micromacro.summary: Summarizing the Micro-Macro Multilevel Linear Model Fitting...
In MicroMacroMultilevel: Micro-Macro Multilevel Modeling
Description
Usage
Arguments
Details
Value
Author(s)
References
See Also
Examples
Description
After fitting a micro-macro multilevel model, this function produces a user-friendly summary table of the results.
Usage
1
micromacro.summary(model.output)
Arguments
model.output
the output of micromacro.lm which contains model results and model specifications.
Details
To date, most multilevel methodologies can only unbiasedly model macro-micro multilevel situations, wherein group-level predictors (e.g., city temperature)
are used to predict an individual-level outcome variable (e.g., citizen personality). In contrast, this R package enables researchers to model micro-macro situations,
wherein individual-level (micro) predictors (and other group-level predictors) are used to predict a group-level (macro) outcome variable in an unbiased way.
To conduct micro-macro multilevel modeling with the current package, one must first compute the adjusted group means with the function adjusted.predictors.
This is because in micro-macro multilevel modeling, it is statistically biased to directly regress the group-level outcome variable on the unadjusted group means of individual-level predictors (Croon & van Veldhoven, 2007).
Instead, one should use the best linear unbiased predictors (BLUP) of the group means (i.e., the adjusted group means), which is conveniently computed by adjusted.predictors.
Once produced by adjusted.predictors, the adjusted group means can be used as one of the inputs of the micromacro.lm function, which reports estimation results and inferential statistics of the micro-macro multilevel model of interest.
If group size is the same across all groups (i.e., unequal.groups = FALSE), then OLS standard errors are reported and used to determine the inferential statistics in this micro-macro model.
If group size is different across groups (i.e., unequal.groups = TRUE), however, then the heteroscedasticity-consistent standard errors are reported and used determine the inferential statistics in this micro-macro model (White, 1980).
micromacro.summary produces a detailed summary on the model fitting and specifications, given the outputs of micromacro.lm.
Value
table a summary table.
Author(s)
Jackson G. Lu, Elizabeth Page-Gould, Nancy R. Xu (maintainer, nancyranxu@gmail.com).
References
Akinola, M., Page-Gould, E., Mehta, P. H., & Lu, J. G. (2016). Collective hormonal profiles predict group performance. Proceedings of the National Academy of Sciences, 113 (35), 9774-9779.
Croon, M. A., & van Veldhoven, M. J. (2007). Predicting group-level outcome variables from variables measured at the individual level: a latent variable multilevel model. Psychological methods, 12(1), 45-57.
See Also
micromacro.lm for fitting the micro-macro multilevel linear model of interest.
Examples
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######## 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 are 3 individual-level predictors, thus 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 two data frames assumes unequal-sized groups (Step 3a), whereas the other assumes
# equal-sized groups (Step 3b):
# Step 3a. Generate the individual-level predictors
# 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=TRUE) )[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 3b. Generate the individual-level predictors
# 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 3. Generate a G-by-1 data frame of group-level outcome 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 4a. Generate a G-by-1 matrix of group ID, z.gid. Then generate an N-by-1 matrix of
# each individual's group ID, x.gid, where the group sizes are different
z.gid = seq(1:40)
x.gid = x.data.unequal$group.id
# Step 5a. Generate the best linear unbiased predictors that are calcualted from
# individual-level data
x.data = x.data.unequal[,c("x.var1","x.var2","x.var3")]
results = adjusted.predictors(x.data, z.data, x.gid, z.gid)
# Note: Given the fixed random seed, the output should be as below
results$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 6a. Fit a micro-macro multilevel model when group sizes are different
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:
# Estimate Uncorrected S.E. Corrected S.E. df t Pr(>|t|) 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$statistics
# Estimate Uncorrected S.E. Corrected S.E. df t Pr(>|t|) r
# (Intercept) 78.1232185 121.5103390 122.1367432 34 0.6396373 0.5266952 0.10904278
# BLUP.x.var1 -0.7589602 1.4954434 1.7177575 34 -0.4418320 0.6614084 0.07555696
# BLUP.x.var2 0.4263309 0.7070773 0.6299759 34 0.6767416 0.5031484 0.11528637
# BLUP.x.var3 0.2658078 2.4662049 2.4051691 34 0.1105152 0.9126506 0.01894980
# z.var1 0.4315941 1.0855707 1.0614535 34 0.4066068 0.6868451 0.06956356
# z.var2 -0.3949955 0.5573789 0.4230256 34 -0.9337390 0.3570228 0.15812040
model.output$rsquared
# 0.0400727607
model.output$rsquared.adjusted
# -0.1010930098
######## EXAMPLE 2. GROUP SIZE IS THE SAME ACROSS ALL GROUPS ########
######## Need to use adjusted.predictors() in the same package ######
# Step 4b. Generate a G-by-1 matrix of group ID, z.gid. Then generate an N-by-1 matrix of
# each individual's group ID, x.gid, where group size is the same across all groups
z.gid = seq(1:40)
x.gid = x.data.equal$group.id
# Step 5b. Generate the best linear unbiased predictors that are calcualted from
# individual-level data
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$adjusted.group.means[1:5, ]
# BLUP.x.var1 BLUP.x.var2 BLUP.x.var3 group.id z.var1 z.var2 gid
# 1 50.91373 19.12994 -10.051647 1 -0.56047565 98.61059 1
# 2 50.19068 19.17978 -10.814382 2 -0.23017749 99.58417 2
# 3 50.13390 20.98893 -9.952348 3 1.55870831 97.46921 3
# 4 49.68169 19.60632 -10.612717 4 0.07050839 104.33791 4
# 5 50.28579 22.07469 -10.245505 5 0.12928774 102.41592 5
# Step 6b. Fit a micro-macro multilevel model when group size is the same across groups
model.output2 = micromacro.lm(model.formula, results$adjusted.group.means, y,
results$unequal.groups)
micromacro.summary(model.output2)
