README.md

In MicroMacroMultilevel: Micro-Macro Multilevel Modeling

1. Description: This package fits micro-macro multilevel models, wherein individual-level (micro) explanatory variables are used to predict a group-level (macro) outcome variable in an unbiased way.

2. Test Run:

MicroMacroMultilevel package, test run

Nancy, Jackson, 20160919

Elizabeth, 20161016

Nancy, Jackson, 20161018

path_to_file <- "MicroMacroMultilevel_0.2.0.tar.gz"

install.packages(path_to_file, repos = NULL, type="source")

file: MicroMacroMultilevel_0.2.0.tar.gz

library("MicroMacroMultilevel") help("adjusted.predictors") help("micromacro.lm") help("micromacro.summary") # the name is not unique; but it is unique in this package specifically.

## SETUP: DATA GENERATING PROCESSES

set.seed(123)

Step 1, generate a G-by-q data frame of group-level predictors (e.g., control variables), z.data.

In this example, G = 40, q = 2

group.id = seq(1, 40) z.var1 = rnorm(40, mean=0, sd=1) z.var2 = rnorm(40, mean=100, sd=2) z.data = data.frame(group.id, z.var1, z.var2)

Step 2, generate a G-by-P data frame of group-level means for the predictors that will be used to generate x.data

In this example, there will be 3 level 1 predictors, P = 3

x.var1.means = rnorm(40, mean=50, sd = .05) x.var2.means = rnorm(40, mean=20, sd = .05) x.var3.means = rnorm(40, mean=-10, sd = .05) x.data.means = data.frame(group.id, x.var1.means, x.var2.means, x.var3.means)

Step 3, generate two N-by-P data frames of individual-level predictors, "x.data."

One of these data frames has unequal-sized groups, the other has equal-sized groups

Step 3a, generate the Level 1 group values

In this example, N = 200 and group size is equal

x.data.equal = data.frame( group.id=rep(1:40, each=5) ) x.data.equal = merge( x.data.equal, x.data.means, by="group.id" ) x.data.equal = within( x.data.equal, { x.var1 = x.var1.means + rnorm(200, mean=0, sd = 2) x.var2 = x.var2.means + rnorm(200, mean=0, sd = 6) x.var3 = x.var3.means + rnorm(200, mean=0, sd = 1.5) })

Step 3b, generate the Level 1 group values

In this example, N = 200 and group size is unequal

x.data.unequal = data.frame( group.id=rep(1:40, times=sample( c(4,5,6), 40, replace=T) )[1:200] ) x.data.unequal = merge( x.data.unequal, data.frame( group.id, x.var1.means, x.var2.means, x.var3.means ), by="group.id" ) x.data.unequal = within( x.data.unequal, { x.var1 = x.var1.means + rnorm(200, mean=0, sd = 2) x.var2 = x.var2.means + rnorm(200, mean=0, sd = 6) x.var3 = x.var3.means + rnorm(200, mean=0, sd = 1.5) })

Step 3, generate a G-by-1 data frame of group-level outcome variable (dependent variable), y.

In this example, G = 40

y = rnorm(40, mean=6, sd=5)

apply(x.data.equal,2,mean)

group.id x.var1.means x.var2.means x.var3.means x.var3 x.var2 x.var1

20.500000 50.000393 19.994708 -9.999167 -10.031995 20.185361 50.084635

apply(x.data.unequal,2,mean)

group.id x.var1.means x.var2.means x.var3.means x.var3 x.var2 x.var1

20.460000 50.002286 19.994605 -9.997034 -9.983146 19.986111 50.123591

apply(z.data,2,mean)

z.var1 z.var2

0.04518332 99.98656817

mean(y)

6.457797

## EXAMPLE 1, GROUP SIZE IS DIFFERENT ACROSS GROUPS

## need to use adjusted.predictors() in the same package

Step 4, generate a G-by-1 matrix of group id, z.gid, and an N-by-1 matrix of individuals' group id, x.gid, where the group sizes are different.

z.gid = seq(1:40) x.gid = x.data.unequal$group.id

Step 5, generate the best linear unbiased predictors that are calcualted from individual-level data.

