Testing for inverse correlation in grouped data
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Christoph Ruehlemann
Jul 15, 2023, 8:03:59 AM7/15/23
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Hi All,
I have data on word frequencies (column `f_0`) in speech turns (`Turnid`), pupil sizes during these turns (`p_0`); the turns are grouped in terms of the number of words they contain (column `size`). I hypothesize that `f_0` and `p_0` are inversely correlated. How can I test this hypothesis?
My hunch is that a mixed-effects model is required to control for `size`which would perhaps best be considered a fixed effect) but am unsure as to how to run the test.
Help is much appreciated.
Chris
df <- structure(list(Turnid = c(2L, 2L, 2L, 7L, 7L, 7L, 8L, 8L, 8L,
8L, 8L, 8L, 8L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 10L, 10L, 10L, 10L,
10L, 15L, 15L, 15L, 15L, 15L, 16L, 16L, 16L, 16L, 16L, 16L, 16L,
35L, 35L, 35L, 35L, 35L, 36L, 36L, 36L, 38L, 38L, 38L, 41L, 41L,
41L, 46L, 46L, 46L, 46L, 46L, 46L, 46L, 47L, 47L, 47L, 52L, 52L,
52L, 52L, 52L, 55L, 55L, 55L, 56L, 56L, 56L, 56L, 56L, 60L, 60L,
60L, 61L, 61L, 61L, 62L, 62L, 62L, 64L, 64L, 64L, 74L, 74L, 74L,
74L, 74L, 74L, 74L, 77L, 77L, 77L, 77L, 77L, 77L, 77L, 78L, 78L,
78L, 78L, 78L, 79L, 79L, 79L, 79L, 79L, 83L, 83L, 83L, 83L, 83L,
83L, 83L, 84L, 84L, 84L, 84L, 84L, 84L, 84L, 87L, 87L, 87L, 89L,
89L, 89L, 89L, 89L, 90L, 90L, 90L, 92L, 92L, 92L, 95L, 95L, 95L,
96L, 96L, 96L, 96L, 96L, 96L, 96L, 98L, 98L, 98L, 99L, 99L, 99L,
99L, 99L, 101L, 101L, 101L, 102L, 102L, 102L, 103L, 103L, 103L,
105L, 105L, 105L, 111L, 111L, 111L, 119L, 119L, 119L, 122L, 122L,
122L, 122L, 122L, 125L, 125L, 125L, 125L, 125L, 132L, 132L, 132L,
132L, 132L, 132L, 132L, 134L, 134L, 134L, 134L, 134L, 137L, 137L,
137L), f_0 = c(0L, 0L, 0L, 0L, -305L, -302L, 0L, -4932L, -5898L,
-5969L, -4342L, -5412L, -5165L, 0L, -657L, 3517L, -693L, -813L,
-847L, -693L, 0L, -1660L, 6367L, -2160L, -2221L, 0L, -8534L,
-8077L, -7727L, -8113L, 0L, -7004L, -6211L, -8563L, -8077L, -7727L,
-8295L, 0L, 828L, -190L, -368L, -14L, 0L, 2713L, 2155L, 0L, 23L,
-5L, 0L, -7655L, -4982L, 0L, -693L, 1530L, -314L, 1402L, -467L,
1439L, 0L, 2845L, -938L, 0L, 2611L, -5044L, -2371L, -5730L, 0L,
-8624L, -7471L, 0L, 92L, -784L, 3609L, -576L, 0L, -54L, -170L,
0L, -7879L, -8572L, 0L, -4245L, -3472L, 0L, 3015L, -521L, 0L,
85L, 242L, 5823L, 37L, 23L, 1161L, 0L, 1340L, -141L, 1198L, 238L,
-342L, -336L, 0L, -1481L, -1679L, 2143L, -1681L, 0L, 839L, 1108L,
12L, 1041L, 0L, 1511L, -5L, 555L, 250L, -2L, -27L, 0L, -7095L,
-8547L, -8634L, -6625L, -2928L, -8558L, 0L, 2218L, -2327L, 0L,
-1082L, 711L, -993L, -1134L, 0L, 5928L, -95L, 0L, -575L, -1632L,
0L, 6998L, -1275L, 0L, -19L, 992L, 1L, 30L, 133L, 15L, 0L, -3472L,
-758L, 0L, -317L, -317L, -5684L, -4179L, 0L, 696L, 2914L, 0L,
-3645L, -3823L, 0L, 103L, -50L, 0L, -574L, -1178L, 0L, 172L,
-3598L, 0L, 6023L, 1681L, 0L, -5982L, -4139L, -3695L, -2159L,
0L, -7996L, -6618L, -7527L, -8635L, 0L, 799L, 8415L, -54L, 86L,
987L, -217L, 0L, 1468L, 3686L, -645L, -687L, 0L, 0L, 0L), pp_0 = c(0,
-10.2489999999999, -76.742, 0, -84.3345, -52.9315, 0, -86.1054999999999,
-202.575, -345.8325, -365.4495, -111.11, -283.1155, 0, -74.1494999999999,
113.13, -24.8049999999998, -226.261, -150.2925, -65.6869999999999,
0, 211.1485, 283.7575, 293.5085, 298.5055, 0, -3.16000000000008,
-20.6205, -26.8615000000001, -23.2415000000001, 0, -24.9465,
-11.634, 28.2910000000001, -12.6045, 16.0475, 9.73900000000003,
0, -512.149, 160.531, 193.6885, 100.648, 0, 43.2165, 27.6395,
0, -60.3140000000001, -48.638, 0, -144.267, -86.039, 0, 0.774499999999989,
-6.91149999999993, 11.1030000000001, -242.4975, -1032.6445, 11.5074999999999,
0, 83.5169999999999, -323.5835, 0, 154.5645, 185.205, 195.114,
138.33, 0, -28.8835000000001, -77.9325000000001, 0, 6.3195, 23.904,
38.377, 48.04, 0, 68.8395, -26.1135, 0, 89.5195, 255.0685, 0,
-43.836, 19.4335, 0, 1.16800000000001, -485.191, 0, 481.2175,
388.632, 388.112, 401.2195, 399.2115, 419.231, 0, 463.162, 526.033,
