# Aster Models Aster models are exponential family graphical models that combine aspects of generalized linear models and survival analysis. This package is still under development, only about half finished. However, it does do maximum likelihood for unconditional aster models with dependence groups, which the old package `aster` does not. The main differences between this package and the old package are as follows. 1. The old package had triple indices for model matrices. The first index ran over individuals, the second index over nodes of the graph for an individual, and the third index over regression coefficients. Consequently the model matrix was represented (sometimes, but not consistently) as a three-dimensional array rather than a matrix, which was very confusing, even to the package author. This package ignores individuals, one index runs over all nodes of the combined graph for all individuals. Thus model matrices are always matrices. 2. The old package did not implement dependence groups, although they were described in Geyer, Wagenius and Shaw (2007). This package does. Consequently, this package requires a data frame, a vector `pred` that indicates predecessors, a vector `group` that indicates individuals in the same dependence group, and a vector `fam` that indicates families to specify a saturated aster model (the old package required only the data frame, `pred`, and `fam`). To facilitate the old style model specification, there is a new function `asterdata` that constructs objects of class `"asterdata"` given an old style data frame, `pred`, and `fam`. All other functions of the package take objects of class `"asterdata"` as model specifications. 3. The function `predict.aster` in the old package did some parameter transformations, but not all, and the returned value, when a list, had a component `gradient`, that was undocumented but useful in applying the delta method. The functions `transformSaturated`, `transformConditional`, and `transformUnconditional` in this package transform between any of the following parameter vectors: the conditional canonical parameter $theta$, the unconditional canonical parameter $phi$, the conditional mean value parameter $xi$, the unconditional mean value parameter $mu$, the canonical affine submodel canonical parameter $beta$, and (unconditional aster models only) the canonical affine submodel mean value parameter $tau$ (this last parameter is new, not discussed in the cited papers below, it is $tau = M^T mu$, where $M$ is the model matrix). The change of parameter from $tau$ to $beta$ is equivalent to maximum likelihood estimation for an unconditional aster model when the value $tau = M^T y$ is used, where $y$ is the response vector. All of these transformation functions also compute derivatives, if requested. See examples. package ## Bugs Functions analogous to `aster`, `anova`, and `predict` in the old package are missing, thus model fitting, hypothesis tests, and confidence intervals are more cumbersome. In fact, since there is no function to calculate log likelihoods (like `mlogl` in the old package), there is no way to do likelihood ratio tests (but Rao or Wald tests could be done, for unconditional aster models, since the derivative of the log likelihood is observed minus expected $M^T (y - mu)$. ## References Geyer, C. J., Wagenius, S., and Shaw, R. G. (2007) Aster Models for Life History Analysis. **Biometrika** 94 415--426. Shaw, R. G., Geyer, C. J., Wagenius, S., Hangelbroek, H. H. and Etterson, J. R. (2008) Unifying Life History Analyses for Inference of Fitness and Population Growth. **American Naturalist**, 172 , E35--E47. ## See Also `asterdata`, `transformSaturated`, `families` ## Examples ```r ## Not run: # perfectly good example but takes longer to run than CRAN allows data(echinacea) #### estimate MLE (simpler model than in Biometrika paper cited, not as good) hdct <- as.numeric(grepl("hdct", as.character(echinacea$redata$varb))) modmat <- model.matrix(resp ~ varb + nsloc + ewloc + pop * hdct - pop, data = echinacea$redata) tau.hat <- as.numeric(t(modmat) %*% echinacea$redata$resp) beta.hat <- transformUnconditional(tau.hat, modmat, echinacea, from = "tau", to = "beta") inverse.fisher <- jacobian(tau.hat, echinacea, transform = "unconditional", from = "tau", to = "beta", modmat = modmat) #### now have MLE (beta.hat) and pseudo-inverse of Fisher information #### (inverse.fisher), pseudo-inverse because modmat is not full rank foo <- cbind(beta.hat, sqrt(diag(inverse.fisher))) foo <- cbind(foo, foo[ , 1]/foo[ , 2]) foo <- cbind(foo, 2 * pnorm(- abs(foo[ , 3]))) dimnames(foo) <- list(colnames(modmat), c("Estimate", "Std. Error", "z value", "Pr(>|z|)")) printCoefmat(foo) #### coefficients constrained to be zero because parameterization is not #### identifiable have estimate zero and std. error zero (and rest NA) #### estimate fitness in populations #### generate new data with one individual in each pop at location (0, 0) pop.names <- levels(echinacea$redata$pop) pop.idx <- match(pop.names, as.character(echinacea$redata$pop)) pop.id <- echinacea$redata$id[pop.idx] newdata <- subset(echinacea, echinacea$redata$id %in% pop.id) newdata$redata[ , "nsloc"] <- 0 newdata$redata[ , "ewloc"] <- 0 hdct <- as.integer(grepl("hdct", as.character(newdata$redata$varb))) #### modmat for new data newmodmat <- model.matrix(resp ~ varb + nsloc + ewloc + pop * hdct - pop, data = newdata$redata) #### matrix that when multiplied mean value parameter vector gives fitness #### in each pop amat <- matrix(NA, nrow = length(pop.id), ncol = nrow(newmodmat)) for (i in 1:nrow(amat)) amat[i, ] <- as.numeric(grepl(paste("^", pop.id[i], ".hdct", sep = ""), rownames(newmodmat))) #### transform to expected fitness parameters efit <- transformUnconditional(beta.hat, newmodmat, newdata, from = "beta", to = "mu") efit <- as.numeric(amat %*% efit) #### jacobian matrix of this transformation jack <- jacobian(beta.hat, newdata, transform = "unconditional", from = "beta", to = "mu", modmat = newmodmat) #### delta method standard errors sefit <- sqrt(diag(amat %*% jack %*% inverse.fisher %*% t(jack) %*% t(amat))) foo <- cbind(efit, sefit) dimnames(foo) <- list(pop.names, c("Est. fitness", "Std. Error")) print(foo) ## End(Not run) ```

aster2-package