Models Available in DSL

Table of Contents

lm: Linear Regression
logit: Logistic Regression
felm: Fixed Effects Linear Regression

Note: We currently cover three models (lm, logit, felm). In the next update, we are planning to add more models, including multinomial-logit regression, poisson regression, and two-stage least squares for the instrumental variable method.

`lm`: Linear Regression

Researchers can implement DSL linear regression by specifying model = "lm".

library(dsl)
data("data_lm") # example data 
head(data_lm)

##          Y   pred_Y         X1         X2         X3        X4         X5
## 1 3.337877 3.288469 0.84678708 0.10927346 0.15178520 0.4336862 0.07082542
## 2 1.283851 1.353864 0.59445495 0.19281988 0.77950672 0.4498675 0.30573402
## 3 3.618762 3.603551 0.91183977 0.97745425 0.19939829 0.3630903 0.97453388
## 4       NA 1.402226 0.24259237 0.03956956 0.02819825 0.8497914 0.95381503
## 5       NA 3.842970 0.51535594 0.78112420 0.31758914 0.5531493 0.46124773
## 6       NA 0.601493 0.09942167 0.28733200 0.44238525 0.5460361 0.83561538

In this example, variable Y requires text annotation (they take NA if a given observation is not labeled by experts). Variable pred_Y represents predictions for Y.

out_lm <- dsl(model = "lm", 
              formula = Y ~ X1 + X2 + X3 + X4 + X5,
              predicted_var = "Y",
              prediction = "pred_Y",
              data = data_lm)

## Cross-Fitting: 1/10..2/10..3/10..4/10..5/10..6/10..7/10..8/10..9/10..10/10..

Argument	Description
`model`	A regression model. `dsl` currently supports `lm` (linear regression), `logit` (logistic regression), and `felm` (fixed-effects regression).
`formula`	A formula used in the specified regression model.
`predicted_var`	A vector of column names in the data that correspond to variables that need to be predicted.
`prediction`	A vector of column names in the data that correspond to predictions of `predicted_var`.
`data`	A data frame. The class should be `data.frame`.

summary(out_lm)

## ==================
## DSL Specification:
## ==================
## Model:  lm
## Call:  Y ~ X1 + X2 + X3 + X4 + X5
## 
## Predicted Variables:  Y
## Prediction:  pred_Y
## 
## Number of Labeled Observations:  245
## Random Sampling for Labeling with Equal Probability: Yes
## 
## =============
## Coefficients:
## =============
##             Estimate Std. Error CI Lower CI Upper p value    
## (Intercept)   0.6450     0.0714   0.5050   0.7850  0.0000 ***
## X1            2.1293     0.0685   1.9951   2.2635  0.0000 ***
## X2            2.1033     0.0645   1.9769   2.2296  0.0000 ***
## X3            0.0448     0.0687  -0.0898   0.1794  0.2572    
## X4            0.0022     0.0635  -0.1223   0.1267  0.4861    
## X5            0.0257     0.0593  -0.0906   0.1419  0.3326    
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 95% confidence intervals (CI) are reported.

`logit`: Logistic Regression

Researchers can implement DSL logistic regression by specifying model = "logit". It requires the same arguments as model = "lm".

data("data_logit") # example data 
head(data_logit)

##    Y         X1 pred_Y    pred_X1         X2          X3          X4
## 1  0 -0.1443742      0  0.9486148 -0.2079232 -0.06932595  1.65748976
## 2  1 -1.2864079      1 -1.8766233 -1.6961906 -0.27274691  1.54678252
## 3  1 -1.4665386      1 -2.4866911 -0.6212224 -0.70787173 -0.27913330
## 4  0 -1.3554115      1  0.5138155  1.2299990 -0.86519213  0.18177847
## 5 NA         NA      1 -2.1116582  0.6624512  1.19504665 -0.02724476
## 6 NA         NA      1 -0.6391120 -0.8971608  1.20072203 -0.51241357
##            X5          X6         X7        X8           X9        X10
## 1  0.96825927  0.05389556 -2.0762690 0.2653279  1.458743948  0.4127003
## 2 -0.46626141  0.73182950 -1.7677551 1.0790758 -0.003172833 -0.5313550
## 3 -0.26973904 -1.75925076 -0.1585703 0.6823146  0.050500221 -1.2679467
## 4  0.41947288 -0.32375937  0.3226157 0.5131867 -2.065367939  1.6111660
## 5 -0.94927647  1.01808653  0.7608077 1.6830265 -1.907959205 -0.6979879
## 6  0.09162689  1.15086391 -0.7917356 0.9765960 -0.144924483 -1.2848539

In this example, variables Y and X1 require text annotation (they take NA if a given observation is not labeled by experts). Variables pred_Y and pred_X1 represent predictions for Y and X1. As in this example, dsl can handle cases when multiple variables require text annotations.

out_logit <- dsl(model = "logit", 
                 formula = Y ~ X1 + X2 + X4,
                 predicted_var = c("Y", "X1"),
                 prediction = c("pred_Y", "pred_X1"),
                 data = data_logit)

## Cross-Fitting: 1/10..2/10..3/10..4/10..5/10..6/10..7/10..8/10..9/10..10/10..

summary(out_logit)

## ==================
## DSL Specification:
## ==================
## Model:  logit
## Call:  Y ~ X1 + X2 + X4
## 
## Predicted Variables:  Y, X1
## Prediction:  pred_Y, pred_X1
## 
## Number of Labeled Observations:  487
## Random Sampling for Labeling with Equal Probability: Yes
## 
## =============
## Coefficients:
## =============
##             Estimate Std. Error CI Lower CI Upper p value    
## (Intercept)  -0.7386     0.1000  -0.9346  -0.5426  0.0000 ***
## X1            0.2208     0.1044   0.0162   0.4255  0.0172   *
## X2            0.0242     0.0974  -0.1667   0.2151  0.4019    
## X4            0.2742     0.1022   0.0739   0.4745  0.0037  **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 95% confidence intervals (CI) are reported.

