Contents: |
Purpose / History / Requirements / Usage / Details / Limitations / See Also |

*PURPOSE:*- The NLEstimate macro allows you to estimate one or more linear or nonlinear combinations of parameters from any model for which you can save the model parameters and their variance-covariance matrix. Most modeling procedures which offer ESTIMATE, CONTRAST, or LSMEANS statements only provide for estimating or testing linear combinations of model parameters. However, common estimation problems often involve nonlinear combinations, particularly in generalized models with nonidentity link functions such as logistic and Poisson models.
*HISTORY:*- The version of the NLEstimate macro that you are using is displayed in the log when you specify
**version**(or any string) as the first argument. For example:%NLEstimate(version)

The NLEstimate macro always attempts to check for a later version of itself. If it is unable to do this (such as if there is no active internet connection available), the macro will issue the following message in the log:

NOTE: Unable to check for newer version

The computations performed by the macro are not affected by the appearance of this message.

*Version**Update Notes*1.51 Minor fix to version printing. 1.5 Added optional title= and listnames= parameters. 1.4 When DF= is omitted, large-sample Wald statistics are produced. When SCORE= is omitted, results are saved in data set EST in addition to being displayed. 1.3 Fixes error that occurred when input model has only a single parameter such as an intercept-only model. 1.2 SAS/IML ^{®}no longer required.1.1 Added **score=**and**outscore=**parameters.1.0 Initial coding *REQUIREMENTS:*- Base SAS
^{®}and SAS/STAT^{®}software are required. You might also need another SAS product to fit the desired model before using the NLEstimate macro. *USAGE:*- Follow the instructions in the Downloads tab of this sample to save the NLEstimate macro definition. Replace the text within quotation marks in the following statement with the location of the NLEstimate macro definition file on your system. In your SAS program or in the SAS editor window, specify this statement to define the NLEstimate macro and make it available for use:
%inc "<location of your file containing the NLEstimate macro>";

Following this statement, you can call the NLEstimate macro. See the Results tab for examples.

There are two basic uses of the macro:

**Display parameter names**. Specify**shownames**as the first argument to display a list of the model parameter estimates and their associated names. The parameter names are needed to write the functions to be estimated in a subsequent run of the macro. The**f=**and**fdata=**parameters can be omitted when using**shownames**. For example:`%NLEstimate(shownames, instore=logmod)`

**Estimation of functions**. Input the saved model using**instore=**(preferred) or both of**inest=**and**incovb=**. Then specify the function or functions to estimate using either the**f=**or**fdata=**parameter (or both). Do not specify**shownames**. The macro again displays the parameter names and also displays estimates of the specified functions. For example:`%NLEstimate(instore=logmod, fdata=funcs)`

Following are the parameters available with the NLEstimate macro. The necessary model information is provided to the macro by specifying either the

