基于混合效应模型和零膨胀模型方法的蒙古栎林分水平枯损模型

doi:10.11707/j.1001-7488.20191104

Abstract

Abstract:

Objective: As an important component of forest growth yield systems,it is necessary to make accurate prediction for stand mortality. Method: About 295 permanent sample plots were established across the natural range of Mongolian oak in the Jilin Province in 1994. All plots were measured every 5 years,and the data were measured three times. 236 plots were used as simulation data and the other 59 plots as validation data. The main objective of this study was to construct stand-level mortality model of Quercus mongolica in relation to stand factor,site factor and climate factor. The basic forms of the model include Poisson distribution model and negative binomial distribution model. Considering the existence of a large number of zero values in the sample plots,the zero-inflated and zero-altered models were added to these basic models. In order to solve the problem of nesting and longitudinal data,the random effects of sample plot were taken into account in the construction of the model. In the end,the validation data was used to verify. Result: The results showed that the basal area of hectare,the number per hectare and the mean warmest month temperature are the most important factors influencing the probability and quantity of mortality. The simulation precision of the model was improved obviously after considering the plot random effects. Due to the over-dispersed of the data the accuracy of the negative binomial distribution model was higher than that of the Poisson distribution. Conclusion: The simulation effects of the model were the best when considering the random effects and the zero-inflated negative binomial distribution model simultaneously. The validation result also supported this conclusion.

Key words: generalized linear mixed-effects models, zero-inflated model, Mongolian oak(Quercus mongolica), mortality, stand

CLC Number:

S757

Chunming Li,Lifang Zhao,Lixue Li. Modeling Stand-Level Mortality of Mongolian Oak(Quercus mongolica)Based on Mixed Effect Model and Zero-Inflated Model Methods[J]. Scientia Silvae Sinicae, 2019, 55(11): 27-36.

Figures/Tables 6

Table 1

Table 2

Table 3

The simulation results of stand-level mortality model"

参数 Parameters			基础模型Basic model
			标准泊松分布 Standard Poisson	零膨胀泊松分布 ZIP	零改变泊松分布 ZAP	标准负二项分布 Standard NB	零膨胀负二项分布 ZINB	零改变负二项分布 ZANB
			M1	M2	M3	M4	M5	M6
不考虑随机效应 Without random effect	模型的零部分 Zero component of the model	α₀		-1.031 9 (0.500 4)^*	-1.031 9 (0.500 4)^*		-1.030 1 (0.501 4)^*	-1.031 9 (0.500 4)^*
		α₁		0.064 8 (0.020 6)^**	0.064 8 (0.020 6)^**		0.064 9 (0.020 6)^**	0.064 8 (0.020 6)^**
		α₂		1.620 8 (0.404 6)^***	1.620 8 (0.404 6)^***		1.619 9 (0.405 6)^***	1.620 7 (0.404 6)^***
	计数的部分 Positive count component of the model	β₀	3.060 0 (0.017 6)^***	3.408 7 (0.018 1)^***	3.408 7 (0.018 1)^***	2.876 1 (0.167 6)^***	3.345 1 (0.119 6)^***	3.345 1 (0.119 6)^***
		β₁	0.018 2 (0.000 5)^***	0.012 8 (0.000 5)^***	0.012 7 (0.000 5)^***	0.022 1 (0.006 0)^***	0.013 9 (0.004 1)^***	0.013 9 (0.004 1)^**
		β₂	0.718 6 (0.006 9)^***	0.633 8 (0.007 0)^***	0.633 8 (0.007 0)^***	0.774 9 (0.084 9)^***	0.656 1 (0.057 2)^***	0.656 1 (0.057 2)^***
		k				1.017 2	0.434 7	0.434 7
	AIC		27 132	21 228	21 228	5 167.6	4 916.2	4 916.2
	BIC		27 144	21 253	21 253	5 184.2	4 945.3	4 945.3
	-2LogL		27 126	21 216	21 216	5 159.6	4 902.2	4 902.2
考虑随机效应 With random effect			M7	M8	M9	M10	M11	M12
	模型的零部分 Zero component of the model	α₀		-1.007 3 (0.506 3)^*	-1.031 9 (0.500 4)^*		-1.030 4 (0.501 0)^*	-1.031 9 (0.500 4)^*
		α₁		0.064 1 (0.020 7)^**	0.064 8 (0.020 6)^**		0.064 8 (0.020 6)^**	0.064 8 (0.020 6)^**
		α₂		1.615 4 (0.405 9)^***	1.620 8 (0.404 6)^***		1.620 1 (0.405 1)^***	1.620 8 (0.404 6)^***
	计数的部分 Positive count component of the model	β₀	-0.276 6 (0.121 2)^*	0.692 2 (0.112 0)^***	0.696 6 (0.111 5)^***	2.758 9 (0.282 7)^***	3.218 7 (0.137 5)^***	3.221 5 (0.137 7)^***
		β₁	0.1310 (0.002 5)^***	0.111 5 (0.002 6)^***	0.111 4 (0.002 6)^***	0.023 0 (0.007 1)^**	0.016 2 (0.004 4)^**	0.016 2 (0.004 4)^**
		β₂	0.895 2 (0.033 4)^***	0.686 3 (0.033 9)^***	0.685 6 (0.033 8)^***	0.824 3 (0.112 1)^***	0.677 1 (0.061 8)^***	0.676 8 (0.061 7)^***
		k				1.053 9	0.370 3	0.371 4
	AIC		11 680	9 597.4	9 597.7	5 170.6	4 912.7	4 913.1
	BIC		11 694	9 621.6	9 621.9	5 188.0	4 940.5	4 940.8
	-2logL		11 672	9 583.4	9 583.7	5 160.6	4 896.7	4 897.1
	随机效应方差协方差矩阵D		1.779 8	1.084 5	1.082 2	0.001 0	0.074 1	0.072 0

