Multinomial (Baseline) Logistic Regression
Carolyn J. Anderson
10/25/2021
This example used the high school and beyond data set that is on the course web-site.
Set up
Libaries
library(nnet)
library(dplyr) # for select function
library(tidyr) # for converting from wide to long formatData
setwd("C:\\Users\\cja\\Dropbox\\edps 589\\8 Multicategory_logit")
hsb <- read.table("hsb_data.txt",header=TRUE)Simple Model
Just achievement test scores mean as predictor:
hsb$hsp <- as.factor(hsb$hsp)
summary( mlogit <- multinom(hsp ~ achieve, data = hsb) )## # weights: 9 (4 variable)
## initial value 659.167373
## final value 541.891723
## converged## Call:
## multinom(formula = hsp ~ achieve, data = hsb)
##
## Coefficients:
## (Intercept) achieve
## 2 -5.039210 0.10990910
## 3 2.899539 -0.05994642
##
## Std. Errors:
## (Intercept) achieve
## 2 0.7834595 0.01496575
## 3 0.8156173 0.01677793
##
## Residual Deviance: 1083.783
## AIC: 1091.783Change Reference Category
If you can to change the reference category, which will give same results in lecture notes.
hsb$hsp <- relevel(hsb$hsp, ref = "3")
summary( mlogit <- multinom(hsp ~ achieve, data = hsb) )## # weights: 9 (4 variable)
## initial value 659.167373
## iter 10 value 541.891723
## iter 10 value 541.891723
## final value 541.891723
## converged## Call:
## multinom(formula = hsp ~ achieve, data = hsb)
##
## Coefficients:
## (Intercept) achieve
## 1 -2.899594 0.05994778
## 2 -7.938918 0.16985890
##
## Std. Errors:
## (Intercept) achieve
## 1 0.8156199 0.01677800
## 2 0.8438590 0.01676059
##
## Residual Deviance: 1083.783
## AIC: 1091.783Estimated Odds Ratios
Estimated odds ratios for 1 unit change in achievement
# -- general vs votech
exp(0.0599778)## [1] 1.061813# -- academic vs votech
exp(0.16985890)## [1] 1.185138# -- general vs achademic
exp(0.0599778-0.16985890)## [1] 0.8959407Estimated odds ratios for 10 unit change in achievement:
# -- general vs votech
exp(0.0599778*10)## [1] 1.821714# -- academic vs votech
exp(0.16985890*10)## [1] 5.466229# -- general vs acahdemic
exp((0.0599778-0.16985890)*10)## [1] 0.3332671Fitted Probabilities
Let’s see was is avaiblible after fitting the model,
names(mlogit)## [1] "n" "nunits" "nconn" "conn"
## [5] "nsunits" "decay" "entropy" "softmax"
## [9] "censored" "value" "wts" "convergence"
## [13] "fitted.values" "residuals" "lev" "call"
## [17] "terms" "weights" "deviance" "rank"
## [21] "lab" "coefnames" "vcoefnames" "xlevels"
## [25] "edf" "AIC"We can get the fitted probabilites
head(mlogit$fitted)## 3 1 2
## 1 0.5338136 0.3121843 0.1540021
## 2 0.4869136 0.3191096 0.1939767
## 3 0.3487466 0.3129113 0.3383421
## 4 0.5438010 0.3101179 0.1460811
## 5 0.4591786 0.3210609 0.2197605
## 6 0.4207942 0.3211342 0.2580716hsb$fitV <- mlogit$fitted[,1]
hsb$fitG <- mlogit$fitted[,2]
hsb$fitA <- mlogit$fitted[,3]And graph them,
hsb <- hsb[order(hsb$achieve),]
# What probabilities look like
plot(hsb$achieve,hsb$fitV, type="l",lwd=2,col="blue",
ylim=c(0,1),
ylab="Fitted Probabilities",
xlab="Achievement",
main="Fitted Probabilities from Baseline Model")
lines(hsb$achieve,hsb$fitG, type="l",lwd=2,col="green")
lines(hsb$achieve,hsb$fitA, type="l",lwd=2,col="red")
legend("topleft",legend=c("P(VoTech)","P(General)", "P(Academic)"),
col=c("blue","green","red"), lwd=2)
Model with 2 explanatory
We’ll add SES first as a nominal and then as a numeric (ordinal) variable. From this we’ll decide whether SES can be nominal or numeric
Nominal SES
# -- SES nominal
hsb$nses <- as.factor(hsb$ses)
hsb$nses <- relevel(hsb$nses, ref = "3")
summary(mlogit2 <- multinom(hsp ~ achieve + nses, data=hsb))## # weights: 15 (8 variable)
## initial value 659.167373
## iter 10 value 532.339273
## final value 532.332956
## converged## Call:
## multinom(formula = hsp ~ achieve + nses, data = hsb)
##
## Coefficients:
## (Intercept) achieve nses1 nses2
## 1 -3.083816 0.06539199 0.1962514 -0.2734260
## 2 -6.800197 0.16108836 -0.9400043 -0.8908714
##
## Std. Errors:
## (Intercept) achieve nses1 nses2
## 1 0.9307217 0.01744422 0.3782999 0.347312
## 2 0.9204186 0.01728872 0.3557693 0.304543
##
## Residual Deviance: 1064.666
## AIC: 1080.666# z=sqrt(wald) statistics for parameters
(z <- summary(mlogit2)$coefficients/summary(mlogit2)$standard.errors)## (Intercept) achieve nses1 nses2
## 1 -3.313359 3.748634 0.518772 -0.7872634
## 2 -7.388157 9.317544 -2.642174 -2.9252728(p <- (1 - pnorm(abs(z), 0, 1)) * 2)## (Intercept) achieve nses1 nses2
## 1 9.218242e-04 0.0001778003 0.603919736 0.431127709
## 2 1.487699e-13 0.0000000000 0.008237584 0.003441543Numeric (Ordinal) SES
# -- SES ordinal
summary(mlogit3 <- multinom(hsp ~ achieve + ses, data=hsb))## # weights: 12 (6 variable)
## initial value 659.167373
## iter 10 value 534.120572
## final value 534.119859
## converged## Call:
## multinom(formula = hsp ~ achieve + ses, data = hsb)
##
## Coefficients:
## (Intercept) achieve ses
## 1 -2.789752 0.06395804 -0.1658336
## 2 -8.288916 0.15922218 0.4398755
##
## Std. Errors:
## (Intercept) achieve ses
## 1 0.8264618 0.01733939 0.1785720
## 2 0.8659226 0.01713701 0.1695085
##
## Residual Deviance: 1068.24
## AIC: 1080.24The anova function does not work to get likelihood ratio test with multinom objects; however, it’s pretty short code to get it.
(lrt <- mlogit3$deviance -mlogit2$deviance)## [1] 3.5738071-pchisq(lrt,2)## [1] 0.167478And some others
# -- test achieve conditional on SES ordinal
(lrt <- mlogit$deviance -mlogit3$deviance)## [1] 15.543731-pchisq(lrt,2)## [1] 0.0004214272# z=sqrt(wald) statistics for parameters
(z <- summary(mlogit3)$coefficients/summary(mlogit3)$standard.errors)## (Intercept) achieve ses
## 1 -3.375537 3.688597 -0.9286651
## 2 -9.572353 9.291129 2.5950056(p <- (1 - pnorm(abs(z), 0, 1)) * 2)## (Intercept) achieve ses
## 1 0.0007367173 0.0002254942 0.353062648
## 2 0.0000000000 0.0000000000 0.009458939Long Format
This is useful it what to test whether slopes are the same for different categoriest of the response variable. First we’ll fit it and then test slopes.