**instore=**parameter or both the**inest=**and**incovb=**parameters. If the modeling procedure provides a STORE statement for saving the fitted model,**instore=**is generally the better method for providing the model information. Additionally, if**shownames**is not specified as the first argument, either the**fdata=**or**f=**parameters (or both) is required.**shownames**- When specified as the first parameter in the macro call and
**score=**is not specified, displays a list of the model parameter estimates and their associated names as mentioned above. **instore=***item-store*- Specifies the fitted model that was saved using the STORE statement in the modeling procedure. The OUT= option in the STORE statement saves the model in a file known as an
*item store*. This is the preferred method for providing the required model information. However, if the modeling procedure does not offer the STORE statement, then you may be able to use the**inest=**and**incovb=**parameters. See Limitations below. **inest=***data-set-name*- Specifies the data set of parameter estimates saved using an ODS OUTPUT statement in the modeling procedure. The parameter estimates of the model should be stored in a variable named ESTIMATE in this data set. An error is issued if the ESTIMATE variable is not found.
**incovb=***data-set-name*- Specifies the data set containing the variance-covariance matrix of model parameters saved using an ODS OUTPUT statement in the modeling procedure. Typically, an option such as COVB is required in the modeling procedure to make this matrix available for saving. If the saved data set contains numeric variables other than those containing the covariance matrix, they should be removed before specifying the data set in this macro parameter in order to avoid a compatibility error. The
**incovb=**data set should have the same number of observations (rows) and variables (columns) as the number of rows in the**inest=**data set in order to be compatible. See Limitations below. **fdata=***data-set-name*- Specifies a data set containing the functions to be estimated (estimands). This parameter can be used when you have more than one function to estimate. This data set must contain two character variables with names LABEL and F. In each observation of the data set, F contains an expression to be estimated involving the parameter names of the model. LABEL contains a text string used to label the estimate of the function in the results. The label does not need to be enclosed in quotes. Do not use double quotes (") in the either the F or LABEL variable. Use single quotes (') instead if needed. The displayed results are also saved in data set Est.
**f=***expression*- Specifies an expression representing a single function to be estimated (the estimand) involving the parameter names. This parameter can be used when only one function is to be estimated. Do not use double quotes (") in the expression. Use single quotes (') instead if needed. Any quotes must appear in pairs. For estimands that involve values from data set variables, also use the
**score=**parameter. When**score=**is not specified, the displayed results are also saved in data set Est. **label=***text-string*- Optionally, can be used to label the single function specified in the
**f=**parameter. Ignored if**f=**is not specified. Do not use quotes surrounding or within*text-string*. **df=***value*- Specifies the degrees of freedom to be used in the test and confidence interval computed for the estimated functions. If omitted, large-sample Wald statistics are given. The degrees of freedom for testing a linear combination of parameters in a linear model would typically be the number of observations used in fitting the model minus the number of parameters estimated in the model – essentially, the error degrees of freedom.
**alpha=***value*- Specifies the alpha level to be used in computing confidence limits. If omitted, alpha=0.05.
**score=***data-set-name*- Specifies a data set for which the function in
**f=**is evaluated for each observation. Use this parameter along with the**f=**parameter when the estimand involves values of variables in the input data set. The**score=**parameter cannot be used with the**fdata=**parameter. **outscore=***data-set-name*- Names a data set to be created that is a copy of the
**score=**data set and has additional variables for the estimated function, its standard error, test statistic, p-value, and confidence limits in each observation. If not specified, the data set is named NLEst. No data set is created if**score=**is not specified. **listnames=yes|no**- Display parameter names or not before the results table.
**listnames=no**suppresses the table of names. The default is**listnames=yes**. **title=***title-text*- Specifies a title for the results table. The
*title-text*must not contain quotes (" or '), ampersands(&), commas(,), or parentheses. If omitted,**title=**Nonlinear Function Estimate.

*DETAILS:*- The NLEstimate macro takes advantage of the ESTIMATE statement in PROC NLMIXED which can estimate nonlinear functions of model parameters. It uses NLMIXED to fit a multivariate normal distribution with mean equal to the input model parameter estimates and variance equal to the input model covariance matrix. This creates a log likelihood that is zero and NLMIXED is able to converge immediately to a model with the specified parameter estimates and covariance matrix. It is then possible to estimate the functions specified in the
**f=**or**fdata=**parameters. *LIMITATIONS:*- Some modeling procedures cannot provide the necessary covariance matrix for some models or estimands. For example, since PROC GLIMMIX cannot provide a covariance matrix that includes the scale parameter, an estimand involving the scale parameter cannot be estimated. Some procedures either do not have a STORE statement (such as PROC FMM) or do not save the necessary model information (such as PROC COUNTREG). In such cases, use
**inest=**and**incovb=**instead of**instore=**. Note that in some cases, such as with PROC FMM, the data set containing the covariance matrix must be modified to remove extraneous numeric variables in order to avoid a compatibility error. *SEE ALSO:*- The NLMeans macro can be used to do multiple comparisons among the levels of a model effect on the mean scale. The macro forms the expressions that must be evaluated and then calls the NLEstimate macro to do the computations. See the NLEstimate macro description for details.

These sample files and code examples are provided by SAS Institute Inc. "as is" without warranty of any kind, either express or implied, including but not limited to the implied warranties of merchantability and fitness for a particular purpose. Recipients acknowledge and agree that SAS Institute shall not be liable for any damages whatsoever arising out of their use of this material. In addition, SAS Institute will provide no support for the materials contained herein.

These sample files and code examples are provided by SAS Institute Inc. "as is" without warranty of any kind, either express or implied, including but not limited to the implied warranties of merchantability and fitness for a particular purpose. Recipients acknowledge and agree that SAS Institute shall not be liable for any damages whatsoever arising out of their use of this material. In addition, SAS Institute will provide no support for the materials contained herein.

