19 DAPI [All layers - P12]

Di-Amidino-2-Phenyl-Indole

❖ Data

❖ Description

Variable	Description
Layer	Cerebellar layer
Mouse	Mouse unique identifier
Condition	Hypoxia condition: Normoxia (N) vs Intermittent Hypoxia (IH)
Nb_Vol	Cell density (10^(-2) cell number/μm^(3))
Avg_Distance	Average distance between cells (μm)

Variable	Description
Layer	Cerebellar layer
Mouse	Mouse unique identifier
Condition	Hypoxia condition: Normoxia (N) vs Intermittent Hypoxia (IH)
Nb_Vol	Cell density (10^(-2) cell number/μm^(3))
Avg_Distance	Average distance between cells (μm)

❖ Correlations

19.1 Cell Density (Volume)

19.1.1 Data Exploration

❖ Distribution:

Condition	Mean	SD	Variance	CoV	IQR	Min	Max	Skewness	Kurtosis	n
N	8.302	0.738	0.545	0.089	0.951	6.005	9.259	−1.273	2.697	24
IH	8.39	0.919	0.845	0.11	0.902	6.063	9.444	−1.347	1.368	17

Condition	Mean	SD	Variance	CoV	IQR	Min	Max	Skewness	Kurtosis	n
N	8.302	0.738	0.545	0.089	0.951	6.005	9.259	−1.273	2.697	24
IH	8.39	0.919	0.845	0.11	0.902	6.063	9.444	−1.347	1.368	17

Condition	Mean	SD	Variance	CoV	IQR	Min	Max	Skewness	Kurtosis	n
N	6.671	0.847	0.717	0.127	1.502	5.42	8.316	0.537	−0.908	23
IH	6.638	1.185	1.403	0.178	2.181	4.137	8.173	−0.216	−0.618	17

Condition	Mean	SD	Variance	CoV	IQR	Min	Max	Skewness	Kurtosis	n
N	6.671	0.847	0.717	0.127	1.502	5.42	8.316	0.537	−0.908	23
IH	6.638	1.185	1.403	0.178	2.181	4.137	8.173	−0.216	−0.618	17

Condition	Mean	SD	Variance	CoV	IQR	Min	Max	Skewness	Kurtosis	n
N	8.19	1.312	1.723	0.16	1.152	4.265	9.711	−1.995	4.391	24
IH	7.788	1.315	1.73	0.169	0.488	4.347	8.673	−2.409	4.757	17

Condition	Mean	SD	Variance	CoV	IQR	Min	Max	Skewness	Kurtosis	n
N	8.19	1.312	1.723	0.16	1.152	4.265	9.711	−1.995	4.391	24
IH	7.788	1.315	1.73	0.169	0.488	4.347	8.673	−2.409	4.757	17

19.1.2 Models & Diagnostics

Exploring some Generalized Linear (Mixed) model candidates:

Gamma (‘log’)
Gaussian (‘log’)

❖ Model call:

```{r}
glmmTMB(formula = Nb_Vol ~ Condition * Layer + (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
411.50	412.77	433.93	0.51	0.28	0.32	0.85	0.13

AIC	AICc	BIC	R2_conditional	R2_marginal	ICC	RMSE	Sigma
411.50	412.77	433.93	0.51	0.28	0.32	0.85	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:

❖ Model call:

```{r}
glmmTMB(formula = Nb_Vol ~ Condition * Layer + (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
390.35	391.62	412.78	0.02	0.01	8.36e-03	0.86	0.91

AIC	AICc	BIC	R2_conditional	R2_marginal	ICC	RMSE	Sigma
390.35	391.62	412.78	0.02	0.01	8.36e-03	0.86	0.91

❖ 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:

19.1.3 Effects Analysis

Chosen model: Gamma (‘log’)

```{r}
glmmTMB(formula = Nb_Vol ~ Condition * Layer + (1 | Mouse), data = data, 
    family = Gamma("log"), REML = TRUE, ziformula = ~0, dispformula = ~1)
```