First we need to set up the data into a long format
hsb$id <- as.factor( seq(1:length(hsb$ses) ))
t <- table(hsb$id,hsb$hsp)
hsb.hsp <- as.data.frame(t)
names(hsb.hsp) <- c("id","program","y")
long <- merge(hsb, hsb.hsp, by=c("id"))
long$id <- as.factor(long$id)
long$program <- as.factor(long$program)Which yields
head(long, n=25)## id sex race ses sctyp hsp locus concpt mot car rdg wrtg math sci civ
## 1 1 2 3 1 1 3 -0.23 0.44 0.33 14 33.6 35.2 40.9 29.3 25.7
## 2 1 2 3 1 1 3 -0.23 0.44 0.33 14 33.6 35.2 40.9 29.3 25.7
## 3 1 2 3 1 1 3 -0.23 0.44 0.33 14 33.6 35.2 40.9 29.3 25.7
## 4 10 1 4 2 1 1 -0.84 -0.57 0.33 2 33.6 33.3 41.0 36.3 35.6
## 5 10 1 4 2 1 1 -0.84 -0.57 0.33 2 33.6 33.3 41.0 36.3 35.6
## 6 10 1 4 2 1 1 -0.84 -0.57 0.33 2 33.6 33.3 41.0 36.3 35.6
## 7 100 1 4 3 2 2 0.71 -0.06 0.67 9 44.2 37.8 49.2 39.0 45.6
## 8 100 1 4 3 2 2 0.71 -0.06 0.67 9 44.2 37.8 49.2 39.0 45.6
## 9 100 1 4 3 2 2 0.71 -0.06 0.67 9 44.2 37.8 49.2 39.0 45.6
## 10 101 1 3 1 1 1 0.45 -0.91 0.33 2 41.6 41.1 42.8 49.8 40.6
## 11 101 1 3 1 1 1 0.45 -0.91 0.33 2 41.6 41.1 42.8 49.8 40.6
## 12 101 1 3 1 1 1 0.45 -0.91 0.33 2 41.6 41.1 42.8 49.8 40.6
## 13 102 2 4 2 1 2 -0.40 -0.22 0.67 9 52.1 38.5 36.1 44.4 45.6
## 14 102 2 4 2 1 2 -0.40 -0.22 0.67 9 52.1 38.5 36.1 44.4 45.6
## 15 102 2 4 2 1 2 -0.40 -0.22 0.67 9 52.1 38.5 36.1 44.4 45.6
## 16 103 2 4 3 1 3 -0.14 -0.86 0.00 9 38.9 46.3 50.1 36.3 45.6
## 17 103 2 4 3 1 3 -0.14 -0.86 0.00 9 38.9 46.3 50.1 36.3 45.6
## 18 103 2 4 3 1 3 -0.14 -0.86 0.00 9 38.9 46.3 50.1 36.3 45.6
## 19 104 2 4 2 1 3 -0.60 -0.26 0.67 4 49.5 41.1 38.4 52.6 35.6
## 20 104 2 4 2 1 3 -0.60 -0.26 0.67 4 49.5 41.1 38.4 52.6 35.6
## 21 104 2 4 2 1 3 -0.60 -0.26 0.67 4 49.5 41.1 38.4 52.6 35.6
## 22 105 2 3 1 1 3 0.31 1.19 1.00 1 40.5 46.9 40.4 39.0 50.6
## 23 105 2 3 1 1 3 0.31 1.19 1.00 1 40.5 46.9 40.4 39.0 50.6
## 24 105 2 3 1 1 3 0.31 1.19 1.00 1 40.5 46.9 40.4 39.0 50.6
## 25 106 2 3 1 1 2 0.06 0.94 0.67 9 45.3 54.7 44.3 33.6 40.6
## type achieve academic ncases fitV fitG fitA nses program y
## 1 case 32.94 0 1 0.6700029 0.2656999 0.06429719 1 3 1
## 2 case 32.94 0 1 0.6700029 0.2656999 0.06429719 1 1 0
## 3 case 32.94 0 1 0.6700029 0.2656999 0.06429719 1 2 0
## 4 case 35.96 0 1 0.6114127 0.2905861 0.09800122 2 1 1
## 5 case 35.96 0 1 0.6114127 0.2905861 0.09800122 2 3 0
## 6 case 35.96 0 1 0.6114127 0.2905861 0.09800122 2 2 0
## 7 case 43.16 1 1 0.4393011 0.3214805 0.23921839 3 2 1
## 8 case 43.16 1 1 0.4393011 0.3214805 0.23921839 3 3 0
## 9 case 43.16 1 1 0.4393011 0.3214805 0.23921839 3 1 0
## 10 case 43.18 0 1 0.4387747 0.3214805 0.23974481 1 1 1
## 11 case 43.18 0 1 0.4387747 0.3214805 0.23974481 1 3 0
## 12 case 43.18 0 1 0.4387747 0.3214805 0.23974481 1 2 0
## 13 case 43.34 1 1 0.4345580 0.3214596 0.24398236 2 1 0
## 14 case 43.34 1 1 0.4345580 0.3214596 0.24398236 2 3 0
## 15 case 43.34 1 1 0.4345580 0.3214596 0.24398236 2 2 1
## 16 case 43.44 0 1 0.4319179 0.3214278 0.24665433 3 1 0
## 17 case 43.44 0 1 0.4319179 0.3214278 0.24665433 3 3 1
## 18 case 43.44 0 1 0.4319179 0.3214278 0.24665433 3 2 0
## 19 case 43.44 0 1 0.4319179 0.3214278 0.24665433 2 3 1
## 20 case 43.44 0 1 0.4319179 0.3214278 0.24665433 2 2 0
## 21 case 43.44 0 1 0.4319179 0.3214278 0.24665433 2 1 0
## 22 case 43.48 0 1 0.4308609 0.3214109 0.24772816 1 1 0
## 23 case 43.48 0 1 0.4308609 0.3214109 0.24772816 1 3 1
## 24 case 43.48 0 1 0.4308609 0.3214109 0.24772816 1 2 0
## 25 case 43.70 1 1 0.4250381 0.3212766 0.25368528 1 1 0Fit the Model using GLM
This take a bit longer than multinom, but it works.
sum1 <- summary(long.mod <- glm(y ~ id + program + program*achieve, data=long, family=poisson))Note that many of the parameters are not of interest (i.e., nuisance).
Test Slopes
This can be done in two ways. We’ll examine both.
Method I
Create a new variable that equates the slopes for general and votech
# no restrictions
summary( logit.3slopes <- glm(y ~ id + program + program*achieve, data=long, family=poisson))##
## Call:
## glm(formula = y ~ id + program + program * achieve, family = poisson,
## data = long)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.3351 -0.7662 -0.5409 0.3957 2.3099
##
## Coefficients: (1 not defined because of singularities)
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -0.40047 1.00367 -0.399 0.689886
## id2 -0.02216 1.41422 -0.016 0.987496
## id3 -0.05939 1.41423 -0.042 0.966502
## id4 -0.06961 1.41423 -0.049 0.960745
## id5 -0.07155 1.41423 -0.051 0.959650
## id6 -0.07350 1.41423 -0.052 0.958549
## id7 -0.07547 1.41424 -0.053 0.957443
## id8 -0.07612 1.41424 -0.054 0.957073
## id9 -0.09151 1.41425 -0.065 0.948408
## id10 -0.09151 1.41425 -0.065 0.948408
## id11 -0.10606 1.41426 -0.075 0.940219
## id12 -0.10960 1.41426 -0.077 0.938230
## id13 -0.11604 1.41427 -0.082 0.934610
## id14 -0.12623 1.41428 -0.089 0.928878
## id15 -0.13142 1.41428 -0.093 0.925964
## id16 -0.13142 1.41428 -0.093 0.925964
## id17 -0.13817 1.41429 -0.098 0.922172
## id18 -0.13817 1.41429 -0.098 0.922172
## id19 -0.15120 1.41431 -0.107 0.914864
## id20 -0.15824 1.41432 -0.112 0.910918
## id21 -0.16458 1.41433 -0.116 0.907363
## id22 -0.16538 1.41433 -0.117 0.906916
## id23 -0.16939 1.41433 -0.120 0.904669
## id24 -0.17100 1.41434 -0.121 0.903766
## id25 -0.17181 1.41434 -0.121 0.903313
## id26 -0.17424 1.41434 -0.123 0.901950
## id27 -0.18327 1.41436 -0.130 0.896900
## id28 -0.19077 1.41437 -0.135 0.892706
## id29 -0.19330 