In addition to the following example, several more examples of using the NLEstimate macro can be found in these notes:

- Estimating differences in probabilities with confidence interval
- Estimating sensitivity, specificity, positive and negative predictive values, and other statistics
- Estimating rate differences (with confidence interval) using a Poisson model
- Estimating relative risks in a multinomial response model
- Confidence interval for a ratio of two linear combinations of model parameters
- Comparing groups with respect to the dose (or predictor value) that yields a specified response probability
- Harmonic mean estimate, confidence interval, and test for lognormal data
- Estimating and comparing counts and rates (with confidence intervals) in zero-inflated models
- Estimating a relative risk (also called risk ratio, prevalence ratio)
- Fitting truncated Poisson and negative binomial models
- Estimating the difference in differences of means

**EXAMPLE: Estimate difference in group means in a log-linked gamma model**- The example titled "Gamma Distribution Applied to Life Data" in the GENMOD documentation presents failure times of 201 machine parts from two manufacturers, denoted A and B. These GENMOD statements fit the log-linked gamma model and use the LSMEANS statement to estimate the manufacturer means. The STORE statement saves the model in an item store for later use by the NLEstimate macro.
proc genmod data = lifdat; class mfg; model lifetime = mfg / dist=gamma link=log; lsmeans mfg / e ilink diff exp; store out=gammod; run;

The values in the Estimate column in "MFG Least Squares Means" table are the estimates of the linear combinations of model parameters defined in the "Coefficients for MFG Least Squares Means" table. This table of coefficients is produced by the E option. That is, the MFG="A" estimate, 6.1501, is the Row1 linear combination defined as 1*Intercept+1*MFG_{A}. Similarly for MFG="B". The Intercept, MFG_{A}, and MFG_{B}estimated model parameters are shown in the "Analysis Of Maximum Likelihood Parameter Estimates" table. Note that since the linear predictor in this gamma model estimates the log gamma mean, linear combinations of the model parameters, such as those from the LSMEANS, ESTIMATE, or CONTRAST statements, also estimate the log gamma mean. Therefore, 6.1501 is the estimated log mean for manufacturer A. The ILINK option in the LSMEANS statement applies the inverse of the link function to the estimates. In this log-linked model, that means that the estimates are exponentiated. The resulting mean estimates are presented in the column labelled "Mean". The estimated mean lifetimes are 468.74 for manufacturer A and 459.51 for manufacturer B. The DIFF option computes the pairwise differences among the LS-mean estimates and presents them in the "Differences of MFG Least Squares Means" table. This produces a difference of the log means, or equivalently a log ratio of means, in the Estimate column. The ratio of means is estimated to be exp(6.1501-6.1302) = 468.74/459.51 = 1.0201. The EXP option exponentiates this difference producing in an estimated ratio of means in the Exponentiated column. Note that the EXP option also exponentiates the estimates in the "MFG Least Squares Means" table resulting in the Exponentiated column that reproduces the Mean column from the ILINK option in this case.Analysis Of Maximum Likelihood Parameter Estimates Parameter DF Estimate Standard

ErrorWald 95% Confidence Limits Wald Chi-Square Pr > ChiSq Intercept 1 6.1302 0.1043 5.9257 6.3347 3451.61 <.0001 MFG A 1 0.0199 0.1559 -0.2857 0.3255 0.02 0.8985 MFG B 0 0.0000 0.0000 0.0000 0.0000 . . Scale 1 0.8275 0.0714 0.6987 0.9800

Coefficients for MFG Least

Squares MeansParameter MFG Row1 Row2 Intercept 1 1 MFG A A 1 MFG B B 1

MFG Least Squares Means MFG Estimate Standard Error z Value Pr > |z| Mean Standard Error

of MeanExponentiated A 6.1501 0.1159 53.07 <.0001 468.74 54.3172 468.74 B 6.1302 0.1043 58.75 <.0001 459.51 47.9468 459.51

Differences of MFG Least Squares Means MFG _MFG Estimate Standard Error z Value Pr > |z| Exponentiated A B 0.01989 0.1559 0.13 0.8985 1.0201 Note that the difference in means cannot be directly estimated by PROC GENMOD using the LSMEANS (or ESTIMATE) statement. Instead, you can estimate the difference in log means (log mean ratio) or ratio of means as shown above. Of course, a point estimate of the mean difference can be computed from the estimated means: 468.74 - 459.51 = 9.23. However, a confidence interval for this difference is not easily obtained. The mean difference is this nonlinear combination of parameters:

mean(A) - mean(B) = exp(Intercept+MFG

_{A}) - exp(Intercept)This nonlinear function can be estimated with the NLEstimate macro. In order to specify the function to estimate, the names of the parameters must be known. Running the NLEstimate macro with

**shownames**as the first argument displays the parameter names. The model information is provided in the**instore=**macro parameter by specifying the name of the item store saved previously by the STORE statement.%NLEstimate(shownames, instore=gammod)

The resulting table displays the parameter names you need to write the functions you want to estimate.

