matchprop: Matched sample data frame based on propensity scores

Description

Creates a matched sample data frame based on propensity scores

Usage

matchprop(form,data=NULL,distance="logit",discard="both",
  reestimate="FALSE",m.order="none",nclose=0,ytreat=1)

Arguments

form

Model formula

data

A data frame containing the data. Default: use data in the current working directory

distance

The link formula to be passed on to the glm command -- usually "probit" or "logit", but other standard options also work.

discard

Observations to be discarded based on the propensity score or the value of the mahalanobis distance measure if distance="mahal". If discard = "control", only control observations are discarded. If di

reestimate

If reestimate=TRUE, the propensity score is reestimated after observations are discarded

m.order

Order by which estimated distances are sorted before starting the matching process. Options: "decreasing", "increasing", "random", and "none".

nclose

If nclose>0, sorts the matched observations by the distance measure and chooses the nclose matches with the smallest distances.

ytreat

The value of the dependent variable for the treatment group. Default: ytreat = 1. Constructs matched samples for all other values of the dependent variable. If discard="treat" or discard="both", only treatment observatio

Value

Returns the matched sample data frame. Adds the following variables to the data set: origobs: The observation number in the original data set matchobs: The observation number in the matched data set to which the observation is matched. matchobs refers to the observation's number in the original data set, i.e., to the variable emph{origobs}. emph{Note:} If the original data set includes variables named emph{origobs} and emph{matchobs}, they will be overwritten by the variables produced by emph{matchprop}. } seealso{ code{matchmahal} code{matchqreg} } examples{ set.seed(189) n = 1000 x <- rnorm(n) x <- sort(x) y <- x*1 + rnorm(n, 0, sd(x)/2) y <- ifelse(y>0,1,0) table(y) fit <- matchprop(y~x,m.order="largest",ytreat=1) table(fit$y) } details{ Creates a matched sample data set using procedures based on the emph{MatchIt} program. emph{MatchIt}'s routines are generally preferable for creating a single matched data set, although by doing less the matchprop command is somewhat faster than MatchIt. matchprop is particularly useful for creating a series of matched sample data sets over time relative to a base time period. Unless distance = "mahal", the glm command is used to estimate the propensity scores using a series of discrete choice models for the probability, p, that the dependent variable equals ytreat rather than each alternative value of the dependent variable. The default link function is distance = "logit". Alternative link functions are specified using the distance option. Links include the standard ones for a glm model with family = binomial, e.g., "probit", "cauchit", "log", and "cloglog". If mahal= T, matchprop implements MatchIt's version of mahalanobis matching. Letting X be the matrix of explanatory variables specified in form, the mahalanobis measure of distance from the vector of mean values is $p = mahalanobis(X, colMeans(X), cov(X))$. Although this version of mahalanobis matching is fast, it may not be the best way to construct matches because it treats observations that are above and below the mean symmetrically. For example, if X is a single variable with $mean(X)$ = .5 and $var(X)$ = 1, mahalanobis matching treats X =.3 and X = .7 the same: mahalanobis(.3,.5,1) = .04 and mahalanobis(.7,.5,.1) = .04. The function matchmahal is slower but generally preferable for mahalanobis matching because it pairs each treatment observation with the closest control observation, i.e., $min(mahalanobis(X0, X1[i,], cov(X)))$, where X0 is the matrix of explanatory variables for the control observations, X1 is the matrix for the treatment observations, X is the pooled explanatory variable matrix, and i is the target treatment observation. To illustrate how matchprop constructs matched samples, suppose that the dependent variable takes on three values, y = 1, 2, 3, and assume that y = 1 is the treatment group. First, the y = 1 and y = 2 observations are pooled and a propensity score p is constructed by, e.g., estimating a logit model for the probability that y = 1 rather than 2. Unless m.order = "none", the data frame is then sorted by p -- from largest to smallest if m.order = "largest", from smallest to largest if m.order = "smallest", and randomly if m.order = "random". The first treatment observation is then paired with the closest control observation, the second treatment observation is paired with the closest of the remaining control observations, and so on until the last observation is reached for one of the groups. No control observation is matched to more than one treatment observation, and only pairwise matching is supported using matchprop. The process is then repeated using the y = 1 and y = 3 observations. If the number of treatment observations is n1, the final data set will have roughly 3*n1 observations -- the n1 treatment observations and n1 observations each from the y = 2 and y = 3 observations. The exact number of observations will differ depending on how observations are treated by the discard option, and there will be fewer than n1 observations for, e.g., group 2 if n2discard option determines how observations are handled that are outside the probability support. In the above example, let p be the propensity score for the logit model for the probability that y = 1 rather than 2. If discard = "control", observations with p[y==2]discard = "treat", observations with p[y==1]>max(p[y==2]) are discarded from the y==1 sample. If discard = "both", both sets of observations are deleted. The process is then repeated for the y = 1 and y = 3 observations. If discard = "treat" or "both", a different set of treatment observations may be discarded as being outside the support of the two propensity measures. Only treatment observations that are rejected by both models will end up being omitted from the final data set. If reestimate = T, the propensity scores are reestimated after any observations are discarded. Otherwise, matches are based on the original propensity scores.

References

Deng, Yongheng, Sing Tien Foo, and Daniel P. McMillen, "Private Residential Price Indices in Singapore," Regional Science and Urban Economics, (forthcoming). Ho, D., Imai, K., King, G, Stuart, E., "Matching as Nonparametric Preprocessing for Reducing Model Dependence in Parametric Causal Inference," Political Analysis 15 (2007), 199-236. Ho, D., Imai, K., King, G, Stuart, E., "MatchIt: Nonparametric preprocessing for parametric causal inference," Journal of Statistical Software 42 (2011), 1-28.. McMillen, Daniel P., "Repeat Sales as a Matching Estimator," Real Estate Economics (forthcoming).