# Summarizing Results

# Extracting summary tables

The most common function used to view an overall summary of a model is the `summary()` function:

    library(logitr)

    model <- logitr(
      data    = yogurt,
      outcome = "choice",
      obsID   = "obsID",
      pars    = c("price", "feat", "brand")
    )

    summary(model)
    #> =================================================
    #>
    #> Model estimated on: Wed Sep 27 11:04:22 2023
    #>
    #> Using logitr version: 1.1.1
    #>
    #> Call:
    #> logitr(data = yogurt, outcome = "choice", obsID = "obsID", pars = c("price",
    #>     "feat", "brand"))
    #>
    #> Frequencies of alternatives:
    #>        1        2        3        4
    #> 0.402156 0.029436 0.229270 0.339138
    #>
    #> Exit Status: 3, Optimization stopped because ftol_rel or ftol_abs was reached.
    #>
    #> Model Type:    Multinomial Logit
    #> Model Space:          Preference
    #> Model Run:                1 of 1
    #> Iterations:                   21
    #> Elapsed Time:        0h:0m:0.01s
    #> Algorithm:        NLOPT_LD_LBFGS
    #> Weights Used?:             FALSE
    #> Robust?                    FALSE
    #>
    #> Model Coefficients:
    #>               Estimate Std. Error  z-value  Pr(>|z|)
    #> price        -0.366555   0.024365 -15.0441 < 2.2e-16 ***
    #> feat          0.491439   0.120062   4.0932 4.254e-05 ***
    #> brandhiland  -3.715477   0.145417 -25.5506 < 2.2e-16 ***
    #> brandweight  -0.641138   0.054498 -11.7645 < 2.2e-16 ***
    #> brandyoplait  0.734519   0.080642   9.1084 < 2.2e-16 ***
    #> ---
    #> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    #>
    #> Log-Likelihood:         -2656.8878790
    #> Null Log-Likelihood:    -3343.7419990
    #> AIC:                     5323.7757580
    #> BIC:                     5352.7168000
    #> McFadden R2:                0.2054148
    #> Adj McFadden R2:            0.2039195
    #> Number of Observations:  2412.0000000

The summary prints out a table of the model coefficients as well as other information about the model, such as the log-likelihood, the number of observations, etc.

You can extract the coefficient from the summary table as a `data.frame` using `coef(summary(model))`:

    coefs <- coef(summary(model))
    coefs
    #>                Estimate Std. Error    z-value     Pr(>|z|)
    #> price        -0.3665546 0.02436526 -15.044150 0.000000e+00
    #> feat          0.4914392 0.12006175   4.093221 4.254226e-05
    #> brandhiland  -3.7154773 0.14541671 -25.550553 0.000000e+00
    #> brandweight  -0.6411384 0.05449794 -11.764450 0.000000e+00
    #> brandyoplait  0.7345195 0.08064229   9.108366 0.000000e+00

## The {broom} package

Another approach for extracting the model coefficients as a data frame is to use the `tidy()` function from the {broom} package:

    library(broom)

    coefs <- tidy(model)
    coefs
    #> # A tibble: 5 × 5
    #>   term         estimate std.error statistic   p.value
    #>   <chr>           <dbl>     <dbl>     <dbl>     <dbl>
    #> 1 price          -0.367    0.0244    -15.0  0
    #> 2 feat            0.491    0.120       4.09 0.0000425
    #> 3 brandhiland    -3.72     0.145     -25.6  0
    #> 4 brandweight    -0.641    0.0545    -11.8  0
    #> 5 brandyoplait    0.735    0.0806      9.11 0

The `tidy()` function returns a `tibble` and provides a more standardized output and interfaces well with other packages. You can also append a confidence interval to the data frame:

    coefs <- tidy(model, conf.int = TRUE, conf.level = 0.95)
    coefs
    #> # A tibble: 5 × 7
    #>   term         estimate std.error statistic   p.value conf.low conf.high
    #>   <chr>           <dbl>     <dbl>     <dbl>     <dbl>    <dbl>     <dbl>
    #> 1 brandhiland    -3.72     0.145     -25.6  0           -4.01     -3.43
    #> 2 brandweight    -0.641    0.0545    -11.8  0           -0.747    -0.535
    #> 3 brandyoplait    0.735    0.0806      9.11 0            0.576     0.890
    #> 4 feat            0.491    0.120       4.09 0.0000425    0.256     0.728
    #> 5 price          -0.367    0.0244    -15.0  0           -0.413    -0.318

# Extracting other values

You can also extract other values of interest at the solution, such as:

The estimated coefficients

    coef(model)
    #>        price         feat  brandhiland  brandweight brandyoplait
    #>   -0.3665546    0.4914392   -3.7154773   -0.6411384    0.7345195

The estimated standard errors

    se(model)
    #>        price         feat  brandhiland  brandweight brandyoplait
    #>   0.02436526   0.12006175   0.14541671   0.05449794   0.08064229

The log-likelihood

    logLik(model)
    #> 'log Lik.' -2656.888 (df=5)

The variance-covariance matrix

    vcov(model)
    #>                      price          feat  brandhiland  brandweight
    #> price         0.0005936657  5.729619e-04  0.001851795 1.249988e-04
    #> feat          0.0005729619  1.441482e-02  0.000855011 5.092011e-06
    #> brandhiland   0.0018517954  8.550110e-04  0.021146019 1.490080e-03
    #> brandweight   0.0001249988  5.092012e-06  0.001490080 2.970026e-03
    #> brandyoplait -0.0015377721 -1.821331e-03 -0.003681036 7.779428e-04
    #>               brandyoplait
    #> price        -0.0015377721
    #> feat         -0.0018213311
    #> brandhiland  -0.0036810363
    #> brandweight   0.0007779427
    #> brandyoplait  0.0065031782

You can also view a summary of statistics about the model using the `glance()` function from the {broom} package:

    glance(model)
    #> # A tibble: 1 × 7
    #>   logLik null.logLik   AIC   BIC r.squared adj.r.squared  nobs
    #>    <dbl>       <dbl> <dbl> <dbl>     <dbl>         <dbl> <dbl>
    #> 1 -2657.      -3344. 5324. 5353.     0.205         0.204  2412

# Formatted summary tables

## The {gtsummary} package

Often times you will need to create summary tables that are formatted for publication. The {gtsummary} package offers a convenient solution that works well with `logitr`models. For example, a formatted summary table can be obtained using the `tbl_regression()` function:

    library(gtsummary)

    model |>
      tbl_regression()

Characteristic | Beta | 95% CI 1 | p-value
--- | --- | --- | ---
brand |  |  |
dannon | — | — |
hiland | -3.7 | -4.0, -3.4 | <0.001
weight | -0.64 | -0.75, -0.53 | <0.001
yoplait | 0.73 | 0.58, 0.89 | <0.001
feat | 0.49 | 0.26, 0.73 | <0.001
price | -0.37 | -0.41, -0.32 | <0.001
1 CI = Confidence Interval

The `tbl_regression()` function has many options for customizing the output table. For example, you can change the coefficient names with the `label` argument:

    model |>
      tbl_regression(
        label = list(
            feat = "Newspaper ad shown?",
            brand = "Yogurt's brand"
        )
      )

Characteristic | Beta | 95% CI 1 | p-value
--- | --- | --- | ---
Yogurt's brand |  |  |
dannon | — | — |
hiland | -3.7 | -4.0, -3.4 | <0.001
weight | -0.64 | -0.75, -0.53 | <0.001
yoplait | 0.73 | 0.58, 0.89 | <0.001
Newspaper ad shown? | 0.49 | 0.25, 0.73 | <0.001
price | -0.37 | -0.41, -0.32 | <0.001
1 CI = Confidence Interval

The {gtsummary} package supports a wide variety of output types, including support for LaTeX. One you create the table with `tbl_regression()`, you can print it a variety of ways. For example, once you’ve created a table `x`,

    x <- model |>
      tbl_regression()

you can print it to LaTeX with any of the following ways:

- `as_gt(x) |> gt::as_latex()`
- `as_kable_extra(x, format = "latex")`
- `as_hux_table(x) |> to_latex()`
- `as_kable(x, format = "latex")`

Multiple models can also be printed in the same table:

    model1 <- model

    model2 <- logitr(
      data    = yogurt,
      outcome = "choice",
      obsID   = "obsID",
      pars    = c("price*feat", "brand")
    )

    # Make individual tables
    t1 <- tbl_regression(model1)
    t2 <- tbl_regression(model2)

    # Merge tables
    tbl_merge(
      tbls = list(t1, t2),
      tab_spanner = c("**Baseline**", "**Interaction**")
    )

Characteristic | Baseline | Interaction
--- | --- | ---
Beta | 95% CI 1 | p-value | Beta | 95% CI 1 | p-value
brand |  |  |  |  |  |
dannon | — | — |  | — | — |
hiland | -3.7 | -4.0, -3.4 | <0.001 | -3.7 | -4.0, -3.4 | <0.001
weight | -0.64 | -0.75, -0.53 | <0.001 | -0.64 | -0.75, -0.53 | <0.001
yoplait | 0.73 | 0.58, 0.89 | <0.001 | 0.72 | 0.57, 0.88 | <0.001
feat | 0.49 | 0.26, 0.72 | <0.001 | 1.2 | 0.39, 1.9 | 0.002
price | -0.37 | -0.41, -0.32 | <0.001 | -0.36 | -0.41, -0.31 | <0.001
price * feat |  |  |  | -0.09 | -0.18, 0.01 | 0.068
1 CI = Confidence Interval

## The {texreg} package

Another option for obtaining a formatted table is to use the {texreg} package. This is particularly useful for obtaining tables formatted for use in LaTeX.