Name Estimate B_p1 6.1302 B_p2 0.01989 B_p3 0 The nonlinear function above can then be written and specified in the

**f=**macro parameter.%NLEstimate( instore=gammod, label=Mean Diff, f=exp(B_p1+B_p2)-exp(B_p1) )

The estimated mean difference is 9.2309, agreeing with the value computed above. A large-sample 95% confidence interval for the mean difference is (-132.77, 151.23). Note that a warning message is produced in this example since the default GLM parameterization is used for the CLASS variable, MFG, which is not a full-rank parameterization. The results are still correct. If a full rank parameterization was used, such as reference parameterization as requested with the PARAM=REF option in the CLASS statement, the warning would not appear and the results are the same.

Nonlinear Function Estimate

Label Estimate Standard Error Wald Chi-Square Pr > ChiSq Alpha Lower Upper Mean Diff 9.2309 72.4517 0.016233 0.8986 0.05 -132.77 151.23 The function to estimate can also be specified in a data set using the

**fdata=**macro parameter. This method is particularly useful when there are multiple functions to estimate. The following statements create a data set with the required variables, LABEL and F, for estimating the manufacturer means and their difference. Each observation in the data set specifies a function to estimate in F and a label for the function in LABEL.data fd; length label f $32767; infile datalines delimiter=','; input label f; datalines; Mfg A,exp(B_p1+B_p2) Mfg B,exp(B_p1) Mean Diff,exp(B_p1+B_p2)-exp(B_p1) ; %NLEstimate(instore=gammod, fdata=fd)

The mean estimates match those from the LSMEANS statement above and the difference estimate is the same as from the previous NLEstimate call.

Nonlinear Function Estimate

Label Estimate Standard Error Wald Chi-Square Pr > ChiSq Alpha Lower Upper Mfg A 468.74 54.3172 74.4726 <.0001 0.05 362.28 575.20 Mfg B 459.51 47.9468 91.8495 <.0001 0.05 365.54 553.49 Mean Diff 9.2309 72.4517 0.0162 0.8986 0.05 -132.77 151.23 Note that the desired model and nonlinear functions of the parameters can be estimated by using PROC NLMIXED. The ESTIMATE statement in NLMIXED can estimate nonlinear functions of model parameters. This is fairly easy for model like the gamma model above since the gamma distribution is directly supported in the MODEL statement of NLMIXED. But this can be more difficult for distributions that are not directly available such as the multinomial, beta, lognormal, and other distributions as well as special distributions like truncated or zero-inflated distributions. The NLEstimate macro uses NLMIXED and its ESTIMATE statement by adopting the fitted model parameters and covariance matrix supplied by other modeling procedures. This enables you to fit the desired model using the most natural and convenient procedure and can greatly simplify estimation of nonlinear functions of model parameters such as differences of means in generalized models when using a link function other than the identity link.

These statements fit the gamma model above (using reference parameterization for MFG) and again estimate the means and mean difference. The use of very large degrees of freedom (df=1e8) essentially produces a large-sample test and confidence interval like the default from the NLEstimate macro.

proc nlmixed data=lifdat; mu=exp(b1+b2*(mfg="A")); model lifetime ~ gamma(scale,mu/scale); estimate "Mfg A" exp(b1+b2) df=1e8; estimate "Mfg B" exp(b1) df=1e8; estimate "Mean Diff" exp(b1+b2)-exp(b1) df=1e8; run;

The results are very close to those from the NLEstimate macro above differing only because of minor estimation method differences.

Right-click on the link below and select **Save** to save the NLEstimate macro definition to a file. It is recommended that you name the file nlestimate.sas.

Download and save nlestimate.sas

The NLEstimate macro allows you to estimate one or more linear or nonlinear combinations of parameters from any model for which you can save the model parameters and their variance-covariance matrix.

#### Operating System and Release Information

Type: | Sample |

Topic: | Analytics ==> Regression SAS Reference ==> Procedures ==> NLMIXED SAS Reference ==> Macro |

Date Modified: | 2018-06-04 17:18:08 |

Date Created: | 2016-08-11 14:16:41 |

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