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Options:

Choose from the following items for name. The possibilities include items stored as is in dbuf (and so could also be retrieved with the Gauss command vread), calculated from dbuf, special optional items that can be added ahead of time, and additional items that can be computed but require the added items. From the perspective of the user, items in each of these categories can be treated identically, as all calculations are automatic. Items are not case sensitive. (Items that use true values from individual-level data will only work if you have vput this information into _Eres prior to running ei under the name truth. These are useful for verifying the method if individual-level data are available, but they are not useful for most ecological inference applications, where this information is not available. The options are included here only because I needed them while writing the book.)

When used with an EI2 output data buffer (i.e., for $2\times C$ tables), eiread uses use the mean posterior estimate for $X_i$ for some items; the correct multiply imputed values of $x_i$ (x2) are used only where specifically noted.

_EalphaB

value of this global (priors on $\alpha^b$)

_EalphaW

value of this global (priors on $\alpha^w$)

_Ebeta

value of this global (priors on $\breve{\mathfrak{B}}$)

_Ebounds

value of this global (bounds for CML, not quantities of interest).

_Ecdfbvn

value of this global (method of calculating CDF of the bivariate normal)

_EdirTol

value of this global (CML convergence tolerance)

_EdoML

value of this global (do maxlik)

_EdoML_phi

value of this global (input $\phi$'s). Only relevant if _EdoML=0.

_EdoML_vcphi

value of this global (input variance-covariance of $\phi$'s). Only relevant if _EdoML=0.

_Eeta

value of this global (expanded model specifications; see Chapter 9).

_EI_bma_prior

value of this global (prior model probabilities for Bayesian Model Averaging).

_EI_vc

value of this global (variance matrix computation)

_EImodels_save

value of this global (file name for eimodels_run).

_EIgraph_bvsmth

value of this global (smoothing parameter for nonparametric density estimation)

_EisChk

value of this global (check importance sampling)

_EisFac

value of this global (number to multiply by variance matrix by in importance sampling or $-1$ for normal approximation)

_EisN

value of this global (first stage importance sampling factor)

_EisT

value of this global (multivariate $t$ or normal for importance sampling)

_EmaxIter

value of this global (maximum iterations for CML)

_EnonEval

value of this global (number of nonparametric density evaluations for each tomography line). Only relevant if _Enonpar=1.

_EnonNumInt

value of this global (number of points to evaluate for numerical integration in computing the denominator for the bivariate kernel density). Only relevant if _Enonpar=1.

_EnonPar

value of this global (0, parametric or 1, nonparametric, estimation).

_EnumTol

value of this global (numerical tolerance for homogeneous and unanimous precincts)

_Erho

value of this global (prior on $\rho$). See Section 7.4.

_Eselect

value of this global (vector of 0/1 to delete/select observations during likelihood stage, or 1 to select all).

_EselRnd

value of this global (fraction of observations to select randomly).

_Esigma

value of this global (priors on $\breve{\sigma}_b$ and $\breve{\sigma}_w$). See Section 7.4.

_Esims

value of this global (number of simulations). See Appendix F.

_Estval

value of this global when ei was run (starting values).

_n

$p\times 1$: the original variable $N_i$ from the first stage EI analysis. This works only for EI2.

_t

$p\times 1$: the original variable $T_i$ from the first stage EI analysis. This works only for EI2.

_EvTol

value of this global (numerical tolerance for the conditional variance).

_x

$p\times 1$: the original variable $X_i$ from the first stage EI analysis. This works only for EI2.

_Ez

$2\times 1$: number of covariates (see Chapter 9), including implied constant term for Zb$\vert$Zw; also clears and sets this in global memory.

ABounds

$2\times 2$: aggregate bounds rows:lower,upper; columns:betab,betaw. See Chapter 5.

ABounds2

$2\times 2$: aggregate bounds for the $\lambda$'s from EI2, rows:lower,upper; columns:lambdaB,lambdaW. See Chapter 5.