For example, you can print a summary to the screen using `screenreg()`:

    library(texreg)

    screenreg(model, stars = c(0.01, 0.05, 0.1))
    #>
    #> ============================
    #>                 Model 1
    #> ----------------------------
    #> price              -0.37 ***
    #>                    (0.02)
    #> feat                0.49 ***
    #>                    (0.12)
    #> brandhiland        -3.72 ***
    #>                    (0.15)
    #> brandweight        -0.64 ***
    #>                    (0.05)
    #> brandyoplait        0.73 ***
    #>                    (0.08)
    #> ----------------------------
    #> Log Likelihood  -2656.89
    #> null.logLik     -3343.74
    #> AIC              5323.78
    #> BIC              5352.72
    #> R^2                 0.21
    #> Adj. R^2            0.20
    #> nobs             2412.00
    #> ============================
    #> *** p < 0.01; ** p < 0.05; * p < 0.1

Likewise, you can print the LaTeX code for a summary table using `texreg()`

    library(texreg)

    texreg(model, stars = c(0.01, 0.05, 0.1))
    #>
    #> \begin{table}
    #> \begin{center}
    #> \begin{tabular}{l c}
    #> \hline
    #>  & Model 1 \\
    #> \hline
    #> price          & $-0.37^{***}$ \\
    #>                & $(0.02)$      \\
    #> feat           & $0.49^{***}$  \\
    #>                & $(0.12)$      \\
    #> brandhiland    & $-3.72^{***}$ \\
    #>                & $(0.15)$      \\
    #> brandweight    & $-0.64^{***}$ \\
    #>                & $(0.05)$      \\
    #> brandyoplait   & $0.73^{***}$  \\
    #>                & $(0.08)$      \\
    #> \hline
    #> Log Likelihood & $-2656.89$    \\
    #> null.logLik    & $-3343.74$    \\
    #> AIC            & $5323.78$     \\
    #> BIC            & $5352.72$     \\
    #> R$^2$          & $0.21$        \\
    #> Adj. R$^2$     & $0.20$        \\
    #> nobs           & $2412.00$     \\
    #> \hline
    #> \multicolumn{2}{l}{\scriptsize{$^{***}p<0.01$; $^{**}p<0.05$; $^{*}p<0.1$}}
    #> \end{tabular}
    #> \caption{Statistical models}
    #> \label{table:coefficients}
    #> \end{center}
    #> \end{table}

Similar to {gtsummary}, multiple models can be printed using `screenreg()` or `texreg()`:

    model1 <- model

    model2 <- logitr(
      data    = yogurt,
      outcome = "choice",
      obsID   = "obsID",
      pars    = c("price*feat", "brand")
    )

    screenreg(
      list(
        model1,
        model2
      ),
      stars = c(0.01, 0.05, 0.1),
      custom.model.names = c("Baseline", "Interaction")
    )
    #>
    #> ==========================================
    #>                 Baseline      Interaction
    #> ------------------------------------------
    #> price              -0.37 ***     -0.36 ***
    #>                    (0.02)        (0.02)
    #> feat                0.49 ***      1.16 ***
    #>                    (0.12)        (0.38)
    #> brandhiland        -3.72 ***     -3.72 ***
    #>                    (0.15)        (0.15)
    #> brandweight        -0.64 ***     -0.64 ***
    #>                    (0.05)        (0.05)
    #> brandyoplait        0.73 ***      0.72 ***
    #>                    (0.08)        (0.08)
    #> price:feat                       -0.09 *
    #>                                  (0.05)
    #> ------------------------------------------
    #> Log Likelihood  -2656.89      -2655.54
    #> null.logLik     -3343.74      -3343.74
    #> AIC              5323.78       5323.08
    #> BIC              5352.72       5357.81
    #> R^2                 0.21          0.21
    #> Adj. R^2            0.20          0.20
    #> nobs             2412.00       2412.00
    #> ==========================================
    #> *** p < 0.01; ** p < 0.05; * p < 0.1