x.data = x.data.unequal[,c("x.var1","x.var2","x.var3")] results = adjusted.predictors(x.data, z.data, x.gid, z.gid)

Note: given the fixed random seed, exact answers shoule be obtained.

results$unequal.groups

TRUE

names(results$adjusted.group.means)

"BLUP.x.var1" "BLUP.x.var2" "BLUP.x.var3" "z.var1" "z.var2" "gid"

head(results$adjusted.group.means)

BLUP.x.var1 BLUP.x.var2 BLUP.x.var3 group.id z.var1 z.var2 gid

1 50.05308 20.83911 -10.700361 1 -0.56047565 98.61059 1

2 48.85559 22.97411 -9.957270 2 -0.23017749 99.58417 2

3 50.16357 19.50001 -9.645735 3 1.55870831 97.46921 3

4 49.61853 21.25962 -10.459398 4 0.07050839 104.33791 4

5 50.49673 21.38353 -9.789924 5 0.12928774 102.41592 5

6 50.86154 19.15901 -9.245675 6 1.71506499 97.75378 6

Step 6, fitting micro-macro multilevel models with different group sizes

model.formula = as.formula(y ~ BLUP.x.var1 + BLUP.x.var2 + BLUP.x.var3 + z.var1 + z.var2) model.output = micromacro.lm(model.formula, results$adjusted.group.means, y, results$unequal.groups) micromacro.summary(model.output)

Call:

micromacro.lm( y ~ BLUP.x.var1 + BLUP.x.var2 + BLUP.x.var3 + z.var1 + z.var2, ...)

Residuals:

Min 1Q Median 3Q Max

-13.41505 -2.974074 1.13077 3.566021 6.975819

Coefficients:

b uncorrected se corrected se df t p(t|H_0) r

(Intercept) 78.1232185 121.5103390 122.1367432 34 0.6396373 0.5266952 0.10904278

BLUP.x.var1 -0.7589602 1.4954434 1.7177575 34 -0.4418320 0.6614084 0.07555696

BLUP.x.var2 0.4263309 0.7070773 0.6299759 34 0.6767416 0.5031484 0.11528637

BLUP.x.var3 0.2658078 2.4662049 2.4051691 34 0.1105152 0.9126506 0.01894980

z.var1 0.4315941 1.0855707 1.0614535 34 0.4066068 0.6868451 0.06956356

z.var2 -0.3949955 0.5573789 0.4230256 34 -0.9337390 0.3570228 0.15812040

---

Residual standard error: 5.1599 on 34 degrees of freedom

Multiple R-squared: 0.0400727607, Adjusted R-squared: -0.1010930098

F-statistic: 0.28387 on 5 and 34 DF, p-value: 0.91869

model.output$statistics

b uncorrected se corrected se df t p(t|H_0) r

(Intercept) 81.0599615 120.9407698 120.4980034 34 0.6727079 0.5056798 0.11460827

BLUP.x.var1 -0.7100024 1.4900552 1.6690023 34 -0.4254053 0.6732219 0.07276302

BLUP.x.var2 0.6539548 0.7798135 0.7417115 34 0.8816834 0.3841388 0.14950797

BLUP.x.var3 0.6176659 2.4941350 2.4158888 34 0.2556682 0.7997475 0.04380464

z.var1 0.3205106 1.0912964 1.0802985 34 0.2966870 0.7685104 0.05081567

z.var2 -0.4592063 0.5627968 0.4388888 34 -1.0462930 0.3028075 0.17661694

model.output$rsquared

0.04881028

model.output$rsquared.adjusted

-0.09107056

## EXAMPLE 2, GROUP SIZE IS THE SAME FOR ALL GROUPS

## need to use adjusted.predictors() in the same package

Generate an N-by-1 matrix of individuals' group id, x.gid, where group sizes is the same for all groups.

z.gid = seq(1:40) x.gid = x.data.equal$group.id x.data = x.data.equal[,c("x.var1","x.var2","x.var3")] results = adjusted.predictors(x.data, z.data, x.gid, z.gid) results$unequal.groups

FALSE

names(results$adjusted.group.means)