1.41437 -0.137 0.891295
## id30 -0.19753 1.41438 -0.140 0.888929
## id31 -0.20094 1.41439 -0.142 0.887024
## id32 -0.20870 1.41440 -0.148 0.882695
## id33 -0.20957 1.41440 -0.148 0.882210
## id34 -0.21569 1.41441 -0.152 0.878797
## id35 -0.22455 1.41443 -0.159 0.873860
## id36 -0.22724 1.41444 -0.161 0.872364
## id37 -0.23174 1.41445 -0.164 0.869857
## id38 -0.23174 1.41445 -0.164 0.869857
## id39 -0.23628 1.41446 -0.167 0.867331
## id40 -0.23811 1.41446 -0.168 0.866316
## id41 -0.24178 1.41447 -0.171 0.864276
## id42 -0.24919 1.41448 -0.176 0.860160
## id43 -0.24919 1.41448 -0.176 0.860160
## id44 -0.25012 1.41449 -0.177 0.859642
## id45 -0.25012 1.41449 -0.177 0.859642
## id46 -0.25293 1.41449 -0.179 0.858084
## id47 -0.25387 1.41450 -0.179 0.857563
## id48 -0.25575 1.41450 -0.181 0.856519
## id49 -0.26429 1.41452 -0.187 0.851783
## id50 -0.26429 1.41452 -0.187 0.851783
## id51 -0.26525 1.41452 -0.188 0.851253
## id52 -0.27296 1.41454 -0.193 0.846985
## id53 -0.27296 1.41454 -0.193 0.846985
## id54 -0.27783 1.41455 -0.196 0.844293
## id55 -0.27783 1.41455 -0.196 0.844293
## id56 -0.27880 1.41456 -0.197 0.843752
## id57 -0.28175 1.41456 -0.199 0.842125
## id58 -0.28175 1.41456 -0.199 0.842125
## id59 -0.28175 1.41456 -0.199 0.842125
## id60 -0.28273 1.41457 -0.200 0.841582
## id61 -0.28470 1.41457 -0.201 0.840492
## id62 -0.28867 1.41458 -0.204 0.838302
## id63 -0.29166 1.41459 -0.206 0.836652
## id64 -0.29166 1.41459 -0.206 0.836652
## id65 -0.29869 1.41461 -0.211 0.832775
## id66 -0.30477 1.41463 -0.215 0.829421
## id67 -0.30579 1.41463 -0.216 0.828859
## id68 -0.30579 1.41463 -0.216 0.828859
## id69 -0.30989 1.41464 -0.219 0.826605
## id70 -0.30989 1.41464 -0.219 0.826605
## id71 -0.31401 1.41465 -0.222 0.824337
## id72 -0.31816 1.41467 -0.225 0.822058
## id73 -0.31920 1.41467 -0.226 0.821486
## id74 -0.33075 1.41470 -0.234 0.815143
## id75 -0.33075 1.41470 -0.234 0.815143
## id76 -0.33607 1.41472 -0.238 0.812228
## id77 -0.33714 1.41472 -0.238 0.811642
## id78 -0.34575 1.41475 -0.244 0.806931
## id79 -0.35009 1.41477 -0.247 0.804557
## id80 -0.35337 1.41478 -0.250 0.802767
## id81 -0.35446 1.41478 -0.251 0.802169
## id82 -0.36662 1.41482 -0.259 0.795538
## id83 -0.36773 1.41483 -0.260 0.794931
## id84 -0.37109 1.41484 -0.262 0.793103
## id85 -0.37221 1.41484 -0.263 0.792492
## id86 -0.37221 1.41484 -0.263 0.792492
## id87 -0.37785 1.41486 -0.267 0.789427
## id88 -0.38239 1.41488 -0.270 0.786960
## id89 -0.38925 1.41490 -0.275 0.783235
## id90 -0.39617 1.41493 -0.280 0.779482
## id91 -0.39849 1.41494 -0.282 0.778225
## id92 -0.40316 1.41495 -0.285 0.775700
## id93 -0.40316 1.41495 -0.285 0.775700
## id94 -0.40550 1.41496 -0.287 0.774433
## id95 -0.40550 1.41496 -0.287 0.774433
## id96 -0.40668 1.41497 -0.287 0.773799
## id97 -0.41021 1.41498 -0.290 0.771890
## id98 -0.41139 1.41499 -0.291 0.771252
## id99 -0.41613 1.41500 -0.294 0.768693
## id100 -0.42210 1.41503 -0.298 0.765476
## id101 -0.42330 1.41503 -0.299 0.764830
## id102 -0.43296 1.41507 -0.306 0.759635
## id103 -0.43905 1.41510 -0.310 0.756362
## id104 -0.43905 1.41510 -0.310 0.756362
## id105 -0.44150 1.41511 -0.312 0.755048
## id106 -0.45511 1.41517 -0.322 0.747761
## id107 -0.45635 1.41517 -0.322 0.747094
## id108 -0.45760 1.41518 -0.323 0.746426
## id109 -0.45760 1.41518 -0.323 0.746426
## id110 -0.46136 1.41519 -0.326 0.744418
## id111 -0.46136 1.41519 -0.326 0.744418
## id112 -0.46136 1.41519 -0.326 0.744418
## id113 -0.46388 1.41520 -0.328 0.743075
## id114 -0.46514 1.41521 -0.329 0.742403
## id115 -0.46514 1.41521 -0.329 0.742403
## id116 -0.47402 1.41525 -0.335 0.737673
## id117 -0.48299 1.41529 -0.341 0.732905
## id118 -0.48686 1.41531 -0.344 0.730850
## id119 -0.48815 1.41531 -0.345 0.730163
## id120 -0.48815 1.41531 -0.345 0.730163
## id121 -0.49205 1.41533 -0.348 0.728099
## id122 -0.49989 1.41537 -0.353 0.723949
## id123 -0.50252 1.41538 -0.355 0.722560
## id124 -0.50779 1.41541 -0.359 0.719772
## id125 -0.50912 1.41541 -0.360 0.719074
## id126 -0.50912 1.41541 -0.360 0.719074
## id127 -0.51444 1.41544 -0.363 0.716271
## id128 -0.52247 1.41548 -0.369 0.712044
## id129 -0.52382 1.41548 -0.370 0.711337
## id130 -0.52651 1.41550 -0.372 0.709920
## id131 -0.53329 1.41553 -0.377 0.706366
## id132 -0.53601 1.41554 -0.379 0.704939
## id133 -0.53738 1.41555 -0.380 0.704225
## id134 -0.54148 1.41557 -0.383 0.702077
## id135 -0.54286 1.41558 -0.383 0.701359
## id136 -0.54423 1.41559 -0.384 0.700641
## id137 -0.55252 1.41563 -0.390 0.696316
## id138 -0.55391 1.41564 -0.391 0.695593
## id139 -0.55669 1.41565 -0.393 0.694144
## id140 -0.55948 1.41567 -0.395 0.692692
## id141 -0.55948 1.41567 -0.395 0.692692
## id142 -0.56508 1.41570 -0.399 0.689780
## id143 -0.56508 1.41570 -0.399 0.689780
## id144 -0.56649 1.41570 -0.400 0.689050
## id145 -0.56930 1.41572 -0.402 0.687588
## id146 -0.57213 1.41573 -0.404 0.686123
## id147 -0.57354 1.41574 -0.405 0.685390
## id148 -0.58208 1.41579 -0.411 0.680974
## id149 -0.59646 1.41587 -0.421 0.673558
## id150 -0.59791 1.41588 -0.422 0.672813
## id151 -0.60373 1.41591 -0.426 0.669825
## id152 -0.60811 1.41594 -0.429 0.667576
## id153 -0.60811 1.41594 -0.429 0.667576
## id154 -0.60958 1.41594 -0.431 0.666825
## id155 -0.61546 1.41598 -0.435 0.663815
## id156 -0.61546 1.41598 -0.435 0.663815
## id157 -0.61693 1.41599 -0.436 0.663061
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## id513 -2.32697 1.43855 -1.618 0.105753
