Title: Factor Model Estimation Using Proxy Variables
Version: 1.0
Description: Functions to estimate a factor model using discrete and continuous proxy variables. The function 'dproxyme' estimates a factor model of discrete proxy variables using an EM algorithm (Dempster, Laird, Rubin (1977) <doi:10.1111/j.2517-6161.1977.tb01600.x>; Hu (2008) <doi:10.1016/j.jeconom.2007.12.001>; Hu(2017) <doi:10.1016/j.jeconom.2017.06.002> ). The function 'cproxyme' estimates a linear factor model (Cunha, Heckman, and Schennach (2010) <doi:10.3982/ECTA6551>).
License: GPL-3
Encoding: UTF-8
RoxygenNote: 7.1.1
Imports: dplyr, nnet, pracma, stats, utils, gtools
Suggests: knitr, rmarkdown
VignetteBuilder: knitr
NeedsCompilation: no
Packaged: 2021-06-01 16:45:31 UTC; yujung
Author: Yujung Hwang ORCID iD [aut, cre]
Maintainer: Yujung Hwang <yujungghwang@gmail.com>
Repository: CRAN
Date/Publication: 2021-06-04 07:40:05 UTC

cproxyme

Description

This function estimates a linear factor model using continuous variables. The linear factor model to estimate has the following form. proxy = intercept + factorloading * (latent variable) + measurement error The measurement error is assumed to follow a Normal distribution with a mean zero and a variance, which needs to be estimated.

Usage

cproxyme(dat, anchor = 1, weights = NULL)

Arguments

dat

A proxy variable data frame list.

anchor

This is a column index of an anchoring proxy variable. Default is 1. That is, the code will use the first column in dat data frame as an achoring variable.

weights

An optional weight vector

Value

Returns a list of 3 components :

alpha0

This is a vector of intercepts in a linear factor model. The k-th entry is the intercept of k-th proxy variable factor model.

alpha1

This is a vector of factor loadings. The k-th entry is the factor loading of k-th proxy variable. The factor loading of anchoring variable is normalized to 1.

varnu

This is a vector of variances of measurement errors in proxy variables. The k-th entry is the variance of k-th proxy measurement error. The measurement error is assumed to follow a Normal distribution with mean 0.

mtheta

This is a mean of the latent variable. It is equal to the mean of the anchoring proxy variable.

vartheta

This is a variance of the latent variable.

Author(s)

Yujung Hwang, yujungghwang@gmail.com

References

Cunha, F., Heckman, J. J., & Schennach, S. M. (2010)

Estimating the technology of cognitive and noncognitive skill formation. Econometrica, 78(3), 883-931. doi: 10.3982/ECTA6551

Hwang, Yujung (2021)

Bounding Omitted Variable Bias Using Auxiliary Data. Working Paper.

Examples

dat1 <- data.frame(proxy1=c(1,2,3),proxy2=c(0.1,0.3,0.6),proxy3=c(2,3,5))
cproxyme(dat=dat1,anchor=1)
## you can specify weights
cproxyme(dat=dat1,anchor=1,weights=c(0.1,0.5,0.4))

dproxyme

Description

This function estimates measurement stochastic matrices of discrete proxy variables.

Usage

dproxyme(
  dat,
  sbar = 2,
  initvar = 1,
  initvec = NULL,
  seed = 210313,
  tol = 0.005,
  maxiter = 200,
  miniter = 10,
  minobs = 100,
  maxiter2 = 1000,
  trace = FALSE,
  weights = NULL
)

Arguments

dat

A proxy variable data frame list.

sbar

A number of discrete types. Default is 2.

initvar

A column index of a proxy variable to initialize the EM algorithm. Default is 1. That is, the proxy variable in the first column of "dat" is used for initialization.

initvec

This vector defines how to group the initvar to initialize the EM algorithm.

seed

Seed. Default is 210313 (birthday of this package).

tol

A tolerance for EM algorithm. Default is 0.005.

maxiter

A maximum number of iterations for EM algorithm. Default is 200.

miniter

A minimum number of iterations for EM algorithm. Default is 10.

minobs

Compute likelihood of a proxy variable only if there are more than "minobs" observations. Default is 100.

maxiter2

Maximum number of iterations for "multinom". Default is 1000.

trace

Whether to trace EM algorithm progress. Default is FALSE.

weights

An optional weight vector

Value

Returns a list of 5 components :

M_param

This is a list of estimated measurement (stochastic) matrices. The k-th matrix is a measurement matrix of a proxy variable saved in the kth column of dat data frame (or matrix). The ij-th element in a measurement matrix is the conditional probability of observing j-th (largest) proxy response value conditional on that the latent type is i.