Table 3

Table 4

Table 5

Table 6

References 0

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枯损影响因子 Effect factor		指标Indicator	平均值(标准差) Mean(standard error)	最大值Max.	最小值Min.
林分因子 Stand factor	1999	胸径DBH/cm	12.7(7.5)	82.7	5.0
		林分平均直径Mean diameter/cm	15.3(4.2)	30.9	6.3
		断面积Basal area/(m²·hm^-2)	22.9(9.4)	57.7	3.0
		株数Number of stems/hm^-2	1343(621)	3 317	250
	2004	胸径DBH/cm	12.9(7.6)	83.6	5
		林分平均直径Mean diameter/cm	15.7(4.1)	31.3	6.3
		断面积Basal area/(m²·hm^-2)	24.1(8.8)	59.7	3.8
		株数Number of stems/hm^-2	1 370(618)	3 250	350
	2009	胸径DBH/cm	13.5(8.0)	84.9	5.0
		林分平均直径Mean diameter/cm	16.5(4.1)	32.6	6.6
		断面积Basal area/(m²·hm^-2)	26.2(8.5)	61.2	7.3
		株数Number of stems/hm^-2	1 347(584)	3 550	367
		海拔Elevation/m	596(196)	1 280	100
立地因子 Site factor		坡度Slope/(°)	21(8.5)	45	0
立地因子 Site factor		坡向Aspect	按方位角从0~360°，共分成9个坡向It is divided into 9 aspects according to the azimuth angle from 0° to 360°

气象因子 Climate variables	最小 Min.	最大 Max.	平均 Mean
年平均温度Mean annual temperature(MAT)/℃	1.34	6.56	3.93
最暖月平均气温Mean warmest month temperature(MWMT)/℃	18.30	23.58	20.91
最冷月平均气温Mean coldest month temperature(MCMT)/℃	-19.00	-11.50	-16.08
年降水量Mean annual precipitation(MAP)/mm	498.60	1 139.20	675.81
年平均夏季(5—9月)降水量 Mean annual summer (May to Sept.) precipitation(MSP)/mm	389.80	884.20	527.15
无霜期天数The number of frost-free days(NFFD)/d	154.80	196.80	175.30
上一年8月至当年7月的降雪量 Precipitation as snow between Aug. in previous year and Jul. in current year(PAS)/mm	35.20	154.60	67.73

模型Model	LRT	P
M1/M2	5 910	< 0.000 1
M4/M5	257.4	< 0.000 1
M1/M7	15 454	< 0.000 1
M4/M10	1	>0.05
M1/M3	5 910	< 0.000 1
M4/M6	257.4	< 0.000 1
M2/M8	11 632.6	< 0.000 1
M5/M11	5.5	0.023
M2/M3	0	1
M5/M6	0	1
M3/M9	11 632.3	< 0.000 1
M6/M12	5.1	0.028

参数 Parameter	考虑气象因子的零膨胀负二项分布模拟结果M13 ZINB with climate variables		考虑气象因子及随机效应的零膨胀负二项分布模拟结果M14 Random ZINB with climate variables
参数 Parameter	模拟值Simulated value	P	模拟值Simulated value	P
α₀	-133.57 (44.324 1)	0.002 7	-133.56 (44.316 3)	0.002 9
α₁	0.169 5 (0.065 6)	0.010 2	0.169 5 (0.065 6)	0.010 5
α₂	4.152 6 (1.771 7)	0.019 5	4.152 7 (1.771 4)	0.019 9
α₃	5.985 0 (1.999 2)	0.002 9	5.984 7 (1.998 9)	0.003 0
β₀	3.345 5 (0.957 8)	0.000 5	3.373 5 (1.026 8)	0.001 2
β₁	0.013 9 (0.004 3)	0.001 6	0.016 0 (0.004 7)	0.000 8
β₂	0.655 8 (0.058 6)	< 0.000 1	0.675 2 (0.062 9)	< 0.000 1
β₃	0.000 1(0.038 91)	0.999 6	-0.006 3 (0.041 9)	0.879 3
AIC	4 681.2		4 677.6
BIC	4 718.6		4 712.3
-2logL	4 663.2		4 657.6
k	0.433 6		0.369 1
随机效应方差 Random effect matrix			0.074 8

评价指标 Evaluating indicator	不考虑随机效应 Without random effect						考虑随机效应 With random effect
评价指标 Evaluating indicator	M1	M2	M3	M4	M5	M6	M7	M8	M9	M10	M11	M12	M13	M14
R²	0.87	0.89	0.89	0.87	0.89	0.89	0.89	0.85	0.85	0.89	0.89	0.89	0.88	0.83
RMSE	82.1	85.7	85.7	75.7	83.4	83.4	73.9	76.1	76.1	78.9	74.8	78.8	85.2	87.8
\|${\bar E}$\|	60.5	61.6	61.6	55.2	59.8	59.8	48.4	51.7	51.7	53.4	51.6	53.6	64.6	67.6

Modeling Stand-Level Mortality of Mongolian Oak(Quercus mongolica)Based on Mixed Effect Model and Zero-Inflated Model Methods

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