## id514 -2.32697 1.43855 -1.618 0.105753
## id515 -2.33556 1.43872 -1.623 0.104513
## id516 -2.34416 1.43889 -1.629 0.103284
## id517 -2.35563 1.43913 -1.637 0.101662
## id518 -2.36138 1.43924 -1.641 0.100857
## id519 -2.36138 1.43924 -1.641 0.100857
## id520 -2.37289 1.43948 -1.648 0.099263 .
## id521 -2.37865 1.43959 -1.652 0.098472 .
## id522 -2.38153 1.43965 -1.654 0.098079 .
## id523 -2.38153 1.43965 -1.654 0.098079 .
## id524 -2.38730 1.43977 -1.658 0.097295 .
## id525 -2.40462 1.44013 -1.670 0.094972 .
## id526 -2.40752 1.44019 -1.672 0.094589 .
## id527 -2.41620 1.44037 -1.677 0.093447 .
## id528 -2.42199 1.44049 -1.681 0.092691 .
## id529 -2.44812 1.44103 -1.699 0.089344 .
## id530 -2.45684 1.44121 -1.705 0.088249 .
## id531 -2.46558 1.44140 -1.711 0.087164 .
## id532 -2.46849 1.44146 -1.713 0.086805 .
## id533 -2.47141 1.44152 -1.714 0.086446 .
## id534 -2.48892 1.44189 -1.726 0.084319 .
## id535 -2.49185 1.44195 -1.728 0.083969 .
## id536 -2.50355 1.44220 -1.736 0.082577 .
## id537 -2.50941 1.44232 -1.740 0.081888 .
## id538 -2.51527 1.44245 -1.744 0.081203 .
## id539 -2.55936 1.44340 -1.773 0.076204 .
## id540 -2.56525 1.44353 -1.777 0.075556 .
## id541 -2.58001 1.44385 -1.787 0.073954 .
## id542 -2.58592 1.44398 -1.791 0.073320 .
## id543 -2.58888 1.44404 -1.793 0.073005 .
## id544 -2.60071 1.44430 -1.801 0.071755 .
## id545 -2.60367 1.44437 -1.803 0.071445 .
## id546 -2.60960 1.44450 -1.807 0.070828 .
## id547 -2.61256 1.44456 -1.809 0.070521 .
## id548 -2.61256 1.44456 -1.809 0.070521 .
## id549 -2.61849 1.44469 -1.812 0.069911 .
## id550 -2.61849 1.44469 -1.812 0.069911 .
## id551 -2.63334 1.44502 -1.822 0.068402 .
## id552 -2.63631 1.44509 -1.824 0.068103 .
## id553 -2.64523 1.44529 -1.830 0.067213 .
## id554 -2.68697 1.44622 -1.858 0.063180 .
## id555 -2.71390 1.44683 -1.876 0.060690 .
## id556 -2.74691 1.44759 -1.898 0.057752 .
## id557 -2.75293 1.44773 -1.902 0.057230 .
## id558 -2.75293 1.44773 -1.902 0.057230 .
## id559 -2.76798 1.44807 -1.911 0.055942 .
## id560 -2.78305 1.44842 -1.921 0.054677 .
## id561 -2.78606 1.44849 -1.923 0.054427 .
## id562 -2.78908 1.44856 -1.925 0.054178 .
## id563 -2.80721 1.44899 -1.937 0.052702 .
## id564 -2.81628 1.44920 -1.943 0.051976 .
## id565 -2.81931 1.44927 -1.945 0.051735 .
## id566 -2.83445 1.44963 -1.955 0.050548 .
## id567 -2.84355 1.44984 -1.961 0.049846 *
## id568 -2.85265 1.45006 -1.967 0.049152 *
## id569 -2.85569 1.45013 -1.969 0.048923 *
## id570 -2.87392 1.45056 -1.981 0.047564 *
## id571 -2.88914 1.45092 -1.991 0.046455 *
## id572 -2.89218 1.45100 -1.993 0.046235 *
## id573 -2.89218 1.45100 -1.993 0.046235 *
## id574 -2.89523 1.45107 -1.995 0.046017 *
## id575 -2.91048 1.45144 -2.005 0.044938 *
## id576 -2.93185 1.45195 -2.019 0.043461 *
## id577 -2.94715 1.45232 -2.029 0.042432 *
## id578 -2.95327 1.45247 -2.033 0.042025 *
## id579 -2.95633 1.45255 -2.035 0.041823 *
## id580 -2.98086 1.45315 -2.051 0.040237 *
## id581 -2.99928 1.45360 -2.063 0.039079 *
## id582 -3.01466 1.45398 -2.073 0.038136 *
## id583 -3.01466 1.45398 -2.073 0.038136 *
## id584 -3.02697 1.45428 -2.081 0.037396 *
## id585 -3.04547 1.45474 -2.093 0.036307 *
## id586 -3.04547 1.45474 -2.093 0.036307 *
## id587 -3.05781 1.45505 -2.102 0.035596 *
## id588 -3.06399 1.45521 -2.106 0.035245 *
## id589 -3.07325 1.45544 -2.112 0.034724 *
## id590 -3.08253 1.45567 -2.118 0.034209 *
## id591 -3.16007 1.45765 -2.168 0.030164 *
## id592 -3.19743 1.45861 -2.192 0.028372 *
## id593 -3.22552 1.45934 -2.210 0.027087 *
## id594 -3.24114 1.45972 -2.220 0.026392 *
## id595 -3.30380 1.46140 -2.261 0.023777 *
## id596 -3.31008 1.46157 -2.265 0.023528 *
## id597 -3.33837 1.46232 -2.283 0.022435 *
## id598 -3.40139 1.46402 -2.323 0.020162 *
## id599 -3.53764 1.46778 -2.410 0.015944 *
## id600 -3.63646 1.47057 -2.473 0.013405 *
## program1 -2.89962 0.81562 -3.555 0.000378 ***
## program2 -7.93876 0.84385 -9.408 < 2e-16 ***
## achieve NA NA NA NA
## program1:achieve 0.05995 0.01678 3.573 0.000353 ***
## program2:achieve 0.16986 0.01676 10.134 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for poisson family taken to be 1)
##
## Null deviance: 1318.3 on 1799 degrees of freedom
## Residual deviance: 1083.8 on 1196 degrees of freedom
## AIC: 3491.8
##
## Number of Fisher Scoring iterations: 8# restrictions
long$program2 <- ifelse(long$program=="2", 0, 1)
table(long$program2,long$program)##
## 3 1 2
## 0 0 0 600
## 1 600 600 0summary( logit.2slopes <- glm(y ~ id + program + program2*achieve, data=long, family=poisson))##
## Call:
## glm(formula = y ~ id + program + program2 * achieve, family = poisson,
## data = long)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.3410 -0.7724 -0.5413 0.4063 2.0152
##
## Coefficients: (2 not defined because of singularities)
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 3.74809 1.10041 3.406 0.000659 ***