AggBias

$4\times 2$: regressions of true $\beta_i^b$ and $\beta_i^w$ on a constant and $X_i$. Requires truth to have been vput into _Eres prior to running ei. See Table 11.1, page 219.

aggs

_Esims$\times 2$: simulations of district-level quantities of interest, $\hat{B}^b\sim\hat{B}^w$. See Section 8.3. (Uses x2 simulations when used with ei2).

AggTruth

$2\times 1$: true district-level $B^b$ and $B^w$. Requires truth to have been vput into _Eres prior to running ei. See Chapter 2.

beta

$p\times 2$ point estimates of $\beta_i^b$ (in the first column) and $\beta_i^w$ (in the second) based on their mean posterior. See Section 8.2. (Uses x2 simulations when used with ei2.)

betaB

$p\times 1$ point estimates of $\beta_i^b$ based on its mean posterior. See Section 8.2. (Uses x2 simulations when used with ei2.)

betaBs

$p\times$_Esims: simulations of $\beta_i^b$. See Chapter 8. (Uses x2 simulations when used with ei2).

betaW

$p\times 1$ point estimate of $\beta_i^w$ based on its mean posterior. See Section 8.2. (Uses x2 simulations when used with ei2).

betaWs

$p\times$_Esims: simulations of $\beta_i^w$. See Section 8.2. (Uses x2 simulations when used with ei2).

bounds

$p\times 4$: bounds on $\beta_i^b$ and $\beta_i^w$, lowerB$\sim$upperB$\sim$lowerW$\sim$upperW. See Chapter 5.

bounds2

$p\times 4$: bounds on $\lambda_i^b$ and $\lambda_i^w$, lowerB$\sim$upperB$\sim$lowerW$\sim$upperW. See Chapter 5, eqns 5.4.

checkR

rows($\phi$)$\times 2$ matrix with rows corresponding to $\phi$, columns corresponding to slightly less$\sim$more (by amount _EdirTol) than the MLEs, and each element indicating that the CDFBVN function is sufficiently precise (when 1) and insufficiently precise (when 0). This function calculates the $R$ portion of the likelihood function to make the comparison (Equation 6.15, p.104). See option R.

CI50b

$p\times 2$: lower$\sim$upper 50% confidence intervals for $\beta_i^b$. See Section 8.2. (Uses x2 simulations when used with ei2).

CI50w

$p\times 2$: lower$\sim$upper 50% confidence intervals for $\beta_i^w$. See Section 8.2. (Uses x2 simulations when used with ei2).

CI80b

$p\times 2$: lower$\sim$upper 80% confidence intervals for $\beta_i^b$. See Section 8.2. (Uses x2 simulations when used with ei2).

CI80bw

$p\times 4$: lowerB$\sim$upperB$\sim$lowerW$\sim$upperW 80% confidence intervals for $\beta_i^b$ and $\beta_i^w$. See Section 8.2. (Uses x2 simulations when used with ei2).

CI80w

$p\times 2$: lower$\sim$upper 80% confidence intervals for $\beta_i^w$. See Section 8.2. (Uses x2 simulations when used with ei2).

CI95b

$p\times 2$: lower$\sim$upper 95% confidence intervals for $\beta_i^b$. See Section 8.2. (Uses x2 simulations when used with ei2).

CI95bw

$p\times 4$: lowerB$\sim$upperB$\sim$lowerW$\sim$upperW 95% confidence intervals for $\beta_i^b$ and $\beta_i^w$. See Section 8.2. (Uses x2 simulations when used with ei2).

CI95w

$p\times 2$: lower$\sim$upper 95% confidence intervals for $\beta_i^w$. See Section 8.2. (Uses x2 simulations when used with ei2).

coverage

$2\times 4$: confidence interval coverage; percent of true values within the 50% and 80% confidence intervals: 50b$\sim$80b$\sim$50w$\sim$80w (1st row = means, 2nd = weighted means). Requires truth to have been vput into _Eres prior to running ei. (Uses x2 simulations when used with ei2).

CsbetaB

$p\times 1$ confidence interval-based standard error of $\beta_i^b$. (Uses x2 simulations when used with ei2).

CsbetaW

$p\times 1$ confidence interval-based standard error of $\beta_i^w$. (Uses x2 simulations when used with ei2).

