Application Of EM Algorithm In Real Estate Hedonic Model

With the formation of the real estate market in China,the questions of housing pricebecome one of the academic focuses.Domestic scholars mainly carry on qualitative study fromthe supply-demand relationship,the composition of the housing price,housing policy etc.Since2002 there is a few domestic scholar begin to research the urban housing price used hedonictheory and model,obtained the quantitative relation between the housing characteristic andhousing price.This paper discussed the case of missing data when we applied hedonic modelto the research of real estate price,and used EM algorithm to estimate the parameter.In chapter one,we introduced the theoretics foundation and the function of hedonicmodel,and the apply of hedonic model in real estate price research.Three models of real estate hedonic model:1. Linear Model:Theβi is the characteristic price.It shows the housing price change when the characteristicvariable changed one unit.2. Half-log Model:Theβi shows the percentage of housing price change when the characteristic variablechanged one unit.3. Log Model:We suppose the housing price increased along with the characteristic's increase,it can be expressed by this function:Make it linear,we get the log model:Theβi is the ?exibility coe?cient of the characteristic variable.It shows the percentageof housing price change when the characteristic variable changed one percent.In application of hedonic model, how to select the characteristic variables and measurethem is an important step. The characteristics can be classified to three group, building,environment and location. We used expert grade method and market research method tomeasure the characteristic variables.In chapter two ,we reviewed the theory of EM algorithm,and gave the algorithm ofestimating the parameter in hedonic model,when there is one missing variable in model ortwo alternate missing variable.EM arithmetic:E-step:M-step:Get theθi+1 which is the maximum value of Q aboutθ,compute untilθi+1 ?θior Q(θi+1,θi) ? Q(θi,θi) is small enough.First,we gave the theory of 2.1,n observations,joint conditional density is the productof all little observations'value.We used the theory in E step to get the joint conditional expectation of missing data.Then, we gave the algorithm of one missing variable and two alternate missing variable. One missing variableHere, we supposed X3 is the missing variable. (b) Substitute B0 into the system of equations (1.4),we get B1;(c) B0 = B1;Repeat (b),(c), until B0 ? B1 is small enough,and B0 is the estimate of parameters.(ii)σis unknown.The algorithm is:(a) Evaluate B0 = (β0,β1,···,β4),σ0;(b) Substitute B0 into the system of equations (1.4),we get B1;(c) Substitute B1 into equation (1.5),we getσ1;(d) (B0,σ0) = (B1,σ1);Repeat (b),(c) and (d), until (B0,σ0) ? (B1,σ1) is small enough, and (B0,σ0) is theestimate of parameters.Two alternate missing variablesWe suppose X2 and X3 are missed alternate, and the first m observations missed X2,the others missed X3. (i)σis unknown.The algorithm is:(a) Evaluate B0 = (β0,β1,···,β4);(b) Substitute B0 into the system of equations (1.6),we get B1;(c) B0 = B1;Repeat (b),(c),until B0 ? B1 is small enough, and B0 is the estimate of parameters. The algorithm is:(a) Evaluate B0 = (β0,β1,···,β4),σ0;(b) Substitute B0 into the system of equations (1.6),we getB1;(c) Substitute B1 into equation (1.7),we getσ1;(d) (B0,σ0) = (B1,σ1);Repeat (b),(c) and (d) until (B0,σ0) ? (B1,σ1) is small enough, and (B0,σ0) is theestimate of parameters.In chapter three, simulation and exchange data analysis. The first part, we createrandom data by distribution of variable, supposed some variable are missed, and used thealgorithm in chapter two to estimate the parameters, and compare with the real parameters.The second part, we used the algorithm to estimate the parameters in hedonic model by thehousing exchange data of Dalian.