second.diff.fitted {catregs}

Computes the second difference in fitted values. Inference in supported via the delta method or bootstrapping.

Description

second.diff.fitted computes the second differences between fitted values, that is, the difference between two first differences, from a regression model.

Supported models include OLS regression via lm, logistic regression via glm, Poisson regression via glm, negative binomial regression via MASS:glm.nb, ordinal logistic regression via MASS::polr, partial proportional odds models via vgam::vglm, multinomial logistic regression via nnet::multinom, zero-inflated Poisson or negative binomial regression via pscl::zeroinfl, hurdle Poisson or negative binomial regression via pscl::hurdle, mixed effects logistic regression via lme4/lmerTest::glmer, mixed effects Poisson regression via lme4/lmerTest::glmer, mixed effects negative binomial regression via lme4/lmerTest::glmer.nb, and mixed effects ordinal logistic regression via ordinal::clmm.

Usage

second.diff.fitted(mod,design.matrix,compare,alpha=.05,rounded=3,
bootstrap="no",num.sample=1000,prop.sample=.9,
data,seed=1234,cum.probs="no")

Arguments

mod

A model object. The model should be regression model for limited dependent variables, such as a logistic regression.

design.matrix

Design matrix of values for the independent variables in the regression model.

compare

A set of four rows in the design matrix to use for computing the fitted values that are used in the calculation of second differences. For example, compare(a,b,c,d) results in computing the fitted values for rows a, b, c, and d of the design matrix, respectively, and then computing the following second difference: (a - b) - (c - d). Only four rows may be compared at a time.

alpha

The alpha value for confidence intervals. Default is .05.

rounded

The number of decimal places to round the output. The default is 3.

bootstrap

By default, inference is based on the Delta Method, as implemented in the marginaleffects package. Alternatively, inference can be based upon a bootstrapped sampling distirbution. To do so, change this to "yes"

num.sample

num.sample is the number samples drawn to compute the sampling distibution when using bootstrapping. Default is 1,000

prop.sample

prop.sample is the proportion of the original sample to include in the sampling distibution samples when using bootstrapping. Default is .9

data

For nonparametric inference, provide the data used in the original model statement.

seed

For models using bootstrapped inference. The seed ensures reproducible results across runs. Default is 1234, but may be changed.

cum.probs

For ordinal logistic regression models, including mixed effects models, do you want the first differences to be based on probabilities of the response categories or cumulative probabilities of the response categories. The default is cum.probs=="no" corresponding to non-cumulative probabilities. Change cum.probs to "yes" for cumulative probabilities.

Value

out

If using parametric inference (delta method): output is a dataframe including the second difference in fitted values ("est"), the standard error ("std.error"), the lower limit ("ll"), and upper limit ("ul") of the confidence interval. Of course, ll and ul are based on the alpha level. If using nonparametric inference (bootstrapping): output is a list of objects. obs.diff is the observed second difference in the response or fitted values. boot.dist is the sorted bootstrapped distribution of second differences in the samples. mean.boot.dist is the average of the second differences in the responses or fitted values. sd.boot.dist is the standard deviation of the sampling distribution. ci.95 is the Lower and Upper limits of the confidence interval; despite it's name, the confidence interval is based upon the alpha level. model.class is just the class of the model that was used to generate the fitted values.

Author(s)

David Melamed

Examples

data("Mize19AH")
m1 <- glm(alcB ~woman*parrole + age + race2 + race3 +
race4 + income + ed1 + ed2 + ed3 +
ed4,family="binomial",data=Mize19AH)
des2<-margins.des(m1,expand.grid(woman=c(0,1),parrole=c(0,1)))
des2
second.diff.fitted(m1,des2,compare=c(4,2,3,1),rounded=5)
# [Pr(Drink | Mothers) - Pr(Drink | Childless Women)] -
# [Pr(Drink | Fathers) - Pr(Drink | Childless Men)]

# Note that this is reported as the "Second Difference" in
# Table 3 of Mize (2019: 104, "Best Practices for Estimating,
# Interpreting, and Presenting Nonlinear Interaction Effect.
# Sociological Science. 6(4): 81-117.")