Reducing two mixed models into one

Dear Jo?o,

Thank you for your clarification. You made two changes in your code
that I wanted to check with you.

First, you rescaled the outcome from -1/RT to -1000/RT. I wonder in
what way that improved the model?

Second, instead of blmer(), you used lmer() but your lmer() random
effects matrix is singular which makes me think if the correlation
(~0.95) estimated by lmer() is as dependable/reliable?

Thanks,
Tim M

On Tue, Jun 13, 2023 at 12:01?PM Jo?o Ver?ssimo<jl.verissimo at gmail.com>  wrote:

Hi Timothy,

The formula I've suggested before is identical to the first parametrization in Thierry's answer, i.e., writing "item_num / Condition" is the same as writing "item_num + item_num:Condition".
That parametrization gives you estimates for the Condition slopes separately for each level of item_num. So the correlation between the corresponding by-subject random slopes is (I believe) what you want:

d <- read.csv("https://raw.githubusercontent.com/fpqq/w/main/d3.csv")
model_1 <- lmer(I(-1000/RT) ~ item_num / Condition + (item_num / Condition|Subject) + (item_num / Condition|Item), data = d)
re.corrs <- attr(VarCorr(model_1)$Subject, "correlation")
re.corrs["item_numEven:Conditionunrelated", "item_numOdd:Conditionunrelated"]

[1] 0.9499885


Jo?o

On 13/06/2023 18:36, Timothy MacKenzie wrote:

Dear Thierry,

Thank you so much for your highly informative answer. If I may, I
wanted to ask a follow-up question.

Previously, from the two separate models, I used to compute a
correlation (0.849635) between the random slopes of subjects in
'Condition==unrelated' for Odd vs. Even items (shown below).

**Question: Could we obtain the latent equivalent of the above
correlation (which may not be numerically the same as 0.849635) from
`attr(VarCorr(First_Parametrization_Model)$Subject, "correlation")`?

Thank you so much again,
Tim M

ranef_model_2_even = data.frame(ranef(model_2)$Subject)
ranef_model_