"BLUP.x.var1" "BLUP.x.var2" "BLUP.x.var3" "z.var1" "z.var2" "gid"

results$adjusted.group.means[1:5, ]

BLUP.x.var1 BLUP.x.var2 BLUP.x.var3 group.id z.var1 z.var2 gid

1 50.91373 19.12994 -10.051647 1 -0.56047565 98.61059 1

2 50.19068 19.17978 -10.814382 2 -0.23017749 99.58417 2

3 50.13390 20.98893 -9.952348 3 1.55870831 97.46921 3

4 49.68169 19.60632 -10.612717 4 0.07050839 104.33791 4

5 50.28579 22.07469 -10.245505 5 0.12928774 102.41592 5

Fitting micro-macro multilevel models with same group sizes

model.output2 = micromacro.lm(model.formula, results$adjusted.group.means, y, results$unequal.groups) micromacro.summary(model.output2)

Call:

micromacro.lm( y ~ BLUP.x.var1 + BLUP.x.var2 + BLUP.x.var3 + z.var1 + z.var2, ...)

Residuals:

Min 1Q Median 3Q Max

-12.94409 -1.898937 0.8615494 3.78739 8.444582

Coefficients:

b se df t p(t|H_0) r

(Intercept) 135.4109966 134.1478457 34 1.0094161 0.3199052 0.17057636

BLUP.x.var1 -2.1984308 2.2203278 34 -0.9901379 0.3291012 0.16741080

BLUP.x.var2 -0.6369600 0.8619558 34 -0.7389706 0.4649961 0.12572678

BLUP.x.var3 -0.5121002 1.7889594 34 -0.2862559 0.7764192 0.04903343

z.var1 0.7718147 1.1347170 34 0.6801826 0.5009945 0.11586471

z.var2 -0.1116209 0.5268130 34 -0.2118795 0.8334661 0.03631307

---

Residual standard error: 5.11849 on 34 degrees of freedom

Multiple R-squared: 0.0554183804, Adjusted R-squared: -0.0834906813

F-statistic: 0.39895 on 5 and 34 DF, p-value: 0.84607

model.output2$statistics

b se df t p(t|H_0) r

(Intercept) 133.4296363 145.0595920 34 0.9198264 0.3641438 0.15582204

BLUP.x.var1 -2.1478275 2.3893696 34 -0.8989097 0.3750231 0.15236187

BLUP.x.var2 -0.6508938 0.9202387 34 -0.7073097 0.4841943 0.12041990

BLUP.x.var3 -0.4530981 1.9468294 34 -0.2327364 0.8173615 0.03988221

z.var1 0.7932642 1.1386801 34 0.6966524 0.4907562 0.11863121

z.var2 -0.1084293 0.5238073 34 -0.2070024 0.8372428 0.03547826

model.output2$rsquared

0.05050317

model.output2$rsquared.adjusted

-0.08912872

## EXAMPLE 3 (following EXAMPLE 2), INTERACTION TERM: MICRO-MICRO INTERACTION

model.formula3 = as.formula(y ~ BLUP.x.var1 * BLUP.x.var2 + BLUP.x.var3 + z.var1 + z.var2) model.output3 = micromacro.lm(model.formula3, results$adjusted.group.means, y, results$unequal.groups) micromacro.summary(model.output3)

Call:

micromacro.lm( y ~ BLUP.x.var1 * BLUP.x.var2 + BLUP.x.var3 + z.var1 + z.var2, ...)

Residuals:

Min 1Q Median 3Q Max

-13.21948 -2.048324 0.7062639 3.843816 7.924922

Coefficients:

b se df t p(t|H_0) r

(Intercept) -1.098875e+03 1962.9182021 33 -0.5598169 0.5793848 0.09699214

BLUP.x.var1 2.231877e+01 38.9620284 33 0.5728339 0.5706400 0.09922547

BLUP.x.var2 5.988568e+01 96.0256433 33 0.6236426 0.5371496 0.10792809

BLUP.x.var3 -9.557605e-01 1.9374178 33 -0.4933167 0.6250560 0.08556050

z.var1 6.116347e-01 1.1727757 33 0.5215274 0.6054822 0.09041443

z.var2 -8.556163e-02 0.5331509 33 -0.1604829 0.8734790 0.02792560

BLUP.x.var1:BLUP.x.var2 -1.209354e+00 1.9186909 33 -0.6303016 0.5328380 0.10906688