# Call:
# micromacro.lm( y ~ BLUP.x.var1 + BLUP.x.var2 + BLUP.x.var3 + z.var1 + z.var2, ...)
#
# Residuals:
# Min 1Q Median 3Q Max
# -12.94409 -1.898937 0.8615494 3.78739 8.444582
#
#
# Coefficients:
# Estimate S.E. df t Pr(>|t|) r
# (Intercept) 135.4109966 134.1478457 34 1.0094161 0.3199052 0.17057636
# BLUP.x.var1 -2.1984308 2.2203278 34 -0.9901379 0.3291012 0.16741080
# BLUP.x.var2 -0.6369600 0.8619558 34 -0.7389706 0.4649961 0.12572678
# BLUP.x.var3 -0.5121002 1.7889594 34 -0.2862559 0.7764192 0.04903343
# z.var1 0.7718147 1.1347170 34 0.6801826 0.5009945 0.11586471
# z.var2 -0.1116209 0.5268130 34 -0.2118795 0.8334661 0.03631307
#
# ---
# Residual standard error: 5.11849 on 34 degrees of freedom
# Multiple R-squared: 0.0554183804, Adjusted R-squared: -0.0834906813
# F-statistic: 0.39895 on 5 and 34 DF, p-value: 0.84607
model.output2$statistics
# Estimate S.E. df t Pr(>|t|) 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
model.output2$rsquared
# 0.0554183804
model.output2$rsquared.adjusted
# -0.0834906813
######## EXAMPLE 3 (after EXAMPLE 2). ADDING A MICRO-MICRO INTERACTION TERM ########
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:
# Estimate S.E. df t Pr(>|t|) 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$statistics
# Estimate S.E. df t Pr(>|t|) r
# (Intercept) -1.098875e+03 1962.9182021 33 -0.5598169 0.5793848 0.09699214
# BLUP.x.var1 2.231877e+01 38.9620284 33 0.5728339 0.5706400 0.09922547
# BLUP.x.var2 5.988568e+01 96.0256433 33 0.6236426 0.5371496 0.10792809
# BLUP.x.var3 -9.557605e-01 1.9374178 33 -0.4933167 0.6250560 0.08556050
# z.var1 6.116347e-01 1.1727757 33 0.5215274 0.6054822 0.09041443
# z.var2 -8.556163e-02 0.5331509 33 -0.1604829 0.8734790 0.02792560
# BLUP.x.var1:BLUP.x.var2 -1.209354e+00 1.9186909 33 -0.6303016 0.5328380 0.10906688
model.output3$rsquared
# 0.0666547309
model.output3$rsquared.adjusted
# -0.103044409
######## EXAMPLE 4 (after EXAMPLE 2). ADDING A MICRO-MACRO INTERACTION TERM ########
model.formula4 = as.formula(y ~ BLUP.x.var1 + BLUP.x.var2 + BLUP.x.var3 * z.var1 + z.var2)
model.output4 = micromacro.lm(model.formula4, results$adjusted.group.means, y,
results$unequal.groups)
micromacro.summary(model.output4)
# Call:
# micromacro.lm( y ~ BLUP.x.var1 + BLUP.x.var2 + BLUP.x.var3 * z.var1 + z.var2, ...)
#
# Residuals:
# Min 1Q Median 3Q Max
# -12.99937 -1.909645 0.8775397 3.712013 8.46591
#
#
# Coefficients:
# Estimate S.E. df t Pr(>|t|) r
# (Intercept) 129.22731579 146.4817031 33 0.8822079 0.3840456 0.15179313
# BLUP.x.var1 -2.10556192 2.3951160 33 -0.8791064 0.3857003 0.15127172
# BLUP.x.var2 -0.63762927 0.8747645 33 -0.7289153 0.4711953 0.12587857
# BLUP.x.var3 -0.53590189 1.8273917 33 -0.2932605 0.7711594 0.05098372
# z.var1 2.95426548 19.1170600 33 0.1545356 0.8781288 0.02689146
# z.var2 -0.09852267 0.5467583 33 -0.1801942 0.8581021 0.03135236
# BLUP.x.var3:z.var1 0.21489002 1.8788995 33 0.1143702 0.9096374 0.01990534
#
# ---
# Residual standard error: 5.11747 on 33 degrees of freedom
# Multiple R-squared: 0.0557926451, Adjusted R-squared: -0.1158814195
# F-statistic: 0.32499 on 6 and 33 DF, p-value: 0.91909
model.output4$statistics
# Estimate S.E. df t Pr(>|t|) 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
model.output4$rsquared
# 0.0557926451
model.output4$rsquared.adjusted
# -0.1158814195
Example output
Warning messages:
1: In x.var1.means + rnorm(200, mean = 0, sd = 2) :
longer object length is not a multiple of shorter object length
2: In x.var2.means + rnorm(200, mean = 0, sd = 6) :
longer object length is not a multiple of shorter object length
3: In x.var3.means + rnorm(200, mean = 0, sd = 1.5) :
longer object length is not a multiple of shorter object length
4: In `[<-.data.frame`(`*tmp*`, nl, value = list(x.var3 = c(-12.0702873063753, :
replacement element 1 has 200 rows to replace 194 rows
5: In `[<-.data.frame`(`*tmp*`, nl, value = list(x.var3 = c(-12.0702873063753, :
replacement element 2 has 200 rows to replace 194 rows
6: In `[<-.data.frame`(`*tmp*`, nl, value = list(x.var3 = c(-12.0702873063753, :
replacement element 3 has 200 rows to replace 194 rows
group.id x.var1.means x.var2.means x.var3.means x.var3 x.var2
20.500000 50.000393 19.994708 -9.999167 -9.985279 19.986214
x.var1
50.121698
group.id x.var1.means x.var2.means x.var3.means x.var3 x.var2
20.118557 50.001697 19.993560 -9.997938 -9.986925 20.225848
x.var1
50.060817
group.id z.var1 z.var2
20.50000000 0.04518332 99.98656817
[1] 6.457797
[1] TRUE
[1] "BLUP.x.var1" "BLUP.x.var2" "BLUP.x.var3" "group.id" "z.var1"
[6] "z.var2" "gid"
BLUP.x.var1 BLUP.x.var2 BLUP.x.var3 group.id z.var1 z.var2 gid
1 50.37630 22.25261 -10.023444 1 -0.56047565 98.61059 1
2 49.88690 22.53537 -10.033116 2 -0.23017749 99.58417 2
3 49.75327 19.53242 -11.197199 3 1.55870831 97.46921 3
4 50.16614 19.55715 -9.663839 4 0.07050839 104.33791 4
5 50.52802 20.74453 -9.646215 5 0.12928774 102.41592 5
6 49.41930 19.90466 -10.481041 6 1.71506499 97.75378 6
Call:
micromacro.lm( y ~ BLUP.x.var1 + BLUP.x.var2 + BLUP.x.var3 + z.var1 + z.var2, ...)
