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SAS/ETS 9.22 User's Guide 100

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982 F Chapter 17: The MDC Procedure. Output 17.5.4 shows the summary table that is produced by the preceding statements.. Output 17.5.4 Average Probabilities of Choosing Each Particular Alternative. Two-level Nested Logit. You apply the same SORT and MEANS procedures as applied earlier to obtain the following summary table in Output 17.5.5.. Output 17.5.5 Average Probabilities of Choosing Each Particular...

SAS/ETS 9.22 User's Guide 101

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The MODEL Procedure. Overview: MODEL Procedure. Getting Started: MODEL Procedure. Syntax: MODEL Procedure. PROC MODEL Statement. Details: Estimation by the MODEL Procedure. 994 F Chapter 18: The MODEL Procedure. Properties of the Estimates. Details: Simulation by the MODEL Procedure. Programming Language Overview: MODEL Procedure. Variables in the Model Program. Examples: MODEL Procedure. Example 18.1: OLS Single Nonlinear Equation. Example 18.2:...

SAS/ETS 9.22 User's Guide 102

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1002 F Chapter 18: The MODEL Procedure. Figure 18.4 Summary of Residual Errors Report. The MODEL Procedure. This table lists the sum of squared errors (SSE), the mean squared error (MSE), the root mean squared error (root MSE), and the R 2 and adjusted R 2 statistics. The R 2 value of 0.7472 means that the estimated model explains approximately...

SAS/ETS 9.22 User's Guide 103

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1012 F Chapter 18: The MODEL Procedure. Syntax: MODEL Procedure. The following statements can be used with the MODEL procedure:. expression ) >. 1014 F Chapter 18: The MODEL Procedure. The statements and options in the MODEL procedure are summarized in the following table.. Data Set Options. specify the input data set for the variables FIT, SOLVE DATA=. specify the...

SAS/ETS 9.22 User's Guide 104

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1022 F Chapter 18: The MODEL Procedure. When BOTH is specified, model files are read from the data set first and read from the SAS catalog only if the data set is not found. Options to List or Analyze the Structure of the Model. These options produce reports on the structure of the model or list the programming statements that...

SAS/ETS 9.22 User's Guide 105

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is a string used to identify the estimate in the printed output and in the OUTEST=. data set.. You can use the following options in the ESTIMATE statement:. specifies the name of the data set in which the estimate of the functions of the parameters are to be written. The format for this data set is identical to the OUTEST=...

SAS/ETS 9.22 User's Guide 106

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1042 F Chapter 18: The MODEL Procedure. HESSIAN=CROSS selects the crossprod- ucts approximation to the Hessian, HESSIAN=GLS selects the generalized least squares approximation to the Hessian, and HESSIAN=FDA selects the finite difference approximation to the Hessian. HESSIAN=GLS is the default.. The default is MAXITER=100.. The default is MAXSUBITER=30. The default is METHOD=GAUSS. If the default GAUSS method fails to converge,...

SAS/ETS 9.22 User's Guide 107

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1052 F Chapter 18: The MODEL Procedure. The NAHEAD= option is used to simulate the process of using the model to produce successive forecasts to a fixed forecast horizon, in which each forecast uses the historical data available at the time the forecast is made.. NAHEAD=2 produces a solution that uses one-step-ahead solutions for the first lag (LAG1 functions return...

SAS/ETS 9.22 User's Guide 108

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The parameter vector that minimizes this objective function is the GMM estimator. GMM estimation is requested in the FIT statement with the GMM option.. The variance of the moment functions, V, can be expressed as. S O n / does not decrease with increasing n, you consider estimators of S 0 n of the form:. where l.n/ is a scalar...

SAS/ETS 9.22 User's Guide 109

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When the HESSIAN= option is used, the default estimator of the variance-covariance of O is the inverse of the Hessian selected.. The probability density function for the multivariate t distribution is. where m is the number of equations and df is the degrees of freedom.. norm of the gradient of the negative log-likelihood function are shown in the estimation summary.....