---

Residual standard error: 5.08795 on 33 degrees of freedom

Multiple R-squared: 0.0666547309, Adjusted R-squared: -0.103044409

F-statistic: 0.39278 on 6 and 33 DF, p-value: 0.87831

model.output3$statistics

b se df t p(t|H_0) r

(Intercept) -1.513846e+03 2018.1480115 33 -0.7501165 0.4584996 0.12947933

BLUP.x.var1 3.056854e+01 40.0495641 33 0.7632677 0.4507262 0.13171033

BLUP.x.var2 8.001370e+01 98.5718506 33 0.8117297 0.4227635 0.13991408

BLUP.x.var3 -1.045778e+00 2.0861011 33 -0.5013072 0.6194828 0.08693599

z.var1 5.656201e-01 1.1775773 33 0.4803252 0.6341650 0.08332313

z.var2 -6.479439e-02 0.5290637 33 -0.1224699 0.9032697 0.02131443

BLUP.x.var1:BLUP.x.var2 -1.612533e+00 1.9704233 33 -0.8183689 0.4190170 0.14103579

model.output3$rsquared

0.0693897

model.output3$rsquared.adjusted

-0.09981217

## EXAMPLE 4 (following EXAMPLE 2), INTERACTION TERM: MICRO-MACRO INTERACTION

model.formula4 = as.formula(y ~ BLUP.x.var1 + BLUP.x.var2 + BLUP.x.var3 * z.var1 + z.var2) model.output4 = micromacro.lm(model.formula4, results$adjusted.group.means, y, results$unequal.groups) micromacro.summary(model.output4)

Call:

micromacro.lm( y ~ BLUP.x.var1 + BLUP.x.var2 + BLUP.x.var3 * z.var1 + z.var2, ...)

Residuals:

Min 1Q Median 3Q Max

-12.99937 -1.909645 0.8775397 3.712013 8.46591

Coefficients:

b se df t p(t|H_0) r

(Intercept) 129.22731579 146.4817031 33 0.8822079 0.3840456 0.15179313

BLUP.x.var1 -2.10556192 2.3951160 33 -0.8791064 0.3857003 0.15127172

BLUP.x.var2 -0.63762927 0.8747645 33 -0.7289153 0.4711953 0.12587857

BLUP.x.var3 -0.53590189 1.8273917 33 -0.2932605 0.7711594 0.05098372

z.var1 2.95426548 19.1170600 33 0.1545356 0.8781288 0.02689146

z.var2 -0.09852267 0.5467583 33 -0.1801942 0.8581021 0.03135236

BLUP.x.var3:z.var1 0.21489002 1.8788995 33 0.1143702 0.9096374 0.01990534

---

Residual standard error: 5.11747 on 33 degrees of freedom

Multiple R-squared: 0.0557926451, Adjusted R-squared: -0.1158814195

F-statistic: 0.32499 on 6 and 33 DF, p-value: 0.91909

model.output4$statistics

b se df t p(t|H_0) r

(Intercept) 120.82434054 159.8637235 33 0.7557959 0.4551330 0.13044304

BLUP.x.var1 -1.96231952 2.5923343 33 -0.7569701 0.4544388 0.13064224

BLUP.x.var2 -0.64947422 0.9335286 33 -0.6957197 0.4914753 0.12023073

BLUP.x.var3 -0.51575816 1.9991585 33 -0.2579876 0.7980186 0.04486466

z.var1 4.90176423 20.3956604 33 0.2403337 0.8115584 0.04180016

z.var2 -0.08181324 0.5474872 33 -0.1494341 0.8821207 0.02600434

BLUP.x.var3:z.var1 0.40549910 2.0097719 33 0.2017637 0.8413401 0.03510092

model.output4$rsquared

0.05167302

model.output4$rsquared.adjusted

-0.1207501

MicroMacroMultilevel documentation built on May 2, 2019, 3:17 p.m.