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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.
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
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
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
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
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