# \[FixedEffectModels.jl\] Switching from Dummy to Categorical Variables

**URL:** <https://discourse.julialang.org/t/fixedeffectmodels-jl-switching-from-dummy-to-categorical-variables/85800>\
**Category:** Statistics\
**Tags:** regression, linear-regression\
**Created:** [August 16, 2022, 12:19am UTC](https://discourse.julialang.org/t/fixedeffectmodels-jl-switching-from-dummy-to-categorical-variables/85800 "2022-08-16T00:19:53Z")\
**Posts on this page:** 3\
**Page:** 1

<div class="post-metadata">

**Author:** ![teamtelefunken](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/teamtelefunken/32/16231_2.png) [@teamtelefunken](https://discourse.julialang.org/u/teamtelefunken)\
**Post date:** [August 16, 2022, 12:19am UTC](https://discourse.julialang.org/t/fixedeffectmodels-jl-switching-from-dummy-to-categorical-variables/85800/1 "2022-08-16T00:19:53Z")

</div>

I am trying to use FixedEffectModels.jl with a dataset with a continuous explanatory variable, and want to run regressions on a binned version of this variable. I have two approaches: a) I can either, via cut, produce categorical variables, or b) via map produce numerical assignments of the bins that can then be treated as dummy variables via “contrasts” (I am sure there is more efficient ways to do the binning)

I have two questions:

1. If I use categorical variables, is there a way to pick a “base” as one is allowed to for dummy variables?
2. It seems that the regressions results differ slightly between the categorical regressions and the dummy variable regression. Why would that be?

```julia
# Categorical regression
                                       Linear Model                                       
===========================================================================================
Number of obs: 1380 Degrees of freedom: 2
R2: 0.092 R2 Adjusted: 0.091
F-Stat: 70.1648 p-value: 0.000
===========================================================================================
Sales | Estimate Std.Error t value Pr(>|t|) Lower 95% Upper 95%
-------------------------------------------------------------------------------------------
CategoricalPrice: [75.0, 100.0) | -5.06421 2.77783 -1.82308 0.069 -10.5135 0.385043
CategoricalPrice: [100.0, 201.9] | -22.4024 1.89182 -11.8417 0.000 -26.1135 -18.6912
(Intercept) | 129.814 0.974587 133.199 0.000 127.902 131.726
===========================================================================================

# Dummy regression
                              Linear Model                              
========================================================================
Number of obs: 1380 Degrees of freedom: 2
R2: 0.095 R2 Adjusted: 0.093
F-Stat: 71.9556 p-value: 0.000
========================================================================
Sales | Estimate Std.Error t value Pr(>|t|) Lower 95% Upper 95%
------------------------------------------------------------------------
DummyPrice: 2 | -4.5169 2.76519 -1.63349 0.103 -9.94134 0.907545
DummyPrice: 3 | -22.6697 1.89169 -11.9838 0.000 -26.3806 -18.9588
(Intercept) | 129.814 0.973439 133.356 0.000 127.904 131.723
========================================================================

```

```julia
# CODE
using DataFrames, RDatasets, FixedEffectModels, CategoricalArrays, StatsBase
# importing data from RDatasets
df = dataset("plm", "Cigar")
# creating categorical price column
c=cut(df.Price,[0;75;100],extend = true)
insertcols!(df,ncol(df)+1,:CategoricalPrice=>c)
# creating dummy price column 
d = map(x -> x>100 ? 3 : (x<75 ? 1 : 2), df[:,"Price"])
insertcols!(df,ncol(df)+1,:DummyPrice=>d)
# regressions
reg(df, @formula(Sales ~ CategoricalPrice)) # running regression with categorical price variable (not sure how to pick base)
reg(df, @formula(Sales ~ DummyPrice); contrasts = Dict(:DummyPrice => DummyCoding())) # running regression with dummy variable (this defaults to base=1)
reg(df, @formula(Sales ~ DummyPrice); contrasts = Dict(:DummyPrice => DummyCoding(base = 3))) # running regression with dummy variable (with base=3 imposed)

```

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<div class="post-metadata">

**Author:** ![nilshg](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/nilshg/32/2283_2.png) [@nilshg](https://discourse.julialang.org/u/nilshg)\
**Post date:** [August 16, 2022, 9:00am UTC](https://discourse.julialang.org/t/fixedeffectmodels-jl-switching-from-dummy-to-categorical-variables/85800/2 "2022-08-16T09:00:47Z")

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My first question would be why you are using FixedEffectModels when you are not actually including fixed effects in your model? Seems like what you’re doing should be doable in plain GLM.