`felm`: Fixed Effects Linear Regression

Researchers can implement DSL fixed effects linear regression by specifying model = "felm".

data("data_lm")  # example data 
head(data_felm)

##     state year  log_gsp pred_log_gsp log_pcap   log_pc unemp
## 1 ALABAMA 1970       NA     9.738913 9.617981 10.48553   4.7
## 2 ALABAMA 1971 10.28790    10.287899 9.648720 10.52675   5.2
## 3 ALABAMA 1972 10.35147    10.351469 9.678618 10.56283   4.7
## 4 ALABAMA 1973 10.41721    10.417209 9.705418 10.59873   3.9
## 5 ALABAMA 1974 10.42671    10.426706 9.726910 10.64679   5.5
## 6 ALABAMA 1975 10.42240    10.422400 9.759401 10.69130   7.7

In this example, variable log_gsp requires text annotation (it takes NA if a given observation is not labeled by experts). Variable pred_log_gsp represents predictions for log_gsp.

One-way Fixed Effects

To implement DSL one-way fixed effects regression, users can set fixed_effect = "oneway". Use index to denote which column defines fixed effects. Users can also cluster standard errors by specifying a variable name in argument cluster (this cluster argument is also avaiable for other models).

out_felm_one <- dsl(model = "felm", 
                    formula = log_pcap ~ log_gsp + log_pc + unemp,
                    predicted_var =  "log_gsp",
                    prediction = "pred_log_gsp",
                    fixed_effect = "oneway", 
                    index = c("state"), 
                    cluster = "state",
                    data = data_felm)

## Cross-Fitting: 1/10..2/10..3/10..4/10..5/10..6/10..7/10..8/10..9/10..10/10..

Argument	Description
`fixed_effect`	A type of fixed effects regression you run. `oneway` (one-way fixed effects) or `twoways` (two-way fixed effects).
`index`	A vector of column names specifying fixed effects. When `fixed_effect = oneway`, it has one element. When `fixed_effect = twoways`, it has two elements, e.g., `index = c("state", "year")`.
`cluster`	A column name in the data that indicates the level at which cluster standard errors are calculated. Default is `NULL`.

summary(out_felm_one)

## ==================
## DSL Specification:
## ==================
## Model:  felm (oneway)
## Call:  log_pcap ~ log_gsp + log_pc + unemp
## Fixed Effects:  state
## 
## Predicted Variables:  log_gsp
## Prediction:  pred_log_gsp
## 
## Number of Labeled Observations:  334
## Random Sampling for Labeling with Equal Probability: Yes
## 
## =============
## Coefficients:
## =============
##         Estimate Std. Error CI Lower CI Upper p value    
## log_gsp   0.0031     0.0020  -0.0007   0.0069  0.0558   .
## log_pc    0.5357     0.0419   0.4537   0.6178  0.0000 ***
## unemp     0.0067     0.0021   0.0025   0.0108  0.0008 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 95% confidence intervals (CI) are reported.
## Standard errors are clustered by state.

Two-way Fixed Effects

To implement DSL two-way fixed effects regression, users can set fixed_effect = "twoways". Use index (a vector of length 2) to denote which columns define fixed effects.

out_felm_two <- dsl(model = "felm", 
                    formula = log_pcap ~ log_gsp + log_pc + unemp,
                    predicted_var =  "log_gsp",
                    prediction = "pred_log_gsp",
                    fixed_effect = "twoways", 
                    index = c("state", "year"), 
                    cluster = "state",
                    data = data_felm)

## Cross-Fitting: 1/10..2/10..3/10..4/10..5/10..6/10..7/10..8/10..9/10..10/10..

summary(out_felm_two)

## ==================
## DSL Specification:
## ==================
## Model:  felm (twoways)
## Call:  log_pcap ~ log_gsp + log_pc + unemp
## Fixed Effects:  state and year
## 
## Predicted Variables:  log_gsp
## Prediction:  pred_log_gsp
## 
## Number of Labeled Observations:  334
## Random Sampling for Labeling with Equal Probability: Yes
## 
## =============
## Coefficients:
## =============
##         Estimate Std. Error CI Lower CI Upper p value    
## log_gsp   0.0025     0.0017  -0.0009   0.0060  0.0722   .
## log_pc    0.4275     0.0748   0.2809   0.5741  0.0000 ***
## unemp     0.0093     0.0034   0.0027   0.0159  0.0028  **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 95% confidence intervals (CI) are reported.
## Standard errors are clustered by state.

lm: Linear Regression

logit: Logistic Regression

felm: Fixed Effects Linear Regression

One-way Fixed Effects

Two-way Fixed Effects

`lm`: Linear Regression

`logit`: Logistic Regression

`felm`: Fixed Effects Linear Regression