DataSet

Zb$\sim$Zw$\sim$x$\sim$t, used for input to eiloglik. If _Eselect is a scalar less than 1 (for random selection of cases). The global _EselRnd is ignored.

date

a string containing the date and time at which execution completed, as well as the version number and date of the program ${\mathfrak{E}I}$ that created the input data buffer.

double

$2\times 1$ coefficients from a double regression. Requires an EI2 data buffer as input. See Section 4.3.

EaggBias

$4\times 2$: regressions of estimated $\beta_i^b$ and $\beta_i^w$ on a constant term and $X_i$. First row: coefficients, second row: standard errors. See Section 9.2.4.

etaC

$2\times 1$ coefficients implied by global _Eeta

etaS

$2\times 1$ standard errors implied by global _Eeta

ExpVarCI

$100\times 4$: 80% confidence intervals for $T_i$ given $X_i$. X$\sim$20%CI$\sim$mean$\sim$80%CI of sims from $P(T_i\vert X)$, where $X$ in this context is 100 numbers equally spaced between 0 and 1. See Section 8.5. (Uses x2 simulations when used with ei2).

ExpVarCI0

$p\times 4$: 80% confidence intervals for $T_i$ given the observed values of $X_i$ and/or Zb and Zw when applicable. T$\sim$20%CI$\sim$mean$\sim$80%CI of sims from $P(T_i\vert X, Zb, Zw)$ (Uses x2 simulations when used with ei2).

ExpVarCIs

$100\times 4$: same as expvarci, but smoothed with LOESS. Used for eigraph's xtfit. See Section 8.5. (Uses x2 simulations when used with ei2).

GEbw

$p\times 3$: $\beta_i^b\sim\beta_i^w\sim$Nsims. Point estimates of $\beta_i^b$ and $\beta_i^w$, based on the mean posterior under the prior that $\beta_i^b\geq\beta_i^w$. Use this option (instead of beta) if you are reasonably certain that $\beta_i^b\geq\beta_i^w$. This procedure is based on simulations for which the inequality holds, and thus also reports Nsims, the number of simulations on which each estimate is based (If Nsims is not close to _Esims, you may wish to question your assumption or increase _Esims).

GEbwa

$p\times 2$: $B^b\sim B^w$. Aggregate level mean posterior estimates, based on simulations where $\beta_i^b\geq\beta_i^w$. See GEbw for more information.

GEwb

$p\times 3$: $\beta_i^b\sim\beta_i^w\sim$Nsims. Point estimates of $\beta_i^b$ and $\beta_i^w$, based on the mean posterior under the prior that $\beta_i^b\leq\beta_i^w$. Use this option (instead of beta) if you are reasonably certain that $\beta_i^b\leq\beta_i^w$. This procedure is based on simulations for which the inequality holds, and thus also reports Nsims, the number of simulations on which each estimate is based (If Nsims is not close to _Esims, you may wish to question your assumption or increase _Esims).

GEwba

$p\times 2$: $B^b\sim B^w$. Aggregate level mean posterior estimates, based on simulations where $\beta_i^b\leq\beta_i^w$. See GEwb for more information.

GhActual

value of the output global _GhActual, the row of _ei_vc for which a positive definite variance matrix was found.

Goodman

$2\times 2$: row 1: Goodman's Regression coefficients, row 2: standard errors. See Section 3.1.

lnIR

If _EisChk=1, this is a _Esims*_Eisn$\times$rows($\phi$)+1 matrix , containing the log of the importance ratio as the first column and normal simulations of $\tilde{\phi}'$ as the remaining columns. If _EisChk=0, this is the scalar mean importance ratio (equivalent to meanIR below).

LogLik

value of log-likelihood at the maximum (unnormalized)

LogLikS

value of log-likelihood at the maximum (unnormalized) for each observation $i$.

LLikSims

If _EiLlikS=1, this is _Esims$\times 1$ vector of log-likelihood values for each simulation; otherwise it is a scalar mean of these.