19.1.3.1 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)	7.570	0.227	(7.14, 8.03)	67.563	< .001
Condition1	1.010	0.030	(0.95, 1.07)	0.348	0.728
Layer1	1.096	0.019	(1.06, 1.13)	5.363	< .001
Layer2	0.871	0.015	(0.84, 0.90)	-8.047	< .001
Condition1 * Layer1	0.987	0.017	(0.95, 1.02)	-0.765	0.444
Condition1 * Layer2	0.998	0.017	(0.96, 1.03)	-0.130	0.897
Model: Nb_Vol ~ Condition * Layer (122 Observations)

Parameter	Coefficient	SE	95% CI	z	p
(Intercept)	7.570	0.227	(7.14, 8.03)	67.563	< .001
Condition1	1.010	0.030	(0.95, 1.07)	0.348	0.728
Layer1	1.096	0.019	(1.06, 1.13)	5.363	< .001
Layer2	0.871	0.015	(0.84, 0.90)	-8.047	< .001
Condition1 * Layer1	0.987	0.017	(0.95, 1.02)	-0.765	0.444
Condition1 * Layer2	0.998	0.017	(0.96, 1.03)	-0.130	0.897
Model: Nb_Vol ~ Condition * Layer (122 Observations)

❖ Main effects (Wald Chi-Square):

car::Anova(mod, type = 3)

term	statistic	df	p.value
Condition	0.12	1	0.730
Layer	67.09	2	<0.001 ***
Condition:Layer	0.94	2	0.630

term	statistic	df	p.value
Condition	0.12	1	0.730
Layer	67.09	2	<0.001 ***
Condition:Layer	0.94	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	370.11	384.13	-180.05	360.11
mod_full	8	375.00	397.43	-179.50	359.00	1.11	3	0.770

model	df	aic	bic	log_lik	deviance	chisq	chi_df	pr_chisq
mod_reduced	5	370.11	384.13	-180.05	360.11
mod_full	8	375.00	397.43	-179.50	359.00	1.11	3	0.770

Important

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

19.1.3.2 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	7.649	0.306	120	7.067	8.279
IH	7.491	0.334	120	6.858	8.183

Condition	response	SE	df	lower.CL	upper.CL
N	7.649	0.306	120	7.067	8.279
IH	7.491	0.334	120	6.858	8.183

- Results are averaged over the levels of: Layer
- 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	1.021	0.061	120	0.907	1.15	1	0.348	0.729

contrast	ratio	SE	df	lower.CL	upper.CL	null	t.ratio	p.value
N / IH	1.021	0.061	120	0.907	1.15	1	0.348	0.729

- Results are averaged over the levels of: Layer
- 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")

Layer	response	SE	df	lower.CL	upper.CL
EGL	8.294	0.286	120	7.748	8.879
ML	6.595	0.228	120	6.159	7.062
IGL	7.93	0.273	120	7.406	8.49

Layer	response	SE	df	lower.CL	upper.CL
EGL	8.294	0.286	120	7.748	8.879
ML	6.595	0.228	120	6.159	7.062
IGL	7.93	0.273	120	7.406	8.49

- 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
EGL / ML	1.258	0.037	120	1.186	1.334	1	7.741	<0.001 ***
EGL / IGL	1.046	0.031	120	0.987	1.109	1	1.525	0.130
ML / IGL	0.832	0.025	120	0.784	0.882	1	−6.22	<0.001 ***

contrast	ratio	SE	df	lower.CL	upper.CL	null	t.ratio	p.value
EGL / ML	1.258	0.037	120	1.186	1.334	1	7.741	<0.001 ***
EGL / IGL	1.046	0.031	120	0.987	1.109	1	1.525	0.130
ML / IGL	0.832	0.025	120	0.784	0.882	1	−6.22	<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	8.273	0.377	120	7.559	9.054
IH	8.316	0.429	120	7.508	9.211

Condition	response	SE	df	lower.CL	upper.CL
N	8.273	0.377	120	7.559	9.054
IH	8.316	0.429	120	7.508	9.211

Condition	response	SE	df	lower.CL	upper.CL
N	6.649	0.305	120	6.072	7.281
IH	6.541	0.338	120	5.905	7.245

Condition	response	SE	df	lower.CL	upper.CL
N	6.649	0.305	120	6.072	7.281
IH	6.541	0.338	120	5.905	7.245

Condition	response	SE	df	lower.CL	upper.CL
N	8.136	0.371	120	7.434	8.904
IH	7.729	0.4	120	6.976	8.563