Residuals:
Min 1Q Median 3Q Max
-12.69188 -2.522461 1.409665 3.255795 7.871104
Coefficients:
Estimate Uncorrected S.E. Corrected S.E. df t Pr(>|t|)
(Intercept) 66.5587984 102.6668607 117.5634133 34 0.5661523 0.5750084
BLUP.x.var1 -0.4761053 2.7655065 3.2242219 34 -0.1476652 0.8834792
BLUP.x.var2 -0.4992712 0.6616701 0.5379883 34 -0.9280335 0.3599319
BLUP.x.var3 0.3322830 1.9182487 1.9275518 34 0.1723860 0.8641561
z.var1 0.6241292 1.1204741 0.8433672 34 0.7400444 0.4643528
z.var2 -0.2290337 0.6890615 0.5705512 34 -0.4014253 0.6906191
r
(Intercept) 0.09663986
BLUP.x.var1 0.02531625
BLUP.x.var2 0.15717816
BLUP.x.var3 0.02955105
z.var1 0.12590658
z.var2 0.06868130
---
Residual standard error: 5.14906 on 34 degrees of freedom
Multiple R-squared: 0.0441001801, Adjusted R-squared: -0.0964733228
F-statistic: 0.31372 on 5 and 34 DF, p-value: 0.90128 Estimate Uncorrected S.E. Corrected S.E. df t Pr(>|t|)
(Intercept) 66.5587984 102.6668607 117.5634133 34 0.5661523 0.5750084
BLUP.x.var1 -0.4761053 2.7655065 3.2242219 34 -0.1476652 0.8834792
BLUP.x.var2 -0.4992712 0.6616701 0.5379883 34 -0.9280335 0.3599319
BLUP.x.var3 0.3322830 1.9182487 1.9275518 34 0.1723860 0.8641561
z.var1 0.6241292 1.1204741 0.8433672 34 0.7400444 0.4643528
z.var2 -0.2290337 0.6890615 0.5705512 34 -0.4014253 0.6906191
r
(Intercept) 0.09663986
BLUP.x.var1 0.02531625
BLUP.x.var2 0.15717816
BLUP.x.var3 0.02955105
z.var1 0.12590658
z.var2 0.06868130
[1] 0.04410018
[1] -0.09647332
[1] FALSE
[1] "BLUP.x.var1" "BLUP.x.var2" "BLUP.x.var3" "group.id" "z.var1"
[6] "z.var2" "gid"
BLUP.x.var1 BLUP.x.var2 BLUP.x.var3 group.id z.var1 z.var2 gid
1 50.05587 20.82469 -10.730297 1 -0.56047565 98.61059 1
2 48.71397 22.85125 -9.915786 2 -0.23017749 99.58417 2
3 50.82770 20.13679 -10.164313 3 1.55870831 97.46921 3
4 49.45720 21.41725 -9.994019 4 0.07050839 104.33791 4
5 50.55675 20.26460 -9.880389 5 0.12928774 102.41592 5
Call:
micromacro.lm( y ~ BLUP.x.var1 + BLUP.x.var2 + BLUP.x.var3 + z.var1 + z.var2, ...)
