Table 4 Effects of fertilizer and year on shoot nitrogen content, shoot dry matter weight, and brown rice yield analyzed by the general linear mixed model (GLMM) with nested random effects.

Explanatory variable		Response variable
		Nitrogen content (kg ha⁻¹)			Dry matter weight (t ha⁻¹)			Brown rice yield (t ha⁻¹)
		Coefficient	Probability		Coefficient	Probability		Coefficient	Probability
Fixed effect
Intercept		55.1	0.001	**	8.65	< 0.001	***	3.56	0.002	**
Fertilizer	1–0	5.0	0.599		0.95	0.335		0.59	0.361
	1–1	2.1	0.825		0.54	0.575		0.53	0.406
	2–0	31.0	0.018	*	3.16	0.017	*	1.84	0.025	*
	2–1	23.5	0.046	*	1.81	0.099	.	1.03	0.139
	3–0	10.2	0.310		0.85	0.387		0.92	0.177
Year	2021	34.8	< 0.001	***	1.00	0.001	**	0.60	0.002	**
Random effect
Location		33.85			0.1699			0.1696
	Kaya	-3.49			-0.22			-0.25
	Ishikawa	+ 3.49			+ 0.22			+ 0.25
Field within location		33.56			0.5600			0.2421
Residual		180.41			0.9557			0.3936
Model fit
Marginal R² (Fixed Effects)		0.643			0.445			0.344
Conditional R² (Fixed + Random Effects)		0.740			0.685			0.680

Shoot nitrogen content, shoot dry matter weight, and brown rice yield were analyzed with fertilizer and year as fixed effects, and location and field nested within location as random effects. The model structure can be expressed as: response ~ fertilizer + year + (1|location/field). Values in the random effect section represent variance components. Values under location names represent Best Linear Unbiased Predictions (BLUPs), showing deviations from the overall mean. Positive values indicate higher than average responses, while negative values indicate lower than average responses. ‘***’, ‘**’, ‘*’, ‘.’ indicate 0.1, 1, 5, and 10% levels of significance, respectively. Marginal R² represents the proportion of variance explained by fixed effects only, while Conditional R² represents the proportion of variance explained by both fixed and random effects.

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