Plot polynomials for (generalized) linear regression

This function plots a scatter plot of a term poly.term against a response variable x and adds - depending on the amount of numeric values in poly.degree - multiple polynomial curves. A loess-smoothed line can be added to see which of the polynomial curves fits best to the data.

Usage

sjp.poly(
  x,
  poly.term,
  poly.degree,
  poly.scale = FALSE,
  fun = NULL,
  axis.title = NULL,
  geom.colors = NULL,
  geom.size = 0.8,
  show.loess = TRUE,
  show.loess.ci = TRUE,
  show.p = TRUE,
  show.scatter = TRUE,
  point.alpha = 0.2,
  point.color = "#404040",
  loess.color = "#808080"
)

Arguments

x: A vector, representing the response variable of a linear (mixed) model; or a linear (mixed) model as returned by lm or lmer.
poly.term: If x is a vector, poly.term should also be a vector, representing the polynomial term (independent variabl) in the model; if x is a fitted model, poly.term should be the polynomial term's name as character string. See 'Examples'.
poly.degree: Numeric, or numeric vector, indicating the degree of the polynomial. If poly.degree is a numeric vector, multiple polynomial curves for each degree are plotted. See 'Examples'.
poly.scale: Logical, if TRUE, poly.term will be scaled before linear regression is computed. Default is FALSE. Scaling the polynomial term may have an impact on the resulting p-values.
fun: Linear function when modelling polynomial terms. Use fun = "lm" for linear models, or fun = "glm" for generalized linear models. When x is not a vector, but a fitted model object, the function is detected automatically. If x is a vector, fun defaults to "lm".
axis.title: Character vector of length one or two (depending on the plot function and type), used as title(s) for the x and y axis. If not specified, a default labelling is chosen. Note: Some plot types may not support this argument sufficiently. In such cases, use the returned ggplot-object and add axis titles manually with labs. Use axis.title = "" to remove axis titles.
geom.colors: user defined color for geoms. See 'Details' in plot_grpfrq.
geom.size: size resp. width of the geoms (bar width, line thickness or point size, depending on plot type and function). Note that bar and bin widths mostly need smaller values than dot sizes.
show.loess: Logical, if TRUE, an additional loess-smoothed line is plotted.
show.loess.ci: Logical, if TRUE, a confidence region for the loess-smoothed line will be plotted.
show.p: Logical, if TRUE (default), p-values for polynomial terms are printed to the console.
show.scatter: Logical, if TRUE (default), adds a scatter plot of data points to the plot.
point.alpha: Alpha value of point-geoms in the scatter plots. Only applies, if show.scatter = TRUE.
point.color: Color of of point-geoms in the scatter plots. Only applies, if show.scatter = TRUE.
loess.color: Color of the loess-smoothed line. Only applies, if show.loess = TRUE.

Value

A ggplot-object.

Details

For each polynomial degree, a simple linear regression on x (resp. the extracted response, if x is a fitted model) is performed, where only the polynomial term poly.term is included as independent variable. Thus, lm(y ~ x + I(x^2) + ... + I(x^i)) is repeatedly computed for all values in poly.degree, and the predicted values of the reponse are plotted against the raw values of poly.term. If x is a fitted model, other covariates are ignored when finding the best fitting polynomial.

This function evaluates raw polynomials, not orthogonal polynomials. Polynomials are computed using the poly function, with argument raw = TRUE.

To find out which polynomial degree fits best to the data, a loess-smoothed line (in dark grey) can be added (with show.loess = TRUE). The polynomial curves that comes closest to the loess-smoothed line should be the best fit to the data.

Examples

library(sjmisc)
data(efc)
# linear fit. loess-smoothed line indicates a more
# or less cubic curve
sjp.poly(efc$c160age, efc$quol_5, 1)
#> Polynomial degrees: 1
#> ---------------------
#> p(x^1): 0.000
#> 
#> `geom_smooth()` using formula = 'y ~ x'


# quadratic fit
sjp.poly(efc$c160age, efc$quol_5, 2)
#> Polynomial degrees: 2
#> ---------------------
#> p(x^1): 0.078
#> p(x^2): 0.533
#> 
#> `geom_smooth()` using formula = 'y ~ x'


# linear to cubic fit
sjp.poly(efc$c160age, efc$quol_5, 1:4, show.scatter = FALSE)
#> Polynomial degrees: 1
#> ---------------------
#> p(x^1): 0.000
#> 
#> Polynomial degrees: 2
#> ---------------------
#> p(x^1): 0.078
#> p(x^2): 0.533
#> 
#> Polynomial degrees: 3
#> ---------------------
#> p(x^1): 0.012
#> p(x^2): 0.001
#> p(x^3): 0.000
#> 
#> Polynomial degrees: 4
#> ---------------------
#> p(x^1): 0.777
#> p(x^2): 0.913
#> p(x^3): 0.505
#> p(x^4): 0.254
#> 
#> `geom_smooth()` using formula = 'y ~ x'



# fit sample model
fit <- lm(tot_sc_e ~ c12hour + e17age + e42dep, data = efc)
# inspect relationship between predictors and response
plot_model(fit, type = "slope")
#> `geom_smooth()` using formula = 'y ~ x'
#> `geom_smooth()` using formula = 'y ~ x'
#> Warning: pseudoinverse used at 4.015
#> Warning: neighborhood radius 2.015
#> Warning: reciprocal condition number  1.5462e-16
#> Warning: There are other near singularities as well. 1

# "e17age" does not seem to be linear correlated to response
# try to find appropiate polynomial. Grey line (loess smoothed)
# indicates best fit. Looks like x^4 has the best fit,
# however, only x^3 has significant p-values.
sjp.poly(fit, "e17age", 2:4, show.scatter = FALSE)
#> Polynomial degrees: 2
#> ---------------------
#> p(x^1): 0.734
#> p(x^2): 0.721
#> 
#> Polynomial degrees: 3
#> ---------------------
#> p(x^1): 0.010
#> p(x^2): 0.011
#> p(x^3): 0.011
#> 
#> Polynomial degrees: 4
#> ---------------------
#> p(x^1): 0.234
#> p(x^2): 0.267
#> p(x^3): 0.303
#> p(x^4): 0.343
#> 
#> `geom_smooth()` using formula = 'y ~ x'


if (FALSE) {
# fit new model
fit <- lm(tot_sc_e ~ c12hour + e42dep + e17age + I(e17age^2) + I(e17age^3),
          data = efc)
# plot marginal effects of polynomial term
plot_model(fit, type = "pred", terms = "e17age")}