# estimateEffect: Estimates regressions using an STM object In stm: Estimation of the Structural Topic Model

## Description

Estimates a regression where documents are the units, the outcome is the proportion of each document about a topic in an STM model and the covariates are document-meta data. This procedure incorporates measurement uncertainty from the STM model using the method of composition.

## Usage

 ```1 2 3 4 5 6 7 8 9``` ```estimateEffect( formula, stmobj, metadata = NULL, uncertainty = c("Global", "Local", "None"), documents = NULL, nsims = 25, prior = NULL ) ```

## Arguments

 `formula` A formula for the regression. It should have an integer or vector of numbers on the left-hand side and an equation with covariates on the right hand side. See Details for more information. `stmobj` Model output from STM `metadata` A dataframe where all predictor variables in the formula can be found. If `NULL` R will look for the variables in the global namespace. It will not look for them in the `STM` object which for memory efficiency only stores the transformed design matrix and thus will not in general have the original covariates. `uncertainty` Which procedure should be used to approximate the measurement uncertainty in the topic proportions. See details for more information. Defaults to the Global approximation. `documents` If uncertainty is set to `Local`, the user needs to provide the documents object (see `stm` for format). `nsims` The number of simulated draws from the variational posterior. Defaults to 25. This can often go even lower without affecting the results too dramatically. `prior` This argument allows the user to specify a ridge penalty to be added to the least squares solution for the purposes of numerical stability. If its a scalar it is added to all coefficients. If its a matrix it should be the prior precision matrix (a diagonal matrix of the same dimension as the `ncol(X)`). When the design matrix is collinear but this argument is not specified, a warning will pop up and the function will estimate with a small default penalty.

## Details

This function performs a regression where topic-proportions are the outcome variable. This allows us to conditional expectation of topic prevalence given document characteristics. Use of the method of composition allows us to incorporate our estimation uncertainty in the dependent variable. Mechanically this means we draw a set of topic proportions from the variational posterior, compute our coefficients, then repeat. To compute quantities of interest we simulate within each batch of coefficients and then average over all our results.

The formula specifies the nature of the linear model. On the left hand-side we use a vector of integers to indicate the topics to be included as outcome variables. If left blank then the default of all topics is used. On the right hand-side we can specify a linear model of covariates including standard transformations. Thus the model `2:4 ~ var1 + s(var2)` would indicate that we want to run three regressions on Topics 2, 3 and 4 with predictor variables `var1` and a b-spline transformed `var2`. We encourage the use of spline functions for non-linear transformations of variables.

The function allows the user to specify any variables in the model. However, we caution that for the assumptions of the method of composition to be the most plausible the topic model should contain at least all the covariates contained in the `estimateEffect` regression. However the inverse need not be true. The function will automatically check whether the covariate matrix is singular which generally results from linearly dependent columns. Some common causes include a factor variable with an unobserved level, a spline with degrees of freedom that are too high, or a spline with a continuous variable where a gap in the support of the variable results in several empty basis functions. In these cases the function will still estimate by adding a small ridge penalty to the likelihood. However, we emphasize that while this will produce an estimate it is only identified by the penalty. In many cases this will be an indication that the user should specify a different model.

The function can handle factors and numeric variables. Dates should be converted to numeric variables before analysis.

We offer several different methods of incorporating uncertainty. Ideally we would want to use the covariance matrix that governs the variational posterior for each document (ν). The updates for the global parameters rely only on the sum of these matrices and so we do not store copies for each individual document. The default uncertainty method `Global` uses an approximation to the average covariance matrix formed using the global parameters. The uncertainty method `Local` steps through each document and updates the parameters calculating and then saving the local covariance matrix. The option `None` simply uses the map estimates for θ and does not incorporate any uncertainty. We strongly recommend the `Global` approximation as it provides the best tradeoff of accuracy and computational tractability.

Effects are plotted based on the results of `estimateEffect` which contains information on how the estimates are constructed. Note that in some circumstances the expected value of a topic proportion given a covariate level can be above 1 or below 0. This is because we use a Normal distribution rather than something constrained to the range between 0 and 1. If a continuous variable goes above 0 or 1 within the range of the data it may indicate that a more flexible non-linear specification is needed (such as using a spline or a spline with greater degrees of freedom).

## Value

 `parameters` A list of K elements each corresponding to a topic. Each element is itself a list of n elements one per simulation. Each simulation contains the MLE of the parameter vector and the variance covariance matrix `topics` The topic vector `call` The original call `uncertainty` The user choice of uncertainty measure `formula` The formula object `data` The original user provided meta data. `modelframe` The model frame created from the formula and data `varlist` A variable list useful for mapping terms with columns in the design matrix

`plot.estimateEffect` `summary.estimateEffect`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13``` ```#Just one topic (note we need c() to indicate it is a vector) prep <- estimateEffect(c(1) ~ treatment, gadarianFit, gadarian) summary(prep) plot(prep, "treatment", model=gadarianFit, method="pointestimate") #three topics at once prep <- estimateEffect(1:3 ~ treatment, gadarianFit, gadarian) summary(prep) plot(prep, "treatment", model=gadarianFit, method="pointestimate") #with interactions prep <- estimateEffect(1 ~ treatment*s(pid_rep), gadarianFit, gadarian) summary(prep) ```