help ie_rate-------------------------------------------------------------------------------

Title

ie_rate-- intrinsic estimator for age, period, cohort (APC) applications

Syntaxie_ratedepvar[indepvars] [if] [in] [weight] [,options]

optionsDescription -------------------------------------------------------------------------irreform resultsoffset()log of exposure for rate parameterizationscale(dev)calculate std. errors using deviance-based mseDescription

ie_ratecomputes coefficients from an APC analysis characterized by a design matrix that is not full rank due to the perfect linear dependence between age, period, and cohort. However, unlikeapc_ie,ie_ratedoes not require strict linear dependence to estimate the APC model. However, it does require care in inputting the proper APC design matrix (described below).The dependent variable for

ie_rateis assumed to be in the form of counts. An offset (log exposure) should be specified in order to estimate a rate model. If an offset is not specified, it defaults to 0 resulting in a standard Poisson regression. Initial values are obtained usingie_reg, which is a companion routine for linear regression on the log rates.In order to obtain APC estimates normalized according to conventional applications (i.e.,

apc_ie), it is necessary that an ANOVA design matrix be constructed using thelastfactor level of each APC factor as the reference as shown below.After estimation the user may request the a display of the full set of ANOVA normalized estimates, including those pertaining to the reference categories, which are obtained using

ie_norm, which is a modified version of Ben Jann'sdevconutility with exactly the same syntax. As mentioned above, it is important to code the APC design with the last category as reference. Additionally, the model must include a constant term.

Example code for ANOVA design codingqui tab age, gen(a) scal arow = r(r) qui tab period, gen(p) scal prow = r(r) qui gen cohort = period - age qui tab cohort, gen(c) scal crow = r(r)

* construct ANOVA normalization using last category as reference

forval i = 1/`=arow' { gen aC`i' = a`i' - a`=arow' }

forval i = 1/`=prow' { gen pC`i' = p`i' - p`=prow' } forval i = 1/`=crow' { gen cC`i' = c`i' - c`=crow' }

Examples

APC rate model. ie_rate d aC1-aC6 pC1-pC3 cC1-cC9, offset(logn)

fully normalized solution. ie_norm, groups(aC1-aC7, pC1-pC4, cC1-cC10)

Estimation Details

ie_rateuses a Newton-Raphson algorithm and employes the method outlined in Fu (2000). Starting values are obtained from a loglinear regression using the empirical rates viaie_reg, which may also be used as a standalone program for a loglinear analysis of empirical rates.

Saved Results

ie_ratesaves the following ine():Scalars

e(N)number of cellse(ll)deviancee(k)number of estimated parameters Macrose(depvar)name of dependent variableMatrices

e(Coef)1 XKvector of estimatese(Var)KXKvariance-covariance matrixFunctions

e(sample)marks estimation sample

ReferencesWenjiang J. Fu (2000). "Ridge Estimator in Singular Design with Application to Age-Period-Cohort Analysis of Disease Rates,

Communications in Statistics - Theory and Methods, 29:2, 263-278Daniel A. Powers (2012). "Black-White Differences in Maternal Age, Maternal Birth Cohort, and Period Effects on Infant Mortality in the U.S. (1983-2002)." Presented at the annual meetings of the Population Research Association of America, San Francisco, CA, May 4 2012.

AuthorDaniel A. Powers, University of Texas at Austin, dpowers@austin.utexas.edu

Also see