Residuals:
Min 1Q Median 3Q Max
-12.18208 -2.799119 0.753945 4.180232 7.390603
Coefficients:
Estimate S.E. df t Pr(>|t|) r
(Intercept) 43.3114483 128.9535039 34 0.3358687 0.7390338 0.05750569
BLUP.x.var1 -0.8162960 1.6429701 34 -0.4968416 0.6224982 0.08490000
BLUP.x.var2 -0.2341391 0.9591321 34 -0.2441156 0.8086084 0.04182883
BLUP.x.var3 -1.6526544 2.4503135 34 -0.6744665 0.5045753 0.11490392
z.var1 0.9115797 1.0819825 34 0.8425087 0.4053911 0.14300401
z.var2 -0.0780441 0.5213088 34 -0.1497080 0.8818795 0.02566625
---
Residual standard error: 5.13546 on 34 degrees of freedom
Multiple R-squared: 0.0491419353, Adjusted R-squared: -0.090690133
F-statistic: 0.35144 on 5 and 34 DF, p-value: 0.87772 Estimate S.E. df t Pr(>|t|) r
(Intercept) 43.3114483 128.9535039 34 0.3358687 0.7390338 0.05750569
BLUP.x.var1 -0.8162960 1.6429701 34 -0.4968416 0.6224982 0.08490000
BLUP.x.var2 -0.2341391 0.9591321 34 -0.2441156 0.8086084 0.04182883
BLUP.x.var3 -1.6526544 2.4503135 34 -0.6744665 0.5045753 0.11490392
z.var1 0.9115797 1.0819825 34 0.8425087 0.4053911 0.14300401
z.var2 -0.0780441 0.5213088 34 -0.1497080 0.8818795 0.02566625
[1] 0.04914194
[1] -0.09069013
Call:
micromacro.lm( y ~ BLUP.x.var1 * BLUP.x.var2 + BLUP.x.var3 + z.var1 + z.var2, ...)
Residuals:
Min 1Q Median 3Q Max
-12.28544 -1.922037 0.7265851 3.159589 7.907561
Coefficients:
Estimate S.E. df t Pr(>|t|)
(Intercept) -2.201834e+03 1267.2993392 33 -1.73742219 0.09163893
BLUP.x.var1 4.382990e+01 25.1286795 33 1.74421806 0.09043042
BLUP.x.var2 1.101108e+02 61.9886614 33 1.77630581 0.08490401
BLUP.x.var3 -2.936592e+00 2.4827499 33 -1.18279830 0.24534100
z.var1 1.421470e+00 1.0874282 33 1.30718556 0.20018509
z.var2 -3.782961e-02 0.5059378 33 -0.07477127 0.94084813
BLUP.x.var1:BLUP.x.var2 -2.211655e+00 1.2423050 33 -1.78028327 0.08423929
r
(Intercept) 0.2894954
BLUP.x.var1 0.2905324
BLUP.x.var2 0.2954146
BLUP.x.var3 0.2016683
z.var1 0.2218798
z.var2 0.0130149
BLUP.x.var1:BLUP.x.var2 0.2960182
---
Residual standard error: 4.9053 on 33 degrees of freedom
Multiple R-squared: 0.1324625585, Adjusted R-squared: -0.0252715217
F-statistic: 0.83978 on 6 and 33 DF, p-value: 0.54836 Estimate S.E. df t Pr(>|t|)
(Intercept) -2.201834e+03 1267.2993392 33 -1.73742219 0.09163893
BLUP.x.var1 4.382990e+01 25.1286795 33 1.74421806 0.09043042
BLUP.x.var2 1.101108e+02 61.9886614 33 1.77630581 0.08490401
BLUP.x.var3 -2.936592e+00 2.4827499 33 -1.18279830 0.24534100
z.var1 1.421470e+00 1.0874282 33 1.30718556 0.20018509
z.var2 -3.782961e-02 0.5059378 33 -0.07477127 0.94084813
BLUP.x.var1:BLUP.x.var2 -2.211655e+00 1.2423050 33 -1.78028327 0.08423929
r
(Intercept) 0.2894954
BLUP.x.var1 0.2905324
BLUP.x.var2 0.2954146
BLUP.x.var3 0.2016683
z.var1 0.2218798
z.var2 0.0130149
BLUP.x.var1:BLUP.x.var2 0.2960182
[1] 0.1324626
[1] -0.02527152
Call:
micromacro.lm( y ~ BLUP.x.var1 + BLUP.x.var2 + BLUP.x.var3 * z.var1 + z.var2, ...)
Residuals:
Min 1Q Median 3Q Max
-11.85723 -2.712176 0.8406733 3.475445 7.199632
Coefficients:
Estimate S.E. df t Pr(>|t|) r
(Intercept) 38.06538844 130.4653427 33 0.2917663 0.7722917 0.05072461
BLUP.x.var1 -0.72524178 1.6653838 33 -0.4354803 0.6660491 0.07559049
BLUP.x.var2 -0.24440581 0.9683719 33 -0.2523884 0.8023063 0.04389283
BLUP.x.var3 -1.69545529 2.4745527 33 -0.6851563 0.4980302 0.11843101
z.var1 15.05477309 23.4496749 33 0.6420035 0.5253059 0.11106700
z.var2 -0.07461297 0.5262803 33 -0.1417742 0.8881204 0.02467221
BLUP.x.var3:z.var1 1.42070644 2.3530008 33 0.6037849 0.5501150 0.10452967
---
Residual standard error: 5.10733 on 33 degrees of freedom
Multiple R-squared: 0.0595314408, Adjusted R-squared: -0.1114628427
F-statistic: 0.34815 on 6 and 33 DF, p-value: 0.90587 Estimate S.E. df t Pr(>|t|) r
(Intercept) 38.06538844 130.4653427 33 0.2917663 0.7722917 0.05072461
BLUP.x.var1 -0.72524178 1.6653838 33 -0.4354803 0.6660491 0.07559049
BLUP.x.var2 -0.24440581 0.9683719 33 -0.2523884 0.8023063 0.04389283
BLUP.x.var3 -1.69545529 2.4745527 33 -0.6851563 0.4980302 0.11843101
z.var1 15.05477309 23.4496749 33 0.6420035 0.5253059 0.11106700
z.var2 -0.07461297 0.5262803 33 -0.1417742 0.8881204 0.02467221
BLUP.x.var3:z.var1 1.42070644 2.3530008 33 0.6037849 0.5501150 0.10452967
[1] 0.05953144
[1] -0.1114628
MicroMacroMultilevel documentation built on May 2, 2019, 3:17 p.m.
