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+GAM Example +
+
+
+
+Calculating Odds Ratio for Static Increases of a Continuous +Variable +
+In this example we take predictor x2 (randomly chosen).
+First we define start and stop values via values.
+or_gam(
+ data = data_gam, model = fit_gam, pred = "x2",
+ values = c(0.099, 0.198)
+)
+#> predictor value1 value2 oddsratio CI_low (2.5%) CI_high (97.5%)
+#> 1 x2 0.099 0.198 23.32353 23.30424 23.34283Inspecting the plot we see that the odds of response y
+happening are 22 times higher when predictor x2 increases
+from 0.099 to 0.198, while holding all other predictors constant.
The detailed steps are
+-
+
- Set all predictors to their mean value +
- Predict the response, +
- Change the selected predictor to a new value and predict the +response again. +
This result in two “log odds” values, which are subsequently +transformed into “odds”. Finally, the odds ratio can be calculated from +these two odds values.
+
+
+
+Odds ratio for Discrete Variables +
+or_gam() is able to handle factor variables. The levels
+which should be be compared need to be passed to
+values.
+or_gam(
+ data = data_gam, model = fit_gam,
+ pred = "x4", values = c("A", "B")
+)
+#> predictor value1 value2 oddsratio CI_low (2.5%) CI_high (97.5%)
+#> 1 x4 A B 1.377537 1.334837 1.421604Here, the change in odds of y happening if predictor
+x4 is changing from level A to B
+is rather small: an increase in odds of 37.8% can be observed.
+
+
+Odds ratio for Percentage increases of a Continuous Variables +
+To get an impression of odds ratio changes throughout the complete +range of the smoothing function of the fitted GAM model for a specific +predictor, odds ratios based on percentage steps of the predictors +distribution.
+Here we slice predictor x2 into five parts by extracting
+the predictor values in 20% steps.
+or_gam(
+ data = data_gam, model = fit_gam, pred = "x2",
+ percentage = 20, slice = TRUE
+)
+#> predictor value1 value2 perc1 perc2 oddsratio CI_low (2.5%) CI_high (97.5%)
+#> 1 x2 0.001 0.200 0 20 2510.77 1091.68 5774.53
+#> 2 x2 0.200 0.400 20 40 0.03 0.03 0.03
+#> 3 x2 0.400 0.599 40 60 0.58 0.56 0.60
+#> 4 x2 0.599 0.799 60 80 0.06 0.06 0.06
+#> 5 x2 0.799 0.998 80 100 0.41 0.75 0.22We can see that there is a high odds ratio reported when increasing
+predictor x2 from 0.008 to 0.206 while all further
+predictor increases decrease the odds of response y
+happening substantially.
+
+
+Plot GAM(M) Smoothing Functions +
+plot_gam() helps to simplify the plotting of GAM
+smoothing functions in R:
+library(ggplot2)
+plot_gam(fit_gam, pred = "x2", title = "Predictor 'x2'") +
+ theme_minimal()
You can further customize the look using other colors or line types.
+Besides making use of the implemented arguments of the function, you can
+save the result of plot_gam() to an object and add more
+ggplot2 calls afterwards.
+
+
+
+Add Odds Ratio Information Into Smoothing Function Plot +
+So far we computed the odds ratios and created a plot of a GAM
+smoothing function. Why not combine both? This is what
+insert_or()aims at. It takes
-
+
-
+
ggplotplotting object containing the smooth function +and
+ - a [data.frame] returned from
or_gam()containing +information about the predictor and the respective values that should be +inserted.
+
+plot_object <- plot_gam(fit_gam, pred = "x2", title = "Predictor 'x2'")
+or_object <- or_gam(
+ data = data_gam, model = fit_gam,
+ pred = "x2", values = c(0.099, 0.198)
+)
+
+plot <- insert_or(plot_object, or_object,
+ or_yloc = 3,
+ values_xloc = 0.05, arrow_length = 0.02,
+ arrow_col = "red"
+)
+plot +
+ theme_minimal()
The odds ratio information is always centered between the two
+vertical lines. Hence it only looks nice if the gap between the two
+chosen values (here 0.099 and 0.198) is large enough. If the smoothing
+line crosses the inserted text, you can correct it by adjusting
+or_yloc. This argument sets the y-location of the inserted
+odds ratio information.
Depending on the digits of your chosen values (here 3), you might +also need to adjust the x-axis location of the two values so that they +do not interfere with the vertical line.
+Let’s do all of this by inserting another odds ratio result into this
+plot. This time we simply take the already produced plot as an input to
+insert_or() and use a new odds ratio result:
+or_object2 <- or_gam(
+ data = data_gam, model = fit_gam,
+ pred = "x2", values = c(0.4, 0.6)
+)
+
+insert_or(plot, or_object2,
+ or_yloc = 2.1, values_yloc = 2,
+ line_col = "green4", text_col = "black",
+ rect_col = "green4", rect_alpha = 0.2,
+ line_alpha = 1, line_type = "dashed",
+ arrow_xloc_r = 0.01, arrow_xloc_l = -0.01,
+ arrow_length = 0.02, rect = TRUE
+) +
+ theme_minimal()
Using rect = TRUE, you can additionally highlight
+certain odds ratio intervals. Aesthetics like opacity or color are fully
+customizable.
+
+
+ GLM Example +
+Fit model.
+
+fit_glm <- glm(admit ~ gre + gpa + rank, data = data_glm, family = "binomial")
+
+
+
+Odds Ratio for Continuous Predictors +
+For GLMs, the odds ratio calculation is simpler because odds ratio +changes correspond to static predictor increases throughout the complete +value range of each predictor
+Hence, [or_glm()] takes the increment steps of each predictor
+directly as an input via argument incr. To avoid false
+predictor/value assignments, the combinations need to be given in a
+named list. Odds ratios of indicator variables are computed
+automatically and always refer to the base factor level.
The indicator predictor rank in this example dataset has
+four levels. Subsequently, we will get three odds ratio outputs
+referring to the base factor level (here: rank1)
The output can be interpreted as follows: “Given rank2
+instead of rank1 while holding all other values constant
+results in a decrease in odds of 49.1% (1-0.509)”.
+or_glm(data = data_glm, model = fit_glm, incr = list(gre = 380, gpa = 5))
+#> predictor oddsratio ci_low (2.5) ci_high (97.5) increment
+#> 1 gre 2.364 1.054 5.396 380
+#> 2 gpa 55.712 2.229 1511.282 5
+#> 3 rank2 0.509 0.272 0.945 Indicator variable
+#> 4 rank3 0.262 0.132 0.512 Indicator variable
+#> 5 rank4 0.212 0.091 0.471 Indicator variableYou can also set other confident intervals for GLM(M) models. The +resulting [data.frame] will automatically adjust the column names to the +specified level.
+
+or_glm(
+ data = data_glm, model = fit_glm,
+ incr = list(gre = 380, gpa = 5), ci = 0.70
+)
+#> predictor oddsratio ci_low (15) ci_high (85) increment
+#> 1 gre 2.364 1.540 3.647 380
+#> 2 gpa 55.712 10.084 314.933 5
+#> 3 rank2 0.509 0.366 0.706 Indicator variable
+#> 4 rank3 0.262 0.183 0.374 Indicator variable
+#> 5 rank4 0.212 0.136 0.325 Indicator variable