Maggs

$2\times 1$: point estimate of 2 district-level parameters, $\hat{B}^b$ and $\hat{B}^w$: meanc(aggs). See Section 8.3. (Uses x2 simulations when used with ei2).

MeanIR

scalar log of the mean importance ratio

mpPsiu

Mean Posterior of $\breve{\psi}$ (rather than MLEs).

N

$p\times 1$: number of individual elements in precinct $i$, ${N_i}$, an input to ei.

Nb

$p\times 1$: denominator of x and t, equal to x.*n, ${N_i^{b}}$ (e.g., number of blacks in the voting age population).

Nb2

for ei2 data buffers only, $p\times$_Esims: denominator of x2 and V, equal to x2.*n, ${N_i^{b}}$ (e.g., number of blacks in the voting age population).

Nt

$p\times 1$: numerator of t, equal to t.*n, $N^t_i$ (e.g., number of people who turnout).

NbN

$p\times 1$: ${N_i^{bN}}$ (e.g., number of blacks who don't vote). Requires truth to have been vput into _Eres prior to running ei. See Chapter 2.

NbT

$p\times 1$: ${N_i^{bT}}$ (e.g., number of blacks who vote). Requires truth to have been vput into _Eres prior to running ei. See Chapter 2.

Neighbor

Freedman et al.'s neighborhood model point estimates (i.e., assuming $\beta_i^b=\beta_i^w$, with implied standard errors of zero).

nobs

scalar: number of observations, $p$.

Nw

$p\times 1$: equal to (1-x).*n, ${N_i^{w}}$ (e.g., number of whites in the voting age population)

Nw2

for ei2 data buffers only, $p\times$_Esims: equal to (1-x2).*n, ${N_i^{w}}$ (e.g., number of whites in the voting age population)

NwN

$p\times 1$ ${N_i^{wN}}$: (e.g., number of whites who don't vote). Requires truth to have been vput into _Eres prior to running ei. See Chapter 2.

NwT

$p\times 1$: ${N_i^{wT}}$ (e.g., number of whites who Turnout). Requires truth to have been vput into _Eres prior to running ei. See Chapter 2.

Paggs

$2\times 2$: row 1: $\hat{B}^b$ and $\hat{B}^w$; row 2: standard errors. See Section 8.3. (Uses x2 simulations when used with ei2).

Palmquist

scalar: Palmquist's Inflation Factor. See Equation 3.14, page 52.

ParNames

character vector of names for $\phi$ (_cml_parnames).

phi

maximum posterior estimates from CML.

PhiSims

If _EisChk==1, PhiSims is a _Esims$\times$rows($\phi$) matrix of random simulations of $\phi$; otherwise, it is a rows($\phi$)$\times 2$ matrix of the means (in the first column) and standard deviations (in the second column) of the simulations (which are the mean and standard deviations of the posterior distribution of $\phi$). See Section 8.2.

Pphi

$2\times 5$ maximum posterior estimates. row 1: $\phi$, row 2: standard errors. See Chapter 7.

psi

reparameterized $\phi$ into ultimate truncated scale. See Section 6.2.2.

PsiTruth

$5\times 1$: true values of $\psi$ (i.e., on truncated scale). Requires truth to have been vput into _Eres prior to running ei. See Table 10.3, page 207.

psiu

$\breve{\psi}$, which was reparameterized from $\phi$ into untruncated scale. See Equation 7.4, page 136.

R

The sum of the log of the volume above the unit square under the bivariate normal, $R(\breve{\mathfrak{B}},\breve{\Sigma})$. This is the last piece of the likelihood function. See checkR.

Ri

The log of the volume above the unit square under the bivariate normal, $R(\breve{\mathfrak{B}},\breve{\Sigma})$ for each $i$. This is the last piece of the likelihood function, and will differ over $i$ only if covariates are included. See checkR.

resamp

number of resampling tries. This number will range between 1 and _Esims and is better if small. If it is greater than 15-20, you can try adjusting _Eisn or _EisFac and rerunning ei.

RetCode

CML return code. zero means everything is ok.

RNbetaBs

$p\times$_Esims: randomly horizontally permuted simulations of $\beta_i^b$. This is essentially equivalent to betaBs except that it randomly permutes estimation variation also. (Uses x2 simulations when used with ei2).