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Description Usage Arguments Details Value Author(s) References See Also Examples
Description
After fitting a micro-macro multilevel model, this function produces a user-friendly summary table of the results.
Usage
1 | micromacro.summary(model.output)
|
Arguments
model.output |
the output of |
Details
To date, most multilevel methodologies can only unbiasedly model macro-micro multilevel situations, wherein group-level predictors (e.g., city temperature) are used to predict an individual-level outcome variable (e.g., citizen personality). In contrast, this R package enables researchers to model micro-macro situations, wherein individual-level (micro) predictors (and other group-level predictors) are used to predict a group-level (macro) outcome variable in an unbiased way.
To conduct micro-macro multilevel modeling with the current package, one must first compute the adjusted group means with the function adjusted.predictors.
This is because in micro-macro multilevel modeling, it is statistically biased to directly regress the group-level outcome variable on the unadjusted group means of individual-level predictors (Croon & van Veldhoven, 2007).
Instead, one should use the best linear unbiased predictors (BLUP) of the group means (i.e., the adjusted group means), which is conveniently computed by adjusted.predictors.
Once produced by adjusted.predictors, the adjusted group means can be used as one of the inputs of the micromacro.lm function, which reports estimation results and inferential statistics of the micro-macro multilevel model of interest.
If group size is the same across all groups (i.e., unequal.groups = FALSE), then OLS standard errors are reported and used to determine the inferential statistics in this micro-macro model. If group size is different across groups (i.e., unequal.groups = TRUE), however, then the heteroscedasticity-consistent standard errors are reported and used determine the inferential statistics in this micro-macro model (White, 1980).
micromacro.summary produces a detailed summary on the model fitting and specifications, given the outputs of micromacro.lm.
Value
table a summary table.
Author(s)
Jackson G. Lu, Elizabeth Page-Gould, Nancy R. Xu (maintainer, nancyranxu@gmail.com).
References
Akinola, M., Page-Gould, E., Mehta, P. H., & Lu, J. G. (2016). Collective hormonal profiles predict group performance. Proceedings of the National Academy of Sciences, 113 (35), 9774-9779.
Croon, M. A., & van Veldhoven, M. J. (2007). Predicting group-level outcome variables from variables measured at the individual level: a latent variable multilevel model. Psychological methods, 12(1), 45-57.
See Also
micromacro.lm for fitting the micro-macro multilevel linear model of interest.
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 | ######## 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 are 3 individual-level predictors, thus 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 two data frames assumes unequal-sized groups (Step 3a), whereas the other assumes
# equal-sized groups (Step 3b):
# Step 3a. Generate the individual-level predictors
# 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=TRUE) )[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 3b. Generate the individual-level predictors
# 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 3. Generate a G-by-1 data frame of group-level outcome 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 4a. Generate a G-by-1 matrix of group ID, z.gid. Then generate an N-by-1 matrix of
# each individual's group ID, x.gid, where the group sizes are different
z.gid = seq(1:40)
x.gid = x.data.unequal$group.id
# Step 5a. Generate the best linear unbiased predictors that are calcualted from
# individual-level data
x.data = x.data.unequal[,c("x.var1","x.var2","x.var3")]
results = adjusted.predictors(x.data, z.data, x.gid, z.gid)
# Note: Given the fixed random seed, the output should be as below
results$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 6a. Fit a micro-macro multilevel model when group sizes are different
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:
# Estimate Uncorrected S.E. Corrected S.E. df t Pr(>|t|) 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$statistics
# Estimate Uncorrected S.E. Corrected S.E. df t Pr(>|t|) r
# (Intercept) 78.1232185 121.5103390 122.1367432 34 0.6396373 0.5266952 0.10904278
# BLUP.x.var1 -0.7589602 1.4954434 1.7177575 34 -0.4418320 0.6614084 0.07555696
# BLUP.x.var2 0.4263309 0.7070773 0.6299759 34 0.6767416 0.5031484 0.11528637
# BLUP.x.var3 0.2658078 2.4662049 2.4051691 34 0.1105152 0.9126506 0.01894980
# z.var1 0.4315941 1.0855707 1.0614535 34 0.4066068 0.6868451 0.06956356
# z.var2 -0.3949955 0.5573789 0.4230256 34 -0.9337390 0.3570228 0.15812040
model.output$rsquared
# 0.0400727607
model.output$rsquared.adjusted
# -0.1010930098
######## EXAMPLE 2. GROUP SIZE IS THE SAME ACROSS ALL GROUPS ########
######## Need to use adjusted.predictors() in the same package ######
# Step 4b. Generate a G-by-1 matrix of group ID, z.gid. Then generate an N-by-1 matrix of
# each individual's group ID, x.gid, where group size is the same across all groups
z.gid = seq(1:40)
x.gid = x.data.equal$group.id
# Step 5b. Generate the best linear unbiased predictors that are calcualted from
# individual-level data
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$adjusted.group.means[1:5, ]
# BLUP.x.var1 BLUP.x.var2 BLUP.x.var3 group.id z.var1 z.var2 gid
# 1 50.91373 19.12994 -10.051647 1 -0.56047565 98.61059 1
# 2 50.19068 19.17978 -10.814382 2 -0.23017749 99.58417 2
# 3 50.13390 20.98893 -9.952348 3 1.55870831 97.46921 3
# 4 49.68169 19.60632 -10.612717 4 0.07050839 104.33791 4
# 5 50.28579 22.07469 -10.245505 5 0.12928774 102.41592 5
# Step 6b. Fit a micro-macro multilevel model when group size is the same across groups
model.output2 = micromacro.lm(model.formula, results$adjusted.group.means, y,
results$unequal.groups)
micromacro.summary(model.output2)