I believe the answer to your second question is this:

```julia
julia> using DataFrames, RDatasets

julia> df = dataset("plm", "Cigar");

julia> df.CategoricalPrice = cut(df.Price, [0; 75; 100], extend = true);

julia> df.DummyPrice = (x -> x > 100 ? 3 : x < 75 ? 1 : 2).(df.Price);

julia> combine(groupby(df, [:CategoricalPrice, :DummyPrice]), nrow)
4×3 DataFrame
 Row │ CategoricalPrice DummyPrice nrow
     │ Categorical… Int64 Int64
─────┼─────────────────────────────────────
   1 │ [0.0, 75.0) 1 919
   2 │ [75.0, 100.0) 2 129
   3 │ [100.0, 201.9] 2 1
   4 │ [100.0, 201.9] 3 331

julia> df[string.(df.CategoricalPrice) .== "[100.0, 201.9]" .&& df.DummyPrice .== 2, :]
1×11 DataFrame
 Row │ State Year Price Pop Pop16 CPI NDI Sales Pimin CategoricalPrice DummyPrice
     │ Int64 Int64 Float64 Float64 Float64 Float64 Float64 Float64 Float64 Categorical… Int64
─────┼───────────────────────────────────────────────────────────────────────────────────────────────────────────
   1 │ 30 86 100.0 1027.0 802.8 109.6 14550.9 195.9 104.9 [100.0, 201.9] 2

```

so `DummyPrice` and `CategoricalPrice` do not put all observations into the same category - you probably want `x >= 100` in the function that assigns dummy variables.

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<div class="post-metadata">

**Author:** ![teamtelefunken](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/teamtelefunken/32/16231_2.png) [@teamtelefunken](https://discourse.julialang.org/u/teamtelefunken)\
**Post date:** [August 16, 2022, 6:01pm UTC](https://discourse.julialang.org/t/fixedeffectmodels-jl-switching-from-dummy-to-categorical-variables/85800/3 "2022-08-16T18:01:13Z")

</div>

Yes, this was an embarrassing mistake on the binning and the inequality on my part, thank you so much for correcting it and thus resolving question 2).

My question 1) was answered by a friend of mine: Setting the base for a categorical variable say for corresponding numerical dummy 3 is given by:

```julia
reg(df, @formula(Sales ~ CategoricalPrice); contrasts = Dict(:CategoricalPrice => DummyCoding(base = "[100.0, 201.9]")))

```

which yields result

```julia
                                      Linear Model                                      
=========================================================================================
Number of obs: 1380 Degrees of freedom: 2
R2: 0.092 R2 Adjusted: 0.091
F-Stat: 70.1648 p-value: 0.000
=========================================================================================
Sales | Estimate Std.Error t value Pr(>|t|) Lower 95% Upper 95%
-----------------------------------------------------------------------------------------
CategoricalPrice: [0.0, 75.0) | 22.4024 1.89182 11.8417 0.000 18.6912 26.1135
CategoricalPrice: [75.0, 100.0) | 17.3382 3.06524 5.65638 0.000 11.3251 23.3512
(Intercept) | 107.411 1.62147 66.2432 0.000 104.231 110.592
=========================================================================================

```

To answer your other question about why I’m using this package at all, I am using fixed effects in my real regression, ergo the use of FixedEffectsModels.jl, but my question above was unrelated to such FE functionality, and therefore I took it out in my minimum viable programming example.