.951 | 1.386 | 1 | 1.463 | 0.148 |
- 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 | 0.333 | 0.035 | 74 | 0.27 | 0.411 |
| IH | 0.374 | 0.038 | 74 | 0.306 | 0.457 |
| Condition | response | SE | df | lower.CL | upper.CL |
|---|---|---|---|---|---|
| N | 0.333 | 0.035 | 74 | 0.27 | 0.411 |
| IH | 0.374 | 0.038 | 74 | 0.306 | 0.457 |
| Condition | response | SE | df | lower.CL | upper.CL |
|---|---|---|---|---|---|
| N | 0.317 | 0.026 | 74 | 0.269 | 0.373 |
| IH | 0.349 | 0.028 | 74 | 0.298 | 0.409 |
| Condition | response | SE | df | lower.CL | upper.CL |
|---|---|---|---|---|---|
| N | 0.317 | 0.026 | 74 | 0.269 | 0.373 |
| IH | 0.349 | 0.028 | 74 | 0.298 | 0.409 |
| Condition | response | SE | df | lower.CL | upper.CL |
|---|---|---|---|---|---|
| N | 0.245 | 0.026 | 74 | 0.198 | 0.302 |
| IH | 0.343 | 0.038 | 74 | 0.275 | 0.428 |
| Condition | response | SE | df | lower.CL | upper.CL |
|---|---|---|---|---|---|
| N | 0.245 | 0.026 | 74 | 0.198 | 0.302 |
| IH | 0.343 | 0.038 | 74 | 0.275 | 0.428 |
- 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 | 0.891 | 0.13 | 74 | 0.666 | 1.192 | 1 | −0.787 | 0.434 |
| contrast | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 0.891 | 0.13 | 74 | 0.666 | 1.192 | 1 | −0.787 | 0.434 |
| contrast | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 0.908 | 0.103 | 74 | 0.724 | 1.138 | 1 | −0.853 | 0.396 |
| contrast | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 0.908 | 0.103 | 74 | 0.724 | 1.138 | 1 | −0.853 | 0.396 |
| contrast | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 0.713 | 0.109 | 74 | 0.525 | 0.968 | 1 | −2.207 | 0.030 * |
| contrast | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 0.713 | 0.109 | 74 | 0.525 | 0.968 | 1 | −2.207 | 0.030 * |
- 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 | 0.982 | 0.179 | 74 | 0.682 | 1.413 | 1 | −0.099 | 0.921 |
| Condition | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 0.982 | 0.179 | 74 | 0.682 | 1.413 | 1 | −0.099 | 0.921 |
| Condition | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 1.25 | 0.263 | 74 | 0.823 | 1.9 | 1 | 1.063 | 0.291 |
| Condition | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 1.25 | 0.263 | 74 | 0.823 | 1.9 | 1 | 1.063 | 0.291 |
| Condition | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 1.273 | 0.241 | 74 | 0.874 | 1.856 | 1 | 1.278 | 0.205 |
| Condition | ratio | SE | df | lower.CL | upper.CL | null | t.ratio | p.value |
|---|---|---|---|---|---|---|---|---|
| N / IH | 1.273 | 0.241 | 74 | 0.874 | 1.856 | 1 | 1.278 | 0.205 |
- Confidence level used: 0.95
- Intervals are back-transformed from the log scale
- Tests are performed on the log scale❖ Boxplot:
