Regression models for prediction of corn yield in the state of Paraná (Brazil) from 2012 to 2014

Seffrin, Rodolfo; Araújo, Everton Coimbra de; Bazzi, Claudio Leones

doi:10.4025/actasciagron.v40i1.36494

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Acta Scientiarum. Agronomy

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BIOMETRY, MODELING AND STATISTICS • Acta Sci., Agron. 40 • 2018 • https://doi.org/10.4025/actasciagron.v40i1.36494 copy

Regression models for prediction of corn yield in the state of Paraná (Brazil) from 2012 to 2014

Modelos de regressão para a predição da produtividade de milho no Estado do Paraná (Brasil) entre os anos de 2012 a 2014

Authorship SCIMAGO INSTITUTIONS RANKINGS

ABSTRACT.

This study aimed to identify areas that showed spatial autocorrelation for corn yield and its predictive variables (i.e., average air temperature, rainfall, solar radiation, soil agricultural potential and altitude) and to determine the most appropriate spatial regression model to explain this culture. The study was conducted using data from the municipalities of the state of Paraná relating to the summer harvests in 2011/2012, 2012/2013, and 2013/2014. The statistical diagnostic of the OLS (Ordinary Least Square regression model) was employed to determine the most suitable regression model to predict corn yield. The SAR (Spatial Lag Model) was recommended for all crop years; however, the Spatial Error Model (CAR) was recommended only for the 2013/2014 crop year. The SAR and CAR spatial regressions chosen to predict corn yield in the various years had better results when compared to a regression model that does not incorporate data spatial autocorrelation (OLS). The coefficient of determination (R²), the Bayesian information criteria (BIC) and the maximum value of the logarithm of likelihood function proved to be better for the estimation of corn yield when SAR and CAR were used.

Keywords:
autoregressive spatial model; moran’s index; spatial autocorrelation; spatial error model; spatial regression

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[1] *Author for correspondence. E-mail: seffrinrodolfo@gmail.com

	Global Moran’s I
Variables	Contiguity (Queen)			Distance between centroids			Nearest Neighbors
Variables	2011/2012	2012/2013	2013/2014	2011/2012	2012/2013	2013/2014	2011/2012	2012/2013	2013/2014
Yield	0.6263** (18.87)	0.6970** (20.37)	0.7885** (24.36)	0.6180** (21.93)	0.6879** (25.49)	0.7651** (27.42)	0.6856** (13.87)	0.7497** (14.85)	0.8306** (17.37)
SPot	0.6757** (21.19)	0.6757** (21.19)	0.6757** (21.19)	0.6000** (21.22)	0.6000** (21.22)	0.6000** (21.22)	0.7315** (15.10)	0.7315** (15.10)	0.7315** (15.10)
Alt	0.6900** (20.32)	0.6900** (20.32)	0.6900** (20.32)	0.6369** (22.74)	0.6369** (22.74)	0.6369** (22.74)	0.6945** (13.86)	0.6945** (13.86)	0.6945** (13.86)
Prec	0.8880** (27.54)	0.7898** (23.75)	0.8423** (25.83)	0.8579** (30.81)	0.7599** (27.15)	0.8029** (27.89)	0.9088** (18.94)	0.8691** (17.95)	0.8927** (17.70)
AvgT	0.9364** (28.41)	0.9299** (27.68)	0.9261** (28.94)	0.9091** (31.21)	0.9027** (31.10)	0.8997** (32.55)	0.9533** (19.51)	0.9500** (20.07)	0.9501** (20.01)
SR	0.8656** (26.58)	0.8827** (26.59)	0.8904** (27.28)	0.8500** (28.53)	0.8732** (30.81)	0.8994** (32.47)	0.9043** (18.56)	0.9257** (19.26)	0.9297** (20.03)

	Bivariate Global Moran’s I
Variables	Contiguity (Queen)			Distance from centroids			Nearest neighbors
Variables	2011/2012	2012/2013	2013/2014	2011/2012	2012/2013	2013/2014	2011/2012	2012/2013	2013/2014
Spot	0.0841** (3.69)	0.0590* (2.39)	-0.0890** (-3.67)	0.0781** (3.81)	0.0475* (2.35)	-0.0968** (-4.70)	0.0784** (2.07)	0.0499 (1.30)	-0.1141** (-3.07)
Alt	0.3043** (11.63)	0.2225** (9.33)	0.2654** (10.27)	0.2915** (12.95)	0.2134** (9.80)	0.2532** (11.88)	0.3072** (7.60)	0.2200** (5.70)	0.2722** (6.98)
Prec	0.1752** (7.04)	0.2838** (11.96)	0.4796** (18.67)	0.1794** (8.03)	0.2842** (12.57)	0.4611** (20.26)	0.1705** (4.40)	0.2950** (7.74)	0.4712** (11.40)
AvgT	-0.3049** (-11.83)	-0.2450** (-9.89)	-0.3713** (-14.22)	-0.3078** (-14.31)	-0.2486** (-11.39)	-0.3673** (-16.99)	-0.3183** (-8.46)	-0.2558** (-6.76)	-0.3746** (-9.79)
SR	-0.1421** (-5.66)	0.0234 (0.99)	-0.0754** (-3.17)	-0.1183** (-5.65)	0.0463* (2.28)	-0.0659** (-3.20)	-0.1267** (-3.49)	0.0385 (1.09)	-0.0507 (-1.37)

Crop years	${\hat{β}}_{0}$	${\hat{β}}_{1}$	${\hat{β}}_{2}$	${\hat{β}}_{3}$	${\hat{β}}_{4}$	${\hat{β}}_{5}$	LM-Error	LM-Lag	R LM-Error	R LM-Lag	R²	MVLF	BIC
2011/12							0.00	0.00	0.89	0.00	20.61	-3246.4	6528.29
2012/13	8808.30	2.33	-503.6	3.04	229.29	1.01	0.00	0.00	0.05	0.00	28.00	-3231	6497.38
2013/14	6979.09	3.84	-771.2	7.07	173.66	0.17	0.00	0.00	0.00	0.00	40.55	-3266.5	6568.38

Model	Crop years	${\hat{β}}_{0}$	${\hat{β}}_{1}$	${\hat{β}}_{2}$	${\hat{β}}_{3}$	${\hat{β}}_{4}$	${\hat{β}}_{5}$	CAR: $\hat{λ}$	R²	BP	LR	MVLF	BIC
Model	Crop years	${\hat{β}}_{0}$	${\hat{β}}_{1}$	${\hat{β}}_{2}$	${\hat{β}}_{3}$	${\hat{β}}_{4}$	${\hat{β}}_{5}$	SAR: $\hat{p}$	R²	BP	LR	MVLF	BIC
SAR	2011/12	1204	0.02	-77.82	0.43	74.10	0.87	0.81	64.06	0.89	0.00	-3128.31	6297.9
SAR	2012/13	714	0.63	-107.8	0.74	83.47	0.69	0.84	72.94	0.84	0.00	-3081.91	6205.1
CAR	2013/14	6016.6	1.51	-314.5	3.48	63.90	0.76	0.89	79.63	0.47	0.00	-3106.15	6247.6
SAR	2013/14	-608.3	0.87	-139.4	1.92	65.56	0.63	0.84	79.54	0.22	0.00	-3101.78	6244.8