help ie_rate

Title

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

Syntax

ie_rate depvar [indepvars] [if] [in] [weight] [,options]

options

eform exp(b) results

offset(logn) log of exposure for rate parameterization

scale(dev) calculate std. errors using deviance-based mse

logit fit logit model (requires binom(n))

binom(n) binomial denominator for logit parameterization

Description

ie_rate computes 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, unlike apc_ie, ie_rate
does 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_rate is 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.
Alternatively, the logit option can be specified with binomial denominator n to fit a logit model. Initial values are obtained using ie_reg, which is a companion routine for linear regression on the log rates or empirical logits.

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 the last factor level of each APC factor
as the reference as shown below.

After estimation the user may request the display of the
full set of ANOVA normalized estimates, including those pertaining to the reference categories. The renormalized estimates are obtained using ie_norm, which is a modified version of Ben Jann's devcon utility and follows
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 coding

qui 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 loglinear rate model

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

APC logit model

. ie_rate d aC1-aC6 pC1-pC3 cC1-cC9, logit binom(n)

fully normalized solution

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

Estimation Details

ie_rate uses a Newton-Raphson algorithm and employes the method outlined in Fu (2000).
Starting values are obtained from a linear regression using the empirical logits or log rates via
ie_reg, which may also be used as a standalone program for a analysis of empirical log rates or logits.

Saved Results

ie_rate saves the following in e():

Scalars

e(N) number of cells

e(ll) deviance

e(k) number of estimated parameters

Macros

e(depvar) name of dependent variable

Matrices

e(b) 1 X K vector of estimates

e(V) K X K variance-covariance matrix

Functions

e(sample) marks estimation sample

References

Wenjiang 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, 263-278

Daniel A. Powers (2012). "Black-White Differences in Maternal Age, Maternal Birth Cohort, and
Period Effects on Infant Mortality in the U.S. (1983-2002)." Social Science Research, 42: 1033-1045.

Author

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

Also see

Online: help for devcon and help for apc_ie if installed.