M_param_col

This is a list of column labels of 'M_param' matrices

M_param_row

This is a list of row labels of 'M_param' matrices. It is simply c(1:sbar).

mparam

This is a list of multinomial logit coefficients which were used to compute 'M_param' matrices. These coefficients are useful to compute the likelihood of proxy responses.

typeprob

This is a type probability matrix of size N-by-sbar. The ij-th entry of this matrix gives the probability of observation i to have type j.

Author(s)

Yujung Hwang, yujungghwang@gmail.com

References

Dempster, Arthur P., Nan M. Laird, and Donald B. Rubin (1977)

"Maximum likelihood from incomplete data via the EM algorithm." Journal of the Royal Statistical Society: Series B (Methodological) 39.1 : 1-22. doi: 10.1111/j.2517-6161.1977.tb01600.x

Hu, Yingyao (2008)

Identification and estimation of nonlinear models with misclassification error using instrumental variables: A general solution. Journal of Econometrics, 144(1), 27-61. doi: 10.1016/j.jeconom.2007.12.001

Hu, Yingyao (2017)

The econometrics of unobservables: Applications of measurement error models in empirical industrial organization and labor economics. Journal of Econometrics, 200(2), 154-168. doi: 10.1016/j.jeconom.2017.06.002

Hwang, Yujung (2021)

Identification and Estimation of a Dynamic Discrete Choice Models with Endogenous Time-Varying Unobservable States Using Proxies. Working Paper.

Hwang, Yujung (2021)

Bounding Omitted Variable Bias Using Auxiliary Data. Working Paper.

Examples

dat1 <- data.frame(proxy1=c(1,2,3),proxy2=c(2,3,4),proxy3=c(4,3,2))
## default minimum num of obs to run an EM algorithm is 10
dproxyme(dat=dat1,sbar=2,initvar=1,minobs=3)
## you can specify weights
dproxyme(dat=dat1,sbar=2,initvar=1,minobs=3,weights=c(0.1,0.5,0.4))

makeDummy

Description

This function is to make dummy variables using a discrete variable.

Usage

makeDummy(tZ)

Arguments

tZ

An input vector

Value

Returns dZ, a matrix of size length(tZ)-by-card(tZ) :

The ij-th element in dZ is 1 if tZ[i] is equal to the j-th largest value of tZ. And the ij-th element in DZ is 0 otherwise. The row sum of dZ must be 1 by construction.

Author(s)

Yujung Hwang, yujungghwang@gmail.com

Examples

makeDummy(c(1,2,3))

weighted.cov

Description

This function is to compute an unbiased sample weighted covariance. The function uses only pairwise complete observations.

Usage

weighted.cov(x, y, w = NULL)

Arguments

x

An input vector to compute a covariance, cov(x,y)

y

An input vector to compute a covariance, cov(x,y)

w

A weight vector

Value

Returns an unbiased sample weighted covariance

Author(s)

Yujung Hwang, yujungghwang@gmail.com

Examples

# If you do not specify weights, 
# it returns the usual unweighted sample covariance 
weighted.cov(x=c(1,3,5),y=c(2,3,1)) 

weighted.cov(x=c(1,3,5),y=c(2,3,1),w=c(0.1,0.5,0.4))

weighted.var

Description

This function is to compute an unbiased sample weighted variance.

Usage

weighted.var(x, w = NULL)

Arguments

x

A vector to compute a variance, var(x)

w

A weight vector

Value

Returns an unbiased sample weighted variance

Author(s)

Yujung Hwang, yujungghwang@gmail.com

Examples

## If you do not specify weights, 
## it returns the usual unweighted sample variance
weighted.var(x=c(1,3,5)) 

weighted.var(x=c(1,3,5),w=c(0.1,0.5,0.4))

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