430.1505, 446.2375, 492.2975, 513.056, 0, 56.345, 113.49, 113.5155,
13.1170000000001, 0, 77.8774999999999, -161.1495, -146.4085,
-42.6850000000001, 0, -11.521, -3.27750000000003, 55.6655000000001,
175.6055, 251.2075, 297.9085, 0, 57.3505, 100.587, -46.7595,
70.2015, -47.6215, -56.2139999999999, 0, -174.103, -144.221,
0, 27.5314999999999, 73.886, 45.2545, 91.1875, 0, -173.5105,
-227.9105, 0, 9.3195, -8.06299999999999, 0, -553.3095, 8.58849999999995,
0, -128.128, -159.1975, -15.4515, 52.7515, 10.034, 14.779, 0,
14.4200000000001, 52.1495, 0, 189.742166666667, -413.083833333333,
320.036666666667, 392.994166666667, 0, -11.6709999999998, 36.393,
0, -40.0230000000001, -14.4065, 0, -69.534, -79.6719999999999,
0, -38.3870000000001, 13.0965, 0, -2.3694999999999, -30.6329999999999,
0, -1.24400000000003, -24.101, 0, -471.8995, -61.6135000000002,
-2.09300000000007, -41.8605, 0, 388.6835, 365.561, 321.0135,
300.5315, 0, 11.213, -36.5010000000001, -103.36, -158.2555, -192.485,
-172.593, 0, -411.262, -48.3770000000001, -41.6995000000001,
-40.2965, 0, 140.4955, 139.6195), size = c(3L, 3L, 3L, 3L, 3L,
3L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 5L,
5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 7L, 7L, 7L, 7L, 7L, 7L, 7L,
5L, 5L, 5L, 5L, 5L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 7L, 7L,
7L, 7L, 7L, 7L, 7L, 3L, 3L, 3L, 5L, 5L, 5L, 5L, 5L, 3L, 3L, 3L,
5L, 5L, 5L, 5L, 5L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L,
3L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 5L,
5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 7L, 7L, 7L, 7L, 7L, 7L, 7L,
7L, 7L, 7L, 7L, 7L, 7L, 7L, 3L, 3L, 3L, 5L, 5L, 5L, 5L, 5L, 3L,
3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 3L,
3L, 3L, 5L, 5L, 5L, 5L, 5L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L,
3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 5L, 5L, 5L, 5L, 5L, 5L, 5L,
5L, 5L, 5L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 5L, 5L, 5L, 5L, 5L, 3L,
3L, 3L)), row.names = c(NA, -199L), class = c("tbl_df", "tbl",
"data.frame"))
--
Albert-Ludwigs-Universität Freiburg
Projekt-Leiter DFG-Forschungsprojekt "Multimodale Turn-Abschlusssignale"
ἰχθύς
Christoph Ruehlemann
Jul 15, 2023, 8:20:15 AM7/15/23
to statforli...@googlegroups.com
Hi All,
Here's my question again in **edited** form:
I have data on word frequencies (column f_0) in speech turns (Turnid), pupil sizes during these turns (pp_0); the turns are grouped in terms of number of words they contain (column size). I hypothesize that f_0 and pp_0 are inversely correlated. How can I test this hypothesis?
My hunch is that a mixed-effects model is required to control for size (which would perhaps best be considered a fixed effect) but am unsure as to how to run the test.
EDIT:
Is this the right way to go?
library(lme4)
# Fit the mixed-effects model
model <- lmer(pp_0 ~ f_0 + Turnid +(1 | size), data = F_PP)
Warning message:
Some predictor variables are on very different scales: consider rescaling
If this is the right way to define the model, what does the summary output (for my actual data, not just the data in df) mean? How can it be interpreted? Does it support the hypothesis?
# Check the model summary
summary(model)
Linear mixed model fit by REML ['lmerMod']
Formula: pp_0 ~ f_0 + Turnid + (1 | size)
Data: F_PP
REML criterion at convergence: 2453971
Scaled residuals:
Min 1Q Median 3Q Max
-20.5629 -0.1791 -0.0117 0.1804 21.3419
Random effects:
Groups Name Variance Std.Dev.
size (Intercept) 273.2 16.53
Residual 194249.0 440.74
Number of obs: 163432, groups: size, 23
Fixed effects:
Estimate Std. Error t value
(Intercept) 12.2150152 4.1253068 2.961
f_0 0.0013172 0.0003139 4.196
Turnid -0.0003027 0.0002107 -1.437
Correlation of Fixed Effects:
(Intr) f_0
f_0 0.116
Turnid -0.465 -0.052
fit warnings:
Some predictor variables are on very different scales: consider rescaling
Data:
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