## id2 0.10114 1.41426 0.072 0.942987
## id3 0.25613 1.41453 0.181 0.856314
## id4 0.29574 1.41464 0.209 0.834405
## id5 0.30315 1.41466 0.214 0.830322
## id6 0.31055 1.41468 0.220 0.826246
## id7 0.31794 1.41470 0.225 0.822179
## id8 0.32041 1.41471 0.226 0.820825
## id9 0.37689 1.41491 0.266 0.789952
## id10 0.37689 1.41491 0.266 0.789952
## id11 0.42814 1.41511 0.303 0.762236
## id12 0.44029 1.41517 0.311 0.755707
## id13 0.46212 1.41527 0.327 0.744028
## id14 0.49595 1.41543 0.350 0.726047
## id15 0.51281 1.41552 0.362 0.717145
## id16 0.51281 1.41552 0.362 0.717145
## id17 0.53443 1.41563 0.378 0.705789
## id18 0.53443 1.41563 0.378 0.705789
## id19 0.57508 1.41586 0.406 0.684620
## id20 0.59650 1.41599 0.421 0.673566
## id21 0.61548 1.41611 0.435 0.663831
## id22 0.61785 1.41612 0.436 0.662621
## id23 0.62968 1.41620 0.445 0.656588
## id24 0.63441 1.41623 0.448 0.654184
## id25 0.63677 1.41624 0.450 0.652984
## id26 0.64385 1.41629 0.455 0.649394
## id27 0.66975 1.41647 0.473 0.636336
## id28 0.69085 1.41662 0.488 0.625780
## id29 0.69787 1.41667 0.493 0.622287
## id30 0.70954 1.41675 0.501 0.616495
## id31 0.71887 1.41682 0.507 0.611887
## id32 0.73979 1.41698 0.522 0.601606
## id33 0.74211 1.41700 0.524 0.600471
## id34 0.75833 1.41713 0.535 0.592569
## id35 0.78141 1.41731 0.551 0.581407
## id36 0.78831 1.41737 0.556 0.578088
## id37 0.79980 1.41747 0.564 0.572586
## id38 0.79980 1.41747 0.564 0.572586
## id39 0.81126 1.41756 0.572 0.567123
## id40 0.81584 1.41760 0.576 0.564949
## id41 0.82498 1.41768 0.582 0.560619
## id42 0.84322 1.41784 0.595 0.552032
## id43 0.84322 1.41784 0.595 0.552032
## id44 0.84549 1.41786 0.596 0.550965
## id45 0.84549 1.41786 0.596 0.550965
## id46 0.85231 1.41792 0.601 0.547776
## id47 0.85458 1.41794 0.603 0.546716
## id48 0.85912 1.41799 0.606 0.544600
## id49 0.87948 1.41817 0.620 0.535157
## id50 0.87948 1.41817 0.620 0.535157
## id51 0.88174 1.41819 0.622 0.534116
## id52 0.89976 1.41836 0.634 0.525842
## id53 0.89976 1.41836 0.634 0.525842
## id54 0.91099 1.41847 0.642 0.520722
## id55 0.91099 1.41847 0.642 0.520722
## id56 0.91323 1.41849 0.644 0.519703
## id57 0.91995 1.41856 0.649 0.516655
## id58 0.91995 1.41856 0.649 0.516655
## id59 0.91995 1.41856 0.649 0.516655
## id60 0.92219 1.41858 0.650 0.515642
## id61 0.92666 1.41863 0.653 0.513621
## id62 0.93559 1.41871 0.659 0.509598
## id63 0.94228 1.41878 0.664 0.506597
## id64 0.94228 1.41878 0.664 0.506597
## id65 0.95784 1.41894 0.675 0.499652
## id66 0.97113 1.41908 0.684 0.493761
## id67 0.97334 1.41910 0.686 0.492784
## id68 0.97334 1.41910 0.686 0.492784
## id69 0.98218 1.41919 0.692 0.488895
## id70 0.98218 1.41919 0.692 0.488895
## id71 0.99099 1.41929 0.698 0.485032
## id72 0.99979 1.41938 0.704 0.481194
## id73 1.00198 1.41940 0.706 0.480238
## id74 1.02606 1.41967 0.723 0.469834
## id75 1.02606 1.41967 0.723 0.469834
## id76 1.03696 1.41979 0.730 0.465169
## id77 1.03913 1.41981 0.732 0.464241
## id78 1.05649 1.42001 0.744 0.456873
## id79 1.06514 1.42011 0.750 0.453227
## id80 1.07162 1.42018 0.755 0.450510
## id81 1.07378 1.42021 0.756 0.449607
## id82 1.09740 1.42048 0.773 0.439784
## id83 1.09955 1.42051 0.774 0.438901
## id84 1.10596 1.42058 0.779 0.436260
## id85 1.10809 1.42061 0.780 0.435383
## id86 1.10809 1.42061 0.780 0.435383
## id87 1.11875 1.42074 0.787 0.431022
## id88 1.12725 1.42084 0.793 0.427562
## id89 1.13997 1.42100 0.802 0.422419
## id90 1.15264 1.42115 0.811 0.417333
## id91 1.15685 1.42121 0.814 0.415651
## id92 1.16526 1.42131 0.820 0.412305
## id93 1.16526 1.42131 0.820 0.412305
## id94 1.16945 1.42137 0.823 0.410641
## id95 1.16945 1.42137 0.823 0.410641
## id96 1.17155 1.42139 0.824 0.409811
## id97 1.17783 1.42147 0.829 0.407333
## id98 1.17992 1.42150 0.830 0.406510
## id99 1.18827 1.42161 0.836 0.403233
## id100 1.19867 1.42174 0.843 0.399172
## id101 1.20075 1.42177 0.845 0.398365
## id102 1.21731 1.42199 0.856 0.391962
## id103 1.22762 1.42212 0.863 0.388010
## id104 1.22762 1.42212 0.863 0.388010
## id105 1.23173 1.42218 0.866 0.386440
## id106 1.25426 1.42248 0.882 0.377918
## id107 1.25630 1.42251 0.883 0.377152
## id108 1.25833 1.42254 0.885 0.376388
## id109 1.25833 1.42254 0.885 0.376388
## id110 1.26444 1.42262 0.889 0.374106
## id111 1.26444 1.42262 0.889 0.374106
## id112 1.26444 1.42262 0.889 0.374106
## id113 1.26850 1.42268 0.892 0.372591
## id114 1.27053 1.42270 0.893 0.371837
## id115 1.27053 1.42270 0.893 0.371837
## id116 1.28469 1.42290 0.903 0.366596
## id117 1.29878 1.42310 0.913 0.361429
## id118 1.30480 1.42318 0.917 0.359238
## id119 1.30680 1.42321 0.918 0.358510
## id120 1.30680 1.42321 0.918 0.358510
## id121 1.31280 1.42330 0.922 0.356337
## id122 1.32476 1.42347 0.931 0.352030
## id123 1.32874 1.42353 0.933 0.350607
## id124 1.33667 1.42364 0.939 0.347778
## id125 1.33865 1.42367 0.940 0.347074
## id126 1.33865 1.42367 0.940 0.347074
## id127 1.34655 1.42378 0.946 0.344274
## id128 1.35835 1.42396 0.954 0.340119
## id129 1.36032 1.42399 0.955 0.339432
## id130 1.36424 1.42404 0.958 0.338062
## id131 1.37401 1.42419 0.965 0.334661
## id132 1.37791 1.42425 0.967 0.333311
## id133 1.37986 1.42428 0.969 0.332639
## id134 1.38569 1.42436 0.973 0.330629
## id135 1.38763 1.42439 0.974 0.329962
## id136 1.38957 1.42442 0.976 0.329296
## id137 1.40117 1.42460 0.984 0.325333
## id138 1.40310 1.42463 0.985 0.324678
## id139 1.40695 1.42468 0.988 0.323371
## id140 1.41080 1.42474 0.990 0.322070
## id141 1.41080 1.42474 0.990 0.322070
## id142 1.41847 1.42486 0.996 0.319485
## id143 1.41847 1.42486 0.996 0.319485
## id144 1.42039 1.42489 0.997 0.318842
## id145 1.42421 1.42495 0.999 0.317561
## id146 1.42803 1.42501 1.002 0.316286
## id147 1.42993 1.42504 1.003 0.315650
## id148 1.44134 1.42521 1.011 0.311866
## id149 1.46022 1.42551 1.024 0.305670
## id150 1.46210 1.42554 1.026 0.305058
## id151 1.46960 1.42565 1.031 0.302623
## id152 1.47521 1.42574 1.035 0.300812
## id153 1.47521 1.42574 1.035 0.300812
## id154 1.47707 1.42577 1.036 0.300211
## id155 1.48452 1.42589 1.041 0.297820
## id156 1.48452 1.42589 1.041 0.297820
## id157 1.48638 1.42592 1.042 0.297226
## id158 1.49194 1.42601 1.046 0.295451
## id159 1.49565 1.42607 1.049 0.294275
## id160 1.51038 1.42630 1.059 0.289623
## id161 1.51222 1.42633 1.060 0.289047
## id162 1.51771 1.42642 1.064 0.287328
## id163 1.51954 1.42645 1.065 0.286758
## id164 1.52684 1.42657 1.070 0.284490
## id165 1.52684 1.42657 1.070 0.284490
## id166 