# Call:
# micromacro.lm( y ~ BLUP.x.var1 + BLUP.x.var2 + BLUP.x.var3 + z.var1 + z.var2, ...)
#
# Residuals:
# Min 1Q Median 3Q Max
# -12.94409 -1.898937 0.8615494 3.78739 8.444582
#
#
# Coefficients:
# Estimate S.E. df t Pr(>|t|) r
# (Intercept) 135.4109966 134.1478457 34 1.0094161 0.3199052 0.17057636
# BLUP.x.var1 -2.1984308 2.2203278 34 -0.9901379 0.3291012 0.16741080
# BLUP.x.var2 -0.6369600 0.8619558 34 -0.7389706 0.4649961 0.12572678
# BLUP.x.var3 -0.5121002 1.7889594 34 -0.2862559 0.7764192 0.04903343
# z.var1 0.7718147 1.1347170 34 0.6801826 0.5009945 0.11586471
# z.var2 -0.1116209 0.5268130 34 -0.2118795 0.8334661 0.03631307
#
# ---
# Residual standard error: 5.11849 on 34 degrees of freedom
# Multiple R-squared: 0.0554183804, Adjusted R-squared: -0.0834906813
# F-statistic: 0.39895 on 5 and 34 DF, p-value: 0.84607
model.output2$statistics
# Estimate S.E. df t Pr(>|t|) 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
model.output2$rsquared
# 0.0554183804
model.output2$rsquared.adjusted
# -0.0834906813
######## EXAMPLE 3 (after EXAMPLE 2). ADDING A MICRO-MICRO INTERACTION TERM ########
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:
# Estimate S.E. df t Pr(>|t|) 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$statistics
# Estimate S.E. df t Pr(>|t|) r
# (Intercept) -1.098875e+03 1962.9182021 33 -0.5598169 0.5793848 0.09699214
# BLUP.x.var1 2.231877e+01 38.9620284 33 0.5728339 0.5706400 0.09922547
# BLUP.x.var2 5.988568e+01 96.0256433 33 0.6236426 0.5371496 0.10792809
# BLUP.x.var3 -9.557605e-01 1.9374178 33 -0.4933167 0.6250560 0.08556050
# z.var1 6.116347e-01 1.1727757 33 0.5215274 0.6054822 0.09041443
# z.var2 -8.556163e-02 0.5331509 33 -0.1604829 0.8734790 0.02792560
# BLUP.x.var1:BLUP.x.var2 -1.209354e+00 1.9186909 33 -0.6303016 0.5328380 0.10906688
model.output3$rsquared
# 0.0666547309
model.output3$rsquared.adjusted
# -0.103044409
######## EXAMPLE 4 (after EXAMPLE 2). ADDING A MICRO-MACRO INTERACTION TERM ########
model.formula4 = as.formula(y ~ BLUP.x.var1 + BLUP.x.var2 + BLUP.x.var3 * z.var1 + z.var2)
model.output4 = micromacro.lm(model.formula4, results$adjusted.group.means, y,
results$unequal.groups)
micromacro.summary(model.output4)
# Call:
# micromacro.lm( y ~ BLUP.x.var1 + BLUP.x.var2 + BLUP.x.var3 * z.var1 + z.var2, ...)
#
# Residuals:
# Min 1Q Median 3Q Max
# -12.99937 -1.909645 0.8775397 3.712013 8.46591
#
#
# Coefficients:
# Estimate S.E. df t Pr(>|t|) r
# (Intercept) 129.22731579 146.4817031 33 0.8822079 0.3840456 0.15179313
# BLUP.x.var1 -2.10556192 2.3951160 33 -0.8791064 0.3857003 0.15127172
# BLUP.x.var2 -0.63762927 0.8747645 33 -0.7289153 0.4711953 0.12587857
# BLUP.x.var3 -0.53590189 1.8273917 33 -0.2932605 0.7711594 0.05098372
# z.var1 2.95426548 19.1170600 33 0.1545356 0.8781288 0.02689146
# z.var2 -0.09852267 0.5467583 33 -0.1801942 0.8581021 0.03135236
# BLUP.x.var3:z.var1 0.21489002 1.8788995 33 0.1143702 0.9096374 0.01990534
#
# ---
# Residual standard error: 5.11747 on 33 degrees of freedom
# Multiple R-squared: 0.0557926451, Adjusted R-squared: -0.1158814195
# F-statistic: 0.32499 on 6 and 33 DF, p-value: 0.91909
model.output4$statistics
# Estimate S.E. df t Pr(>|t|) 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
model.output4$rsquared
# 0.0557926451
model.output4$rsquared.adjusted
# -0.1158814195
|
Example output
Warning messages:
1: In x.var1.means + rnorm(200, mean = 0, sd = 2) :
longer object length is not a multiple of shorter object length
2: In x.var2.means + rnorm(200, mean = 0, sd = 6) :
longer object length is not a multiple of shorter object length
3: In x.var3.means + rnorm(200, mean = 0, sd = 1.5) :
longer object length is not a multiple of shorter object length
4: In `[<-.data.frame`(`*tmp*`, nl, value = list(x.var3 = c(-12.0702873063753, :
replacement element 1 has 200 rows to replace 194 rows
5: In `[<-.data.frame`(`*tmp*`, nl, value = list(x.var3 = c(-12.0702873063753, :
replacement element 2 has 200 rows to replace 194 rows
6: In `[<-.data.frame`(`*tmp*`, nl, value = list(x.var3 = c(-12.0702873063753, :
replacement element 3 has 200 rows to replace 194 rows
group.id x.var1.means x.var2.means x.var3.means x.var3 x.var2
20.500000 50.000393 19.994708 -9.999167 -9.985279 19.986214
x.var1
50.121698
group.id x.var1.means x.var2.means x.var3.means x.var3 x.var2
20.118557 50.001697 19.993560 -9.997938 -9.986925 20.225848
x.var1
50.060817
group.id z.var1 z.var2
20.50000000 0.04518332 99.98656817
[1] 6.457797
[1] TRUE
[1] "BLUP.x.var1" "BLUP.x.var2" "BLUP.x.var3" "group.id" "z.var1"
[6] "z.var2" "gid"
BLUP.x.var1 BLUP.x.var2 BLUP.x.var3 group.id z.var1 z.var2 gid
1 50.37630 22.25261 -10.023444 1 -0.56047565 98.61059 1
2 49.88690 22.53537 -10.033116 2 -0.23017749 99.58417 2
3 49.75327 19.53242 -11.197199 3 1.55870831 97.46921 3
4 50.16614 19.55715 -9.663839 4 0.07050839 104.33791 4
5 50.52802 20.74453 -9.646215 5 0.12928774 102.41592 5
6 49.41930 19.90466 -10.481041 6 1.71506499 97.75378 6
Call:
micromacro.lm( y ~ BLUP.x.var1 + BLUP.x.var2 + BLUP.x.var3 + z.var1 + z.var2, ...)
Residuals:
Min 1Q Median 3Q Max
-12.69188 -2.522461 1.409665 3.255795 7.871104
Coefficients:
Estimate Uncorrected S.E. Corrected S.E. df t Pr(>|t|)
(Intercept) 66.5587984 102.6668607 117.5634133 34 0.5661523 0.5750084
BLUP.x.var1 -0.4761053 2.7655065 3.2242219 34 -0.1476652 0.8834792
BLUP.x.var2 -0.4992712 0.6616701 0.5379883 34 -0.9280335 0.3599319
BLUP.x.var3 0.3322830 1.9182487 1.9275518 34 0.1723860 0.8641561
z.var1 0.6241292 1.1204741 0.8433672 34 0.7400444 0.4643528
z.var2 -0.2290337 0.6890615 0.5705512 34 -0.4014253 0.6906191
r
(Intercept) 0.09663986
BLUP.x.var1 0.02531625
BLUP.x.var2 0.15717816
BLUP.x.var3 0.02955105
z.var1 0.12590658
z.var2 0.06868130
---
Residual standard error: 5.14906 on 34 degrees of freedom
Multiple R-squared: 0.0441001801, Adjusted R-squared: -0.0964733228
F-statistic: 0.31372 on 5 and 34 DF, p-value: 0.90128 Estimate Uncorrected S.E. Corrected S.E. df t Pr(>|t|)
(Intercept) 66.5587984 102.6668607 117.5634133 34 0.5661523 0.5750084
BLUP.x.var1 -0.4761053 2.7655065 3.2242219 34 -0.1476652 0.8834792
BLUP.x.var2 -0.4992712 0.6616701 0.5379883 34 -0.9280335 0.3599319
BLUP.x.var3 0.3322830 1.9182487 1.9275518 34 0.1723860 0.8641561
z.var1 0.6241292 1.1204741 0.8433672 34 0.7400444 0.4643528
z.var2 -0.2290337 0.6890615 0.5705512 34 -0.4014253 0.6906191
r
(Intercept) 0.09663986
BLUP.x.var1 0.02531625
BLUP.x.var2 0.15717816
BLUP.x.var3 0.02955105
z.var1 0.12590658
z.var2 0.06868130
[1] 0.04410018
[1] -0.09647332
[1] FALSE
[1] "BLUP.x.var1" "BLUP.x.var2" "BLUP.x.var3" "group.id" "z.var1"
[6] "z.var2" "gid"
BLUP.x.var1 BLUP.x.var2 BLUP.x.var3 group.id z.var1 z.var2 gid
1 50.05587 20.82469 -10.730297 1 -0.56047565 98.61059 1
2 48.71397 22.85125 -9.915786 2 -0.23017749 99.58417 2
3 50.82770 20.13679 -10.164313 3 1.55870831 97.46921 3
4 49.45720 21.41725 -9.994019 4 0.07050839 104.33791 4
5 50.55675 20.26460 -9.880389 5 0.12928774 102.41592 5
Call:
micromacro.lm( y ~ BLUP.x.var1 + BLUP.x.var2 + BLUP.x.var3 + z.var1 + z.var2, ...)
Residuals:
Min 1Q Median 3Q Max
-12.18208 -2.799119 0.753945 4.180232 7.390603
Coefficients:
Estimate S.E. df t Pr(>|t|) r
(Intercept) 43.3114483 128.9535039 34 0.3358687 0.7390338 0.05750569
BLUP.x.var1 -0.8162960 1.6429701 34 -0.4968416 0.6224982 0.08490000
BLUP.x.var2 -0.2341391 0.9591321 34 -0.2441156 0.8086084 0.04182883
BLUP.x.var3 -1.6526544 2.4503135 34 -0.6744665 0.5045753 0.11490392
z.var1 0.9115797 1.0819825 34 0.8425087 0.4053911 0.14300401
z.var2 -0.0780441 0.5213088 34 -0.1497080 0.8818795 0.02566625
---
Residual standard error: 5.13546 on 34 degrees of freedom
Multiple R-squared: 0.0491419353, Adjusted R-squared: -0.090690133
F-statistic: 0.35144 on 5 and 34 DF, p-value: 0.87772 Estimate S.E. df t Pr(>|t|) r
(Intercept) 43.3114483 128.9535039 34 0.3358687 0.7390338 0.05750569
BLUP.x.var1 -0.8162960 1.6429701 34 -0.4968416 0.6224982 0.08490000
BLUP.x.var2 -0.2341391 0.9591321 34 -0.2441156 0.8086084 0.04182883
BLUP.x.var3 -1.6526544 2.4503135 34 -0.6744665 0.5045753 0.11490392
z.var1 0.9115797 1.0819825 34 0.8425087 0.4053911 0.14300401
z.var2 -0.0780441 0.5213088 34 -0.1497080 0.8818795 0.02566625
[1] 0.04914194
[1] -0.09069013
Call:
micromacro.lm( y ~ BLUP.x.var1 * BLUP.x.var2 + BLUP.x.var3 + z.var1 + z.var2, ...)
Residuals:
Min 1Q Median 3Q Max
-12.28544 -1.922037 0.7265851 3.159589 7.907561
Coefficients:
Estimate S.E. df t Pr(>|t|)
(Intercept) -2.201834e+03 1267.2993392 33 -1.73742219 0.09163893
BLUP.x.var1 4.382990e+01 25.1286795 33 1.74421806 0.09043042
BLUP.x.var2 1.101108e+02 61.9886614 33 1.77630581 0.08490401
BLUP.x.var3 -2.936592e+00 2.4827499 33 -1.18279830 0.24534100
z.var1 1.421470e+00 1.0874282 33 1.30718556 0.20018509
z.var2 -3.782961e-02 0.5059378 33 -0.07477127 0.94084813
BLUP.x.var1:BLUP.x.var2 -2.211655e+00 1.2423050 33 -1.78028327 0.08423929
r
(Intercept) 0.2894954
BLUP.x.var1 0.2905324
BLUP.x.var2 0.2954146
BLUP.x.var3 0.2016683
z.var1 0.2218798
z.var2 0.0130149
BLUP.x.var1:BLUP.x.var2 0.2960182
---
Residual standard error: 4.9053 on 33 degrees of freedom
Multiple R-squared: 0.1324625585, Adjusted R-squared: -0.0252715217
F-statistic: 0.83978 on 6 and 33 DF, p-value: 0.54836 Estimate S.E. df t Pr(>|t|)
(Intercept) -2.201834e+03 1267.2993392 33 -1.73742219 0.09163893
BLUP.x.var1 4.382990e+01 25.1286795 33 1.74421806 0.09043042
BLUP.x.var2 1.101108e+02 61.9886614 33 1.77630581 0.08490401
BLUP.x.var3 -2.936592e+00 2.4827499 33 -1.18279830 0.24534100
z.var1 1.421470e+00 1.0874282 33 1.30718556 0.20018509
z.var2 -3.782961e-02 0.5059378 33 -0.07477127 0.94084813
BLUP.x.var1:BLUP.x.var2 -2.211655e+00 1.2423050 33 -1.78028327 0.08423929
r
(Intercept) 0.2894954
BLUP.x.var1 0.2905324
BLUP.x.var2 0.2954146
BLUP.x.var3 0.2016683
z.var1 0.2218798
z.var2 0.0130149
BLUP.x.var1:BLUP.x.var2 0.2960182
[1] 0.1324626
[1] -0.02527152
Call:
micromacro.lm( y ~ BLUP.x.var1 + BLUP.x.var2 + BLUP.x.var3 * z.var1 + z.var2, ...)
Residuals:
Min 1Q Median 3Q Max
-11.85723 -2.712176 0.8406733 3.475445 7.199632
Coefficients:
Estimate S.E. df t Pr(>|t|) r
(Intercept) 38.06538844 130.4653427 33 0.2917663 0.7722917 0.05072461
BLUP.x.var1 -0.72524178 1.6653838 33 -0.4354803 0.6660491 0.07559049
BLUP.x.var2 -0.24440581 0.9683719 33 -0.2523884 0.8023063 0.04389283
BLUP.x.var3 -1.69545529 2.4745527 33 -0.6851563 0.4980302 0.11843101
z.var1 15.05477309 23.4496749 33 0.6420035 0.5253059 0.11106700
z.var2 -0.07461297 0.5262803 33 -0.1417742 0.8881204 0.02467221
BLUP.x.var3:z.var1 1.42070644 2.3530008 33 0.6037849 0.5501150 0.10452967
---
Residual standard error: 5.10733 on 33 degrees of freedom
Multiple R-squared: 0.0595314408, Adjusted R-squared: -0.1114628427
F-statistic: 0.34815 on 6 and 33 DF, p-value: 0.90587 Estimate S.E. df t Pr(>|t|) r
(Intercept) 38.06538844 130.4653427 33 0.2917663 0.7722917 0.05072461
BLUP.x.var1 -0.72524178 1.6653838 33 -0.4354803 0.6660491 0.07559049
BLUP.x.var2 -0.24440581 0.9683719 33 -0.2523884 0.8023063 0.04389283
BLUP.x.var3 -1.69545529 2.4745527 33 -0.6851563 0.4980302 0.11843101
z.var1 15.05477309 23.4496749 33 0.6420035 0.5253059 0.11106700
z.var2 -0.07461297 0.5262803 33 -0.1417742 0.8881204 0.02467221
BLUP.x.var3:z.var1 1.42070644 2.3530008 33 0.6037849 0.5501150 0.10452967
[1] 0.05953144
[1] -0.1114628
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