Condition	response	SE	df	lower.CL	upper.CL
N	8.136	0.371	120	7.434	8.904
IH	7.729	0.4	120	6.976	8.563

- 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	0.995	0.068	120	0.868	1.14	1	−0.076	0.939

contrast	ratio	SE	df	lower.CL	upper.CL	null	t.ratio	p.value
N / IH	0.995	0.068	120	0.868	1.14	1	−0.076	0.939

contrast	ratio	SE	df	lower.CL	upper.CL	null	t.ratio	p.value
N / IH	1.017	0.07	120	0.887	1.166	1	0.237	0.813

contrast	ratio	SE	df	lower.CL	upper.CL	null	t.ratio	p.value
N / IH	1.017	0.07	120	0.887	1.166	1	0.237	0.813

contrast	ratio	SE	df	lower.CL	upper.CL	null	t.ratio	p.value
N / IH	1.053	0.073	120	0.918	1.207	1	0.745	0.458

contrast	ratio	SE	df	lower.CL	upper.CL	null	t.ratio	p.value
N / IH	1.053	0.073	120	0.918	1.207	1	0.745	0.458

- Confidence level used: 0.95
- Intervals are back-transformed from the log scale
- Tests are performed on the log scale

emmeans(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	0.979	0.058	120	0.87	1.1	1	−0.365	0.715

Condition	ratio	SE	df	lower.CL	upper.CL	null	t.ratio	p.value
N / IH	0.979	0.058	120	0.87	1.1	1	−0.365	0.715

Condition	ratio	SE	df	lower.CL	upper.CL	null	t.ratio	p.value
N / IH	0.945	0.056	120	0.841	1.062	1	−0.96	0.339

Condition	ratio	SE	df	lower.CL	upper.CL	null	t.ratio	p.value
N / IH	0.945	0.056	120	0.841	1.062	1	−0.96	0.339

Condition	ratio	SE	df	lower.CL	upper.CL	null	t.ratio	p.value
N / IH	0.966	0.057	120	0.859	1.086	1	−0.59	0.556

Condition	ratio	SE	df	lower.CL	upper.CL	null	t.ratio	p.value
N / IH	0.966	0.057	120	0.859	1.086	1	−0.59	0.556

- Confidence level used: 0.95
- Intervals are back-transformed from the log scale
- Tests are performed on the log scale

❖ Boxplot:

19.2 Average distance between cells

19.2.1 Data Exploration

❖ Distribution:

Condition	Mean	SD	Variance	CoV	IQR	Min	Max	Skewness	Kurtosis	n
N	9.251	0.309	0.095	0.033	0.499	8.783	9.959	0.465	−0.424	24
IH	9.145	0.402	0.162	0.044	0.513	8.595	10.171	0.941	1.19	17

Condition	Mean	SD	Variance	CoV	IQR	Min	Max	Skewness	Kurtosis	n
N	9.251	0.309	0.095	0.033	0.499	8.783	9.959	0.465	−0.424	24
IH	9.145	0.402	0.162	0.044	0.513	8.595	10.171	0.941	1.19	17

Condition	Mean	SD	Variance	CoV	IQR	Min	Max	Skewness	Kurtosis	n
N	10.445	0.458	0.209	0.044	0.623	9.524	11.193	−0.529	−0.422	23
IH	10.534	0.327	0.107	0.031	0.568	10.028	11.132	0.398	−0.806	17

Condition	Mean	SD	Variance	CoV	IQR	Min	Max	Skewness	Kurtosis	n
N	10.445	0.458	0.209	0.044	0.623	9.524	11.193	−0.529	−0.422	23
IH	10.534	0.327	0.107	0.031	0.568	10.028	11.132	0.398	−0.806	17

Condition	Mean	SD	Variance	CoV	IQR	Min	Max	Skewness	Kurtosis	n
N	8.937	0.323	0.104	0.036	0.392	8.331	9.817	0.374	1.329	24
IH	9.13	0.162	0.026	0.018	0.289	8.901	9.404	0.122	−1.165	17

Condition	Mean	SD	Variance	CoV	IQR	Min	Max	Skewness	Kurtosis	n
N	8.937	0.323	0.104	0.036	0.392	8.331	9.817	0.374	1.329	24
IH	9.13	0.162	0.026	0.018	0.289	8.901	9.404	0.122	−1.165	17