1.52684 1.42657 1.070 0.284490
## id167 1.53048 1.42663 1.073 0.283364
## id168 1.53955 1.42678 1.079 0.280572
## id169 1.54135 1.42681 1.080 0.280017
## id170 1.54496 1.42687 1.083 0.278912
## id171 1.54677 1.42690 1.084 0.278361
## id172 1.55037 1.42696 1.086 0.277263
## id173 1.55755 1.42707 1.091 0.275083
## id174 1.55934 1.42710 1.093 0.274542
## id175 1.55934 1.42710 1.093 0.274542
## id176 1.56471 1.42719 1.096 0.272924
## id177 1.56649 1.42722 1.098 0.272387
## id178 1.57006 1.42728 1.100 0.271318
## id179 1.57539 1.42737 1.104 0.269723
## id180 1.58601 1.42755 1.111 0.266566
## id181 1.58777 1.42758 1.112 0.266045
## id182 1.58777 1.42758 1.112 0.266045
## id183 1.59130 1.42763 1.115 0.265005
## id184 1.59481 1.42769 1.117 0.263970
## id185 1.59657 1.42772 1.118 0.263455
## id186 1.59832 1.42775 1.119 0.262941
## id187 1.60182 1.42781 1.122 0.261916
## id188 1.60707 1.42790 1.125 0.260388
## id189 1.61750 1.42807 1.133 0.257364
## id190 1.61750 1.42807 1.133 0.257364
## id191 1.61923 1.42810 1.134 0.256864
## id192 1.62096 1.42813 1.135 0.256366
## id193 1.62269 1.42816 1.136 0.255869
## id194 1.62615 1.42822 1.139 0.254878
## id195 1.62787 1.42825 1.140 0.254384
## id196 1.63131 1.42831 1.142 0.253400
## id197 1.63131 1.42831 1.142 0.253400
## id198 1.63303 1.42834 1.143 0.252910
## id199 1.63475 1.42837 1.144 0.252421
## id200 1.63818 1.42843 1.147 0.251447
## id201 1.63989 1.42845 1.148 0.250961
## id202 1.64502 1.42854 1.152 0.249512
## id203 1.64672 1.42857 1.153 0.249031
## id204 1.64842 1.42860 1.154 0.248552
## id205 1.65013 1.42863 1.155 0.248074
## id206 1.65183 1.42866 1.156 0.247596
## id207 1.65522 1.42872 1.159 0.246645
## id208 1.65691 1.42875 1.160 0.246172
## id209 1.66536 1.42889 1.165 0.243820
## id210 1.67543 1.42906 1.172 0.241037
## id211 1.68877 1.42929 1.182 0.237388
## id212 1.69043 1.42932 1.183 0.236937
## id213 1.69704 1.42944 1.187 0.235144
## id214 1.69869 1.42947 1.188 0.234699
## id215 1.70199 1.42952 1.191 0.233811
## id216 1.70363 1.42955 1.192 0.233369
## id217 1.71672 1.42978 1.201 0.229871
## id218 1.72322 1.42989 1.205 0.228148
## id219 1.73453 1.43009 1.213 0.225174
## id220 1.73614 1.43012 1.214 0.224753
## id221 1.73935 1.43017 1.216 0.223915
## id222 1.74894 1.43034 1.223 0.221426
## id223 1.75053 1.43037 1.224 0.221015
## id224 1.75212 1.43040 1.225 0.220605
## id225 1.76162 1.43056 1.231 0.218166
## id226 1.76320 1.43059 1.232 0.217763
## id227 1.76320 1.43059 1.232 0.217763
## id228 1.76478 1.43062 1.234 0.217361
## id229 1.76792 1.43067 1.236 0.216560
## id230 1.77575 1.43081 1.241 0.214576
## id231 1.77575 1.43081 1.241 0.214576
## id232 1.77887 1.43086 1.243 0.213789
## id233 1.78043 1.43089 1.244 0.213397
## id234 1.78819 1.43103 1.250 0.211453
## id235 1.79436 1.43114 1.254 0.209915
## id236 1.79436 1.43114 1.254 0.209915
## id237 1.79590 1.43116 1.255 0.209533
## id238 1.79590 1.43116 1.255 0.209533
## id239 1.81270 1.43146 1.266 0.205395
## id240 1.83077 1.43178 1.279 0.201012
## id241 1.83822 1.43191 1.284 0.199226
## id242 1.84119 1.43196 1.286 0.198518
## id243 1.84267 1.43198 1.287 0.198165
## id244 1.84563 1.43204 1.289 0.197463
## id245 1.84710 1.43206 1.290 0.197113
## id246 1.84710 1.43206 1.290 0.197113
## id247 1.84858 1.43209 1.291 0.196764
## id248 1.85005 1.43211 1.292 0.196415
## id249 1.85445 1.43219 1.295 0.195376
## id250 1.85445 1.43219 1.295 0.195376
## id251 1.85884 1.43227 1.298 0.194346
## id252 1.85884 1.43227 1.298 0.194346
## id253 1.85884 1.43227 1.298 0.194346
## id254 1.85884 1.43227 1.298 0.194346
## id255 1.86030 1.43229 1.299 0.194004
## id256 1.86176 1.43232 1.300 0.193663
## id257 1.86176 1.43232 1.300 0.193663
## id258 1.86321 1.43234 1.301 0.193323
## id259 1.86321 1.43234 1.301 0.193323
## id260 1.87046 1.43247 1.306 0.191635
## id261 1.87190 1.43250 1.307 0.191301
## id262 1.87334 1.43252 1.308 0.190967
## id263 1.87478 1.43255 1.309 0.190634
## id264 1.87622 1.43257 1.310 0.190301
## id265 1.87622 1.43257 1.310 0.190301
## id266 1.88053 1.43265 1.313 0.189310
## id267 1.88196 1.43267 1.314 0.188981
## id268 1.88196 1.43267 1.314 0.188981
## id269 1.88624 1.43275 1.317 0.188000
## id270 1.88908 1.43280 1.318 0.187351
## id271 1.89192 1.43285 1.320 0.186704
## id272 1.89757 1.43294 1.324 0.185422
## id273 1.90739 1.43312 1.331 0.183209
## id274 1.91018 1.43316 1.333 0.182585
## id275 1.91157 1.43319 1.334 0.182274
## id276 1.91850 1.43331 1.339 0.180730
## id277 1.92125 1.43336 1.340 0.180119
## id278 1.92263 1.43338 1.341 0.179814
## id279 1.92263 1.43338 1.341 0.179814
## id280 1.92948 1.43350 1.346 0.178303
## id281 1.93221 1.43354 1.348 0.177704
## id282 1.93357 1.43357 1.349 0.177406
## id283 1.93357 1.43357 1.349 0.177406
## id284 1.93629 1.43361 1.351 0.176812
## id285 1.93900 1.43366 1.352 0.176221
## id286 1.93900 1.43366 1.352 0.176221
## id287 1.94305 1.43373 1.355 0.175341
## id288 1.94305 1.43373 1.355 0.175341
## id289 1.94708 1.43380 1.358 0.174467
## id290 1.95244 1.43389 1.362 0.173313
## id291 1.95776 1.43398 1.365 0.172172
## id292 1.96173 1.43405 1.368 0.171323
## id293 1.96437 1.43409 1.370 0.170761
## id294 1.96700 1.43414 1.372 0.170203
## id295 1.97093 1.43421 1.374 0.169370
## id296 1.97615 1.43429 1.378 0.168270
## id297 1.97615 1.43429 1.378 0.168270
## id298 1.97874 1.43434 1.380 0.167724
## id299 1.98133 1.43438 1.381 0.167182
## id300 1.98263 1.43440 1.382 0.166912
## id301 1.98778 1.43449 1.386 0.165838
## id302 1.99162 1.43455 1.388 0.165040
## id303 1.99290 1.43458 1.389 0.164776
## id304 1.99417 1.43460 1.390 0.164512
## id305 1.99544 1.43462 1.391 0.164249
## id306 1.99925 1.43468 1.394 0.163464
## id307 2.00052 1.43470 1.394 0.163203
## id308 2.00178 1.43472 1.395 0.162944
## id309 2.00431 1.43477 1.397 0.162427
## id310 2.00808 1.43483 1.400 0.161656
## id311 2.00933 1.43485 1.400 0.161401
## id312 2.01058 1.43487 1.401 0.161146
## id313 2.01058 1.43487 1.401 0.161146
## id314 2.01183 1.43489 1.402 0.160892
## id315 2.01308 1.43491 1.403 0.160639
## id316 2.01557 1.43495 1.405 0.160134
## id317 2.01681 1.43497 1.405 0.159882
## id318 2.01805 1.43499 1.406 0.159632
## id319 2.01929 1.43501 1.407 0.159382
## id320 2.02176 1.43505 1.409 0.158884
## id321 2.02299 1.43507 1.410 0.158636
## id322 2.02422 1.43509 1.411 0.158388
## id323 2.02545 1.43511 1.411 0.158142
## id324 2.02545 1.43511 1.411 0.158142
## id325 2.02912 1.43517 1.414 0.157406
## id326 2.03763 1.43531 1.420 0.155712
## id327 2.03884 1.43533 