Failed to contrast intercepts through emmeans in R - r

Question

I would like to test the simetry in the response of an observer to a contrast stimuli with different polarity, positive (white) and negative (black). I took the reaction time (RT) as dependent variable, along four different contrasts. It is known that the response time follows a Pieron curve whose asymptotas are placed (1) at observer threshold (Inf) and (2) at a base RT placed somewere between 250 and 450 msec.
The knowledge allows us to linearize the relationship transforming the independent variable (effective contrast EC) as 1/EC^2 (tEC), so the equation linking RT to EC becomes:
RT = m * tEC + RT0
To test the symmetry I established the criteria: same slope and same intercept in the two polarities implies symmetry.
To obtain the coefficients I made a linear model with interaction (coding trough a dummy variable for Polarity: Positive or Negative). The output of lm is clear to me, but some colegues prefer somthing more similar to an ANOVA output. So I decided to use emmeans to make the contrasts. With the slope is all right, but when computing the interceps starts the problem. The intercepts computed by lm are very different from the output of emmeans, and the conclusions are also different. In what follows I reproduce the example.
The question is two fold: It is possible to use emmeans to solve my problem? If not, it is possible to make the contrasts through other packages (which one)?
Data
RT1000
EC
tEC
Polarity
596.3564
-25
0.001600
Negative
648.2471
-20
0.002500
Negative
770.7602
-17
0.003460
Negative
831.2971
-15
0.004444
Negative
1311.3331
15
0.004444
Positive
1173.8942
17
0.003460
Positive
1113.7240
20
0.002500
Positive
869.3635
25
0.001600
Positive
Code
# Model
model <- lm(RT1000 ~ tEC * Polarity, data = Data)
# emmeans
library(emmeans)
# Slopes
m.slopes <- lstrends(model, "Polarity", var="tEC")
# Intercepts
m.intercept <- lsmeans(model, "Polarity")
# Contrasts
pairs(m.slopes)
pairs(m.intercept)
Outputs
Modelo
term
estimate
std.error
statistic
p.value
(Intercept)
449.948
66.829
6.733
0.003
tEC
87205.179
20992.976
4.154
0.014
PolarityPositive
230.946
94.511
2.444
0.071
tEC:PolarityPositive
58133.172
29688.551
1.958
0.122
Slopes (it is all right)
Polarity
tEC.trend
SE
df
lower.CL
upper.CL
Negative
87205.18
20992.98
4
28919.33
145491.0
Positive
145338.35
20992.98
4
87052.51
203624.2
contrast
estimate
SE
df
t.ratio
p.value
Negative - Positive
-58133.17
29688.55
4
-1.958101
0.12182
Intercepts (problem)
Polarity
lsmean
SE
df
lower.CL
upper.CL
Negative
711.6652
22.2867
4
649.7874
773.543
Positive
1117.0787
22.2867
4
1055.2009
1178.957
contrast
estimate
SE
df
t.ratio
p.value
Negative - Positive
-405.4135
31.51816
4
-12.86285
0.000211
Computed intercepts through emmeans differs from the ones computed by lm. I think the problem is that the model is not defined for EC = 0. But I'm not sure.

Answer 1

What you are calling the intercepts are not; they are the model predictions at the mean value of tEC. If you want the intercepts, use instead:
m.intercept <- lsmeans(model, "Polarity", at = list(tEC = 0))
You can tell what reference levels are being used via
ref_grid(model) # or str(m.intercept)
Please note that the model fitted here consists of two lines with different slopes; hence the difference between the predictions changes depending on the value of tEC. Thus, I would strongly recommend against testing the comparison of the intercepts; those are predictions at a tEC value that, as you say, can't even occur. Instead, try to be less of a mathematician and do the comparisons at a few representative values of tEC, e.g.,
LSMs <- lsmeans(model, "Polarity", at = list(tEC = c(0.001, 0.003, 0.005)))
pairs(LSMs, by = tEC)
You can also easily visualize the fitted lines:
emmip(model, Polarity ~ tEC, cov.reduce = range)