SAS/ETS 9.22 User's Guide 110

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Figure 18.24 Diagnostics for Convergence Failure. The MODEL Procedure OLS Estimation. ERROR: The parameter estimates failed to converge for OLS after 100 iterations using CONVERGE=0.001 as the convergence criteria.. The change in the parameters that the Gauss-Newton method computes is very extreme and makes the objective values worse instead of better. Even when this step is shortened by a factor...

SAS/ETS 9.22 User's Guide 111

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1092 F Chapter 18: The MODEL Procedure. The options ITPRINT, ITDETAILS, XPX, I, and ITALL specify a detailed listing of each iteration of the minimization process.. N is the number of usable observations.. Objective is the corrected objective function value.. Trace(S) is the trace of the S matrix.. subit is the number of subiterations required to find a or a...

SAS/ETS 9.22 User's Guide 112

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Figure 18.39 Output for Heteroscedasticity Tests. The MODEL Procedure Heteroscedasticity Test. There are two methods for improving the efficiency of the parameter estimation in the presence of heteroscedastic errors. If the error variance relationships are known, weighted regression can be used or an error model can be estimated. If the error variance relationship is unknown, GMM estimation can be used.....

SAS/ETS 9.22 User's Guide 113

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One of the key assumptions of regression is that the variance of the errors is constant across observations. Correcting for heteroscedasticity improves the efficiency of the estimates.. If you have a model that is heteroscedastic with known form, you can improve the efficiency of the estimates by performing a weighted regression. If the errors for a model are heteroscedastic and...

SAS/ETS 9.22 User's Guide 114

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Figure 18.48 Static Estimation Results for Fish Model. To perform a dynamic estimation of the differential equation, add the DYNAMIC option to the FIT statement.. The results from this estimation are shown in Figure 18.49.. Figure 18.49 Dynamic Estimation Results for Fish Model. To perform a dynamic estimation of the differential equation and estimate the initial value, use the following...

SAS/ETS 9.22 User's Guide 115

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1132 F Chapter 18: The MODEL Procedure. proc model data=exp;. The data set introduces an artificial structural change into the model (the structural change effects the intercept parameter). The output from the requested Chow tests are shown in Figure 18.55.. Figure 18.55 Chow’s Test Results. The MODEL Procedure Structural Change Test Break. Wald-based and likelihood-ratio-based confidence intervals are available in...

SAS/ETS 9.22 User's Guide 116

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The initial lags of the error terms of MA(q ) models can also be modeled in different ways. This reduces the efficiency of the estimates, although they remain unbiased. The initial lagged residuals, extending before the start of the data, are assumed to be 0, their unconditional expected value. Unconditional least squares estimates for the MA(1) process can be produced...

SAS/ETS 9.22 User's Guide 117

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In the following example, the variable y is modeled as a linear function of x, the first lag of x, the second lag of x, and so forth:. Models of this sort can introduce a great many parameters for the lags, and there may not be enough data to compute accurate independent estimates for them all. One common assumption is...

SAS/ETS 9.22 User's Guide 118

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1162 F Chapter 18: The MODEL Procedure. If the COVOUT option is specified, an additional observation is written for each row of the estimate of the covariance matrix of parameter estimates, with the _NAME_ values that contain the parameter names for the rows. OUTPARMS= Data Set. The option OUTPARMS= writes all the parameter estimates to an output data set. This...

SAS/ETS 9.22 User's Guide 119

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1172 F Chapter 18: The MODEL Procedure. The following statements estimate and forecast the three forward-rate models of the following form.. The Monte Carlo simulation specified in the preceding example draws from a multivariate t distri- bution with constant degrees of freedom and forecasted variance, and it computes future states of DEMUSD1M, DEMUSD3M, and DEMUSD6M. The OUTSN= option in the...