《SPSS非线性回归》由会员分享，可在线阅读，更多相关《SPSS非线性回归（79页珍藏版）》请在金锄头文库上搜索。
1、SPSS数据统计分析与实践主讲：周涛副教授北京师范大学资源学院2007-12-18教学网站：http:/ 非线性回归概述2. SPSS实例常用的非线性模型SPSS procedures for Regression1. The Nonlinear Regression procedure allows you to create powerful and flexible models for nonlinear relationships between a dependent variable and one or more independent variables2. The Line
2、ar Regression procedure provides more statistics for models that are intrinsically linear.3. The Curve Estimation procedure allows you to more easily specify certain nonlinear models,and can be useful for quickly comparing several different types of modelsLinear vs. Nonlinear models Regression model
3、s, whether linear or nonlinear, assume that the form of the model is Y=F(X，B) +error5 where Y is the dependent variable, X represents the predictors, and F is a function of X. In linear models, F is of the form:F(X,B) =工b/jWhere Xj is the jth predictor, and bj is the jth regression coefficient. Note
4、 that for a model to be considered linear, F must be a linear function of the parameters, not necessarily the predictors Thus, y=bx2 + error is a linear model. Additionally, some models in which the error is multiplicative, such as y=ebxerror5 are linear models under the log-transformation: ln(y) =
5、bx + In(error) These model are known as intrinsically linear. Nonlinear models are all frms of F njLParameters estimation in Nonlinear Regression A differenee from linear regression is that the solution of the normal equations usually requires an iterative numerical search procedure because analytic
6、al solutionsgen erally cannot be found.To make things still more difficult, multiple solutions may be possible.Examples for Search methodsNoisy data: Hill climbing tioc effective, even with multiple tries.Parameter #1Iterath e improv emeut of initial parameter values toward the global objective func
7、tion minimum卑 JgalueJecJHill climbing finds the local, bur not global maximum-Genetic Algorithm generamany possiblescenarios r then ref ines th巳 search based on the feedback it receivesMethods of parameter estimation (1)解析解(Analytic solution)梯度下降算法(Gradient descent algorithms) Steepest-descent quasi
8、-Newton Levenberg-Marquardt剃度下降法的优点：速度快算法相对简单缺点：通常只能找到Local minimum, 需要提供Gradient vector/yJ = dJ/dykMethods of parameter estimation (2)解析解(Analytic solution)梯度下降算法(Gradient descent algorithms)全参数空间搜索算法(Global search methods)优点：能搜索到全局最优参数(Global minimum)很多算法不需要提供Gradient vector缺点：速度慢,需要消耗较大的计算时间代表性算法
9、:模拟退火(Simulated annealing)遗传算法(Genetic Algorithms)马尔可夫链蒙特卡洛法(Markov chain Monte Carlo)ExampleExampleEvemeen Needleleaf Forest (ENF)DeciduousBroadleaf Forest (DBF)Zvlixed Forest (MF)bodland(W)Wooded Grassland WG)Shmbland (S)Grassland (G)Cropland (C) s0.36O.OS0-47 0. 030-43 0.010.40 0.030-55 0. 010-24
10、 Q. 100.56 t o. 0208 0.06aL0.33 0.030.37 0.020.40 0.010.34 0.020.31 io. 010.34 0.110.42 X 0- 020-76 iO. 0450.33 10.030.37 0.020.40 0. 010.33 0.030.31 0.010.07 0. 05一gR0.34 0.060.26 0.040.20 0.020.33 0. 050.3S 0.010.56 土 d 110.53 0. 020.24 0.04细0.590.080.59 0.090.64 0.C60.53 0.050.58 0. 060.55 0. 070
11、.61 10. 040.50 0.07034 10.070.31 0.03029 0. 04031 0.040.31 0. 030.34 0.060.31 0.0$034 0.066 30.07 0.0203 0.040.07 0. 030.31 0. 040_12 土0.040.11 土 0. 050.03 tO. 010_160.07rI2.730.M1.00 0.001.44 0.022.03 0.041.60 0.053.90 L 390.59 tO. 040.2fi0.19Tw96.7 1.4130.7 0.2939.7 0. 47.7 土 1.0336.3 1.25109 83.
12、B2一&F0.42 0.150.32 0.200.04 0.07033 0.170.29 0.210.37 土0. It0.01 0.020.01 土 0.020.00 0.000.01 0. 010.07 0. OS0.00 0.0C0.06 0.120.00 0. 020.100.000.10 0. 010.01 0.020.10 0. 000_09 0.010.10 土 CL 009.81 0.318.55 1.619.95 0. 206.83 1.719.9S10.0S6.7& 1. 654.71 0. 250.77 0.3317 2 3 .6811-9 4 12IO 1.719.47
13、 2.6319.fi 0. 929.19 1.694.73 0. 251.17 0.3247.9 2.452.411.S45.2 9. 2917.9 6. 294Q.411.2225.S 7. St4.73 tO. 2$1J410.250.S3 0.63O.Si 0.550.94 0. 590.90 0.430.91 0.590.87 0. 650.17 10. Cl0.94 iO. 306.01 0.1Q3.62 0. 032.7S 0. 033.15 0.06L97 10.063.62 2. 947.74 4.3630.2 4. 7219.4 5. IS8.QJ i3.667.42 3.1110.1 3.980.190. S-&lJ.Oi6.0511.2 3.7332.5 4.1224.0 3. 4011.1 4.2CiO S 2. 061$. 3. StS.47 0. 6917 J 6.5536 0 6.4530.2 10. 9533 11.4824.(5 7.9923 0 5.8752.S 15. 5222.92.2135.4 23. S0.03 10.030.05 0.050.05 0.03-0.07 0.040.0