RNbetaWs

$p\times$_Esims: randomly horizontally permuted simulations of $\beta_i^w$. This is essentially equivalent to betaWs except that it randomly permutes estimation variation also. (Uses x2 simulations when used with ei2).

sbetaB

$p\times 1$ standard error for the estimate of $\beta_i^b$, based on the standard deviation of its posterior. See Section 8.2. (Uses x2 simulations when used with ei2).

sbetaW

$p\times 1$ standard error for the estimate of $\beta_i^w$, based on the standard deviation of its posterior. See Section 8.2. (Uses x2 simulations when used with ei2).

STbetaBs

$p\times$_Esims: SORTED simulations of $\beta_i^b$ (e.g., the 80% confidence interval lower bound is STbetaBs[int(0.1*_Esims)]). See Section 8.2. (Uses x2 simulations when used with ei2).

STbetaWs

$p\times$_Esims: SORTED simulations of $\beta_i^w$ (e.g., the 80% confidence interval upper bound is STbetaWs[int(0.9*_Esims)]). See Section 8.2. (Uses x2 simulations when used with ei2).

sum

prints a summary of district-level information

t

$p\times 1$: outcome variable proportion, $T_i$ (e.g., turnout); input to ei. If dbuf is the output from ei2, then this option gives $V_i$ (e.g., Democratic fraction of the major party vote), an input to ei2.

Thomsen

$2\times 1$: Estimates of $B^b\vert B^w$ from Thomsen's Ecological Logit Model.

titl

string: a title with descriptive information. Must have been vput into _Eres prior to running ei.

truPtile

p x 2: percentile of sorted simulates at which the true value falls for $\beta_i^b$ and $\beta_i^w$. Requires truth to have been vput into _Eres prior to running ei. See Figure 10.7, page 213. (Uses x2 simulations when used with ei2).

truth

$p\times 2$: true values of the precinct-level quantities of interest $\beta_i^b\sim\beta_i^w$. Must have been vput into _Eres prior to running ei.

truthB

truth[.,1], the true $\beta_i^b$. Requires truth to have been vput into _Eres prior to running ei.

truthW

truth[.,2], the true $\beta_i^w$. Requires truth to have been vput into _Eres prior to running ei.

tsims

$100\times$_Esims$+1$: simulations of $T_i$ given $X_i$. rows correspond to 100 values of $X_i$ equally spaced between zero and one, columns are $X_i$ and sorted simulations of $T_i\vert X_i$. See Section 8.5. (Uses x2 simulations when used with ei2).

tsims0

$p\times$_Esims$+1$: simulations of $T_i$ given observed values of $X_i$ and/or Zb and Zw. The first column is the actual values of $T_i$ (Uses x2 simulations when used with ei2).

VCaggs

$2\times 2$: variance matrix of 2 district-level parameters, $\hat{B}^b$ and $\hat{B}^w$. See Section 8.3. (Uses x2 simulations when used with ei2).

VCphi

global variance matrix of coefficients phi from gvc(). If $\texttt{\_EI\_vc}$ is set to {-1 0 }, then it returns the inverse of the variance matrix.

x

$p\times 1$: explanatory variable proportion, $X_i$ (e.g., black voting age population); input to ei. (for ei2, this is the mean posterior estimate of $x_i$, as, e.g., the black fraction of those voting).

x2

for ei2 data buffers only, $p\times\texttt{\_Esims}$: simulations of the explanatory variable proportion, $x_i$ (e.g., black fraction of voters).

x2rn

for ei2 data buffers only, $p\times\texttt{\_Esims}$: horizontally randomly permuted simulations of the explanatory variable proportion, $x_i$ (e.g., black fraction of voters). (This is useful because x2 has only _EI2_m unique columns.)

Zb

matrix of covariates for $\beta_i^b$ or 1 for none; as affected by _Eeta; input to ei. See Section 9.2.1.

Zw

matrix of covariates for $\beta_i^w$ or 1 for none; as affected by _Eeta; input to ei. See Section 9.2.1.