1.420 0.155472
## id328 2.04125 1.43537 1.422 0.154995
## id329 2.04486 1.43543 1.425 0.154285
## id330 2.04486 1.43543 1.425 0.154285
## id331 2.04725 1.43547 1.426 0.153814
## id332 2.05201 1.43554 1.429 0.152881
## id333 2.05438 1.43558 1.431 0.152418
## id334 2.05438 1.43558 1.431 0.152418
## id335 2.05675 1.43562 1.433 0.151957
## id336 2.05792 1.43564 1.433 0.151728
## id337 2.05910 1.43566 1.434 0.151499
## id338 2.06028 1.43568 1.435 0.151271
## id339 2.06496 1.43575 1.438 0.150365
## id340 2.06496 1.43575 1.438 0.150365
## id341 2.06612 1.43577 1.439 0.150140
## id342 2.06729 1.43579 1.440 0.149916
## id343 2.06729 1.43579 1.440 0.149916
## id344 2.06845 1.43581 1.441 0.149692
## id345 2.07077 1.43584 1.442 0.149246
## id346 2.07308 1.43588 1.444 0.148803
## id347 2.07654 1.43593 1.446 0.148142
## id348 2.07997 1.43599 1.448 0.147487
## id349 2.07997 1.43599 1.448 0.147487
## id350 2.08453 1.43606 1.452 0.146622
## id351 2.08680 1.43609 1.453 0.146193
## id352 2.08906 1.43613 1.455 0.145766
## id353 2.09019 1.43614 1.455 0.145554
## id354 2.09019 1.43614 1.455 0.145554
## id355 2.09019 1.43614 1.455 0.145554
## id356 2.09019 1.43614 1.455 0.145554
## id357 2.09019 1.43614 1.455 0.145554
## id358 2.09131 1.43616 1.456 0.145342
## id359 2.09131 1.43616 1.456 0.145342
## id360 2.09244 1.43618 1.457 0.145130
## id361 2.09468 1.43621 1.458 0.144709
## id362 2.09803 1.43626 1.461 0.144082
## id363 2.10358 1.43635 1.465 0.143048
## id364 2.10579 1.43638 1.466 0.142638
## id365 2.10689 1.43640 1.467 0.142434
## id366 2.11127 1.43646 1.470 0.141624
## id367 2.11236 1.43648 1.471 0.141423
## id368 2.11454 1.43651 1.472 0.141022
## id369 2.11563 1.43653 1.473 0.140822
## id370 2.11563 1.43653 1.473 0.140822
## id371 2.12103 1.43661 1.476 0.139832
## id372 2.12318 1.43664 1.478 0.139440
## id373 2.12532 1.43667 1.479 0.139050
## id374 2.12852 1.43672 1.482 0.138469
## id375 2.12852 1.43672 1.482 0.138469
## id376 2.13170 1.43676 1.484 0.137892
## id377 2.13276 1.43678 1.484 0.137701
## id378 2.13592 1.43682 1.487 0.137131
## id379 2.13907 1.43687 1.489 0.136566
## id380 2.13907 1.43687 1.489 0.136566
## id381 2.14324 1.43693 1.492 0.135819
## id382 2.14531 1.43696 1.493 0.135449
## id383 2.14738 1.43699 1.494 0.135081
## id384 2.14738 1.43699 1.494 0.135081
## id385 2.14738 1.43699 1.494 0.135081
## id386 2.15150 1.43705 1.497 0.134350
## id387 2.15150 1.43705 1.497 0.134350
## id388 2.15660 1.43712 1.501 0.133448
## id389 2.16266 1.43720 1.505 0.132382
## id390 2.16767 1.43727 1.508 0.131507
## id391 2.16867 1.43728 1.509 0.131333
## id392 2.16966 1.43730 1.510 0.131160
## id393 2.17065 1.43731 1.510 0.130987
## id394 2.17065 1.43731 1.510 0.130987
## id395 2.17065 1.43731 1.510 0.130987
## id396 2.17362 1.43735 1.512 0.130472
## id397 2.17755 1.43740 1.515 0.129792
## id398 2.17951 1.43743 1.516 0.129454
## id399 2.17951 1.43743 1.516 0.129454
## id400 2.18243 1.43747 1.518 0.128952
## id401 2.18437 1.43749 1.520 0.128619
## id402 2.18630 1.43752 1.521 0.128288
## id403 2.18919 1.43755 1.523 0.127795
## id404 2.18919 1.43755 1.523 0.127795
## id405 2.19869 1.43768 1.529 0.126181
## id406 2.20057 1.43770 1.531 0.125863
## id407 2.20895 1.43780 1.536 0.124455
## id408 2.21263 1.43785 1.539 0.123841
## id409 2.21263 1.43785 1.539 0.123841
## id410 2.21538 1.43788 1.541 0.123384
## id411 2.21538 1.43788 1.541 0.123384
## id412 2.21629 1.43789 1.541 0.123233
## id413 2.21901 1.43793 1.543 0.122782
## id414 2.21992 1.43794 1.544 0.122632
## id415 2.22082 1.43795 1.544 0.122483
## id416 2.22082 1.43795 1.544 0.122483
## id417 2.22262 1.43797 1.546 0.122185
## id418 2.22352 1.43798 1.546 0.122037
## id419 2.22975 1.43805 1.551 0.121012
## id420 2.22975 1.43805 1.551 0.121012
## id421 2.23152 1.43807 1.552 0.120723
## id422 2.23240 1.43808 1.552 0.120579
## id423 2.23328 1.43809 1.553 0.120436
## id424 2.23416 1.43810 1.554 0.120292
## id425 2.23679 1.43813 1.555 0.119865
## id426 2.23766 1.43814 1.556 0.119723
## id427 2.23766 1.43814 1.556 0.119723
## id428 2.23766 1.43814 1.556 0.119723
## id429 2.23766 1.43814 1.556 0.119723
## id430 2.24026 1.43817 1.558 0.119301
## id431 2.24285 1.43820 1.559 0.118882
## id432 2.24799 1.43826 1.563 0.118054
## id433 2.24884 1.43827 1.564 0.117917
## id434 2.25223 1.43830 1.566 0.117374
## id435 2.25475 1.43833 1.568 0.116971
## id436 2.25475 1.43833 1.568 0.116971
## id437 2.25475 1.43833 1.568 0.116971
## id438 2.25559 1.43834 1.568 0.116837
## id439 2.26796 1.43847 1.577 0.114875
## id440 2.26877 1.43847 1.577 0.114747
## id441 2.26959 1.43848 1.578 0.114620
## id442 2.26959 1.43848 1.578 0.114620
## id443 2.27039 1.43849 1.578 0.114492
## id444 2.27120 1.43850 1.579 0.114366
## id445 2.27201 1.43851 1.579 0.114239
## id446 2.27201 1.43851 1.579 0.114239
## id447 2.27522 1.43854 1.582 0.113736
## id448 2.27602 1.43854 1.582 0.113612
## id449 2.27761 1.43856 1.583 0.113363
## id450 2.28078 1.43859 1.585 0.112870
## id451 2.28078 1.43859 1.585 0.112870
## id452 2.28313 1.43861 1.587 0.112504
## id453 2.29243 1.43870 1.593 0.111069
## id454 2.29243 1.43870 1.593 0.111069
## id455 2.29243 1.43870 1.593 0.111069
## id456 2.29396 1.43871 1.594 0.110834
## id457 2.29396 1.43871 1.594 0.110834
## id458 2.29700 1.43874 1.597 0.110369
## id459 2.29926 1.43876 1.598 0.110024
## id460 2.30076 1.43877 1.599 0.109795
## id461 2.30226 1.43878 1.600 0.109567
## id462 2.30374 1.43879 1.601 0.109341
## id463 2.30744 1.43882 1.604 0.108780
## id464 2.30744 1.43882 1.604 0.108780
## id465 2.30891 1.43884 1.605 0.108558
## id466 2.30964 1.43884 1.605 0.108448
## id467 2.30964 1.43884 1.605 0.108448
## id468 2.31037 1.43885 1.606 0.108338
## id469 2.31037 1.43885 1.606 0.108338
## id470 2.31110 1.43885 1.606 0.108228
## id471 2.31110 1.43885 1.606 0.108228
## id472 2.31183 1.43886 1.607 0.108118
## id473 2.31328 1.43887 1.608 0.107900
## id474 2.31400 1.43888 1.608 0.107791
## id475 2.31760 1.43890 1.611 0.107252
## id476 2.31974 1.43892 1.612 0.106932
## id477 2.32257 1.43894 1.614 0.106509
## id478 2.32468 1.43896 1.616 0.106196
## id479 2.32608 1.43897 1.616 0.105988
## id480 2.32678 1.43897 1.617 0.105884
## id481 2.32678 1.43897 1.617 0.105884
## id482 2.32678 1.43897 1.617 0.105884
## id483 2.32817 1.43898 1.618 0.105678
## id484 2.33367 1.43902 1.622 0.104865
## id485 2.33639 1.43904 1.624 0.104466
## id486 2.33774 1.43905 1.625 0.104267
## id487 2.33774 1.43905 1.625 0.104267
## id488 2.33909 1.43905 1.625 0.104070
## id489 2.33909 1.43905 1.625 0.104070
## id490 2.34639 1.43910 1.630 0.103005
## id491 2.34835 1.43911 1.632 0.102720
## id492 2.34965 1.43912 1.633 0.102531
## id493 2.35030 1.43912 1.633 0.102437
## id494 2.35735 1.43916 1.638 0.101421
## id495 2.36175 1.43918 1.641 0.100790
## id496 2.36237 1.43918 1.641 0.100701
## id497 2.36423 1.43919 1.643 0.100435
## id498 2.36547 1.43920 1.644 0.100259
## id499 2.36853 1.43921 1.646 0.099822 .
## id500 2.36914 1.43921 1.646 0.099736 .
## id501 2.36914 1.43921 1.646 0.099736 .
## id502 2.37036 1.43922 1.647 0.099564 .
## id503 2.37397 1.43923 1.649 0.099052 .
## id504 2.37397 1.43923 1.649 0.099052 .
## id505 2.37635 1.43924 1.651 0.098716 .
## id506 2.37694 1.43924 1.652 0.098633 .
## id507 2.37753 1.43925 1.652 0.098550 .
## id508 2.37753 1.43925 1.652 0.098550 .
## id509 2.37812 1.43925 1.652 0.098467 .
## id510 2.38337 1.43927 1.656 0.097730 .
## id511 2.38567 1.43927 1.658 0.097408 .
## id512 2.38909 1.43928 1.660 0.096932 .
## id513 2.39078 1.43929 1.661 0.096697 .
## id514 2.39078 1.43929 1.661 0.096697 .
## id515 2.39246 1.43930 1.662 0.096464 .
## id516 2.39413 1.43930 1.663 0.096233 .
## id517 2.39633 1.43930 1.665 0.095927 .
## id518 2.39743 1.43931 1.666 0.095776 .
## id519 2.39743 1.43931 1.666 0.095776 .
## id520 2.39961 1.43931 1.667 0.095475 .
## id521 2.40069 1.43931 1.668 0.095327 .
## id522 2.40123 1.43932 1.668 0.095253 .
## id523 2.40123 1.43932 1.668 0.095253 .
## id524 2.40231 1.43932 1.669 0.095105 .
## id525 2.40551 1.43932 1.671 0.094667 .
## id526 2.40603 1.43932 1.672 0.094595 .
## id527 2.40761 1.43933 1.673 0.094379 .
## id528 2.40866 1.43933 1.673 0.094236 .
## id529 2.41332 1.43933 1.677 0.093603 .
## id530 2.41485 1.43933 1.678 0.093395 .
## id531 2.41637 1.43933 1.679 0.093188 .
## id532 2.41687 1.43933 1.679 0.093121 .
## id533 2.41738 1.43933 1.680 0.093053 .
## id534 2.42037 1.43934 1.682 0.092648 .
## id535 2.42087 1.43933 1.682 0.092579 .
## id536 2.42284 1.43934 1.683 0.092316 .
## id537 2.42382 1.43934 1.684 0.092184 .
## id538 2.42480 1.43934 1.685 0.092054 .
## id539 2.43197 1.43933 1.690 0.091095 .
## id540 2.43291 1.43933 1.690 0.090970 .
## id541 2.43524 1.43933 1.692 0.090660 .
## id542 2.43616 1.43931 1.693 0.090534 .
## id543 2.43662 1.43933 1.693 0.090477 .
## id544 2.43845 1.43932 1.694 0.090234 .
## id545 2.43890 1.43932 1.694 0.090174 .
## id546 2.43981 1.43932 1.695 0.090054 .
## id547 2.44026 1.43932 1.695 0.089995 .
## id548 2.44026 1.43932 1.695 0.089995 .
## id549 2.44116 1.43932 1.696 0.089876 .
## id550 2.44116 1.43932 1.696 0.089876 .
## id551 2.44340 1.43932 1.698 0.089581 .
## id552 2.44384 1.43931 1.698 0.089523 .
## id553 2.44516 1.43931 1.699 0.089349 .
## id554 2.45123 1.43930 1.703 0.088554 .
## id555 2.45502 1.43928 1.706 0.088060 .
## id556 2.45955 1.43927 1.709 0.087471 .
## id557 2.46037 1.43921 1.710 0.087354 .
## id558 2.46037 1.43927 1.709 0.087366 .
## id559 2.46238 1.43926 1.711 0.087106 .
## id560 2.46437 1.43925 1.712 0.086849 .
## id561 2.46476 1.43925 1.713 0.086798 .
## id562 2.46516 1.43925 1.713 0.086747 .
## id563 2.46750 1.43923 1.714 0.086445 .
## id564 2.46866 1.43923 1.715 0.086296 .
## id565 2.46905 1.43923 1.716 0.086247 .
## id566 2.47096 1.43922 1.717 0.086002 .
## id567 2.47209 1.43921 1.718 0.085856 .
## id568 2.47322 1.43911 1.719 0.085691 .
## id569 2.47360 1.43920 1.719 0.085664 .
## id570 2.47582 1.43919 1.720 0.085380 .
## id571 2.47765 1.43918 1.722 0.085147 .
## id572 2.47802 1.43918 1.722 0.085100 .
## id573 2.47802 1.43918 1.722 0.085100 .
## id574 2.47838 1.43918 1.722 0.085054 .
## id575 2.48018 1.43916 1.723 0.084825 .
## id576 2.48267 1.43915 1.725 0.084510 .
## id577 2.48442 1.43914 1.726 0.084289 .
## id578 2.48511 1.43913 1.727 0.084201 .
## id579 2.48546 1.43913 1.727 0.084157 .
## id580 2.48820 1.43911 1.729 0.083812 .
## id581 2.49022 1.43887 1.731 0.083509 .
## id582 2.49188 1.43908 1.732 0.083349 .
## id583 2.49188 1.43908 1.732 0.083349 .
## id584 2.49319 1.43907 1.733 0.083184 .
## id585 2.49514 1.43905 1.734 0.082940 .
## id586 2.49514 1.43905 1.734 0.082940 .
## id587 2.49642 1.43904 1.735 0.082780 .
## id588 2.49706 1.43904 1.735 0.082700 .
## id589 2.49801 1.43903 1.736 0.082582 .
## id590 2.49895 1.43902 1.737 0.082464 .
## id591 2.50654 1.43895 1.742 0.081521 .
## id592 2.51003 1.43830 1.745 0.080961 .
## id593 2.51257 1.43888 1.746 0.080777 .
## id594 2.51397 1.43799 1.748 0.080421 .
## id595 2.51936 1.43880 1.751 0.079945 .
## id596 2.51988 1.43880 1.751 0.079880 .
## id597 2.52221 1.43877 1.753 0.079596 .
## id598 2.52721 1.43870 1.757 0.078988 .
## id599 2.53713 1.43855 1.764 0.077788 .
## id600 2.54365 1.43845 1.768 0.077005 .
## program1 -0.01370 0.11704 -0.117 0.906828
## program2 -6.36844 0.69720 -9.134 < 2e-16 ***
## program2 NA NA NA NA
## achieve NA NA NA NA
## program2:achieve -0.13691 0.01327 -10.316 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for poisson family taken to be 1)
##
## Null deviance: 1318.3 on 1799 degrees of freedom
## Residual deviance: 1097.1 on 1197 degrees of freedom
## AIC: 3503.1
##
## Number of Fisher Scoring iterations: 7anova(logit.2slopes, logit.3slopes, test="LRT")## Analysis of Deviance Table
##
## Model 1: y ~ id + program + program2 * achieve
## Model 2: y ~ id + program + program * achieve
## Resid. Df Resid. Dev Df Deviance Pr(>Chi)
## 1 1197 1097.0
## 2 1196 1083.8 1 13.269 0.0002699 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Method II
This splits the data and just run logistic regression for binary responses
hsb.VG <- sample(hsb[(hsb$hsp != "2"),])
summary(VGmod <- glm(hsp ~ achieve,data=hsb.VG,family=binomial))##
## Call:
## glm(formula = hsp ~ achieve, family = binomial, data = hsb.VG)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.6987 -1.1165 -0.8186 1.1434 1.5398
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -2.96556 0.83419 -3.555 0.000378 ***
## achieve 0.06132 0.01717 3.572 0.000354 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 404.78 on 291 degrees of freedom
## Residual deviance: 391.29 on 290 degrees of freedom
## AIC: 395.29
##
## Number of Fisher Scoring iterations: 4anova(VGmod,test="LRT")## Analysis of Deviance Table
##
## Model: binomial, link: logit
##
## Response: hsp
##
## Terms added sequentially (first to last)
##
##
## Df Deviance Resid. Df Resid. Dev Pr(>Chi)
## NULL 291 404.78
## achieve 1 13.491 290 391.29 0.0002397 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1