19.2.2 Models & Diagnostics

Exploring some Generalized Linear (Mixed) model candidates:

Gamma (‘log’)
Gaussian (‘log’)

❖ Model call:

```{r}
glmmTMB(formula = Avg_Distance ~ Condition * Layer + (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
130.79	132.07	153.22	0.83	0.77	0.29	0.28	0.03

AIC	AICc	BIC	R2_conditional	R2_marginal	ICC	RMSE	Sigma
130.79	132.07	153.22	0.83	0.77	0.29	0.28	0.03

❖ 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 = Avg_Distance ~ Condition * Layer + (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
132.11	133.39	154.55	0.05	0.05	4.78e-03	0.28	0.30

AIC	AICc	BIC	R2_conditional	R2_marginal	ICC	RMSE	Sigma
132.11	133.39	154.55	0.05	0.05	4.78e-03	0.28	0.30

❖ 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:

19.2.3 Effects Analysis

Chosen model: Gamma (‘log’)

```{r}
glmmTMB(formula = Avg_Distance ~ Condition * Layer + (1 | Mouse), 
    data = data, family = Gamma("log"), REML = TRUE, ziformula = ~0, 
    dispformula = ~1)
```

19.2.3.1 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)	9.548	0.063	(9.42, 9.67)	340.030	< .001
Condition1	0.997	0.007	(0.98, 1.01)	-0.460	0.646
Layer1	0.963	0.004	(0.96, 0.97)	-9.395	< .001
Layer2	1.098	0.004	(1.09, 1.11)	23.128	< .001
Condition1 * Layer1	1.009	0.004	(1.00, 1.02)	2.256	0.024 *
Condition1 * Layer2	0.998	0.004	(0.99, 1.01)	-0.380	0.704
Model: Avg_Distance ~ Condition * Layer (122 Observations)

Parameter	Coefficient	SE	95% CI	z	p
(Intercept)	9.548	0.063	(9.42, 9.67)	340.030	< .001
Condition1	0.997	0.007	(0.98, 1.01)	-0.460	0.646
Layer1	0.963	0.004	(0.96, 0.97)	-9.395	< .001
Layer2	1.098	0.004	(1.09, 1.11)	23.128	< .001
Condition1 * Layer1	1.009	0.004	(1.00, 1.02)	2.256	0.024 *
Condition1 * Layer2	0.998	0.004	(0.99, 1.01)	-0.380	0.704
Model: Avg_Distance ~ Condition * Layer (122 Observations)

❖ Main effects (Wald Chi-Square):

car::Anova(mod, type = 3)

term	statistic	df	p.value
Condition	0.21	1	0.650
Layer	541.49	2	<0.001 ***
Condition:Layer	5.85	2	0.050 *

term	statistic	df	p.value
Condition	0.21	1	0.650
Layer	541.49	2	<0.001 ***
Condition:Layer	5.85	2	0.050 *

❖ Main effects (Likelihood Ratio Test):

LRT(mod, pred = "Condition")

model	df	aic	bic	log_lik	deviance	chisq	chi_df	pr_chisq
mod_reduced	5	76.84	90.86	-33.42	66.84
mod_full	8	76.70	99.13	-30.35	60.70	6.15	3	0.100

model	df	aic	bic	log_lik	deviance	chisq	chi_df	pr_chisq
mod_reduced	5	76.84	90.86	-33.42	66.84
mod_full	8	76.70	99.13	-30.35	60.70	6.15	3	0.100

Important

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

19.2.3.2 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	9.519	0.084	120	9.354	9.687
IH	9.577	0.095	120	9.391	9.767

Condition	response	SE	df	lower.CL	upper.CL
N	9.519	0.084	120	9.354	9.687
IH	9.577	0.095	120	9.391	9.767

- Results are averaged over the levels of: Layer
- 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	0.994	0.013	120	0.968	1.02	1	−0.46	0.647

contrast	ratio	SE	df	lower.CL	upper.CL	null	t.ratio	p.value
N / IH	0.994	0.013	120	0.968	1.02	1	−0.46	0.647

- Results are averaged over the levels of: Layer
- 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")

Layer	response	SE	df	lower.CL	upper.CL
EGL	9.195	0.071	120	9.055	9.337
ML	10.481	0.082	120	10.321	10.644
IGL	9.032	0.07	120	8.895	9.172

Layer	response	SE	df	lower.CL	upper.CL
EGL	9.195	0.071	120	9.055	9.337
ML	10.481	0.082	120	10.321	10.644
IGL	9.032	0.07	120	8.895	9.172

- 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
EGL / ML	0.877	0.006	120	0.865	0.889	1	−18.781	<0.001 ***
EGL / IGL	1.018	0.007	120	1.004	1.032	1	2.573	0.011 *
ML / IGL	1.16	0.008	120	1.144	1.177	1	21.339	<0.001 ***

contrast	ratio	SE	df	lower.CL	upper.CL	null	t.ratio	p.value
EGL / ML	0.877	0.006	120	0.865	0.889	1	−18.781	<0.001 ***
EGL / IGL	1.018	0.007	120	1.004	1.032	1	2.573	0.011 *
ML / IGL	1.16	0.008	120	1.144	1.177	1	21.339	<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	9.25	0.095	120	9.065	9.44
IH	9.14	0.106	120	8.932	9.353

Condition	response	SE	df	lower.CL	upper.CL
N	9.25	0.095	120	9.065	9.44
IH	9.14	0.106	120	8.932	9.353

Condition	response	SE	df	lower.CL	upper.CL
N	10.433	0.108	120	10.222	10.648
IH	10.529	0.123	120	10.289	10.775

Condition	response	SE	df	lower.CL	upper.CL
N	10.433	0.108	120	10.222	10.648
IH	10.529	0.123	120	10.289	10.775

Condition	response	SE	df	lower.CL	upper.CL
N	8.937	0.091	120	8.758	9.12
IH	9.128	0.106	120	8.92	9.341

Condition	response	SE	df	lower.CL	upper.CL
N	8.937	0.091	120	8.758	9.12
IH	9.128	0.106	120	8.92	9.341

- 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	1.012	0.016	120	0.981	1.044	1	0.775	0.440

contrast	ratio	SE	df	lower.CL	upper.CL	null	t.ratio	p.value
N / IH	1.012	0.016	120	0.981	1.044	1	0.775	0.440

contrast	ratio	SE	df	lower.CL	upper.CL	null	t.ratio	p.value
N / IH	0.991	0.015	120	0.961	1.022	1	−0.589	0.557

contrast	ratio	SE	df	lower.CL	upper.CL	null	t.ratio	p.value
N / IH	0.991	0.015	120	0.961	1.022	1	−0.589	0.557

contrast	ratio	SE	df	lower.CL	upper.CL	null	t.ratio	p.value
N / IH	0.979	0.015	120	0.949	1.01	1	−1.364	0.175

contrast	ratio	SE	df	lower.CL	upper.CL	null	t.ratio	p.value
N / IH	0.979	0.015	120	0.949	1.01	1	−1.364	0.175

- Confidence level used: 0.95
- Intervals are back-transformed from the log scale
- Tests are performed on the log scale

emmeans(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	1.021	0.014	120	0.994	1.05	1	1.519	0.131

Condition	ratio	SE	df	lower.CL	upper.CL	null	t.ratio	p.value
N / IH	1.021	0.014	120	0.994	1.05	1	1.519	0.131

Condition	ratio	SE	df	lower.CL	upper.CL	null	t.ratio	p.value
N / IH	1.034	0.014	120	1.006	1.062	1	2.389	0.018 *

Condition	ratio	SE	df	lower.CL	upper.CL	null	t.ratio	p.value
N / IH	1.034	0.014	120	1.006	1.062	1	2.389	0.018 *

Condition	ratio	SE	df	lower.CL	upper.CL	null	t.ratio	p.value
N / IH	1.012	0.014	120	0.984	1.04	1	0.859	0.392

Condition	ratio	SE	df	lower.CL	upper.CL	null	t.ratio	p.value
N / IH	1.012	0.014	120	0.984	1.04	1	0.859	0.392

- Confidence level used: 0.95
- Intervals are back-transformed from the log scale
- Tests are performed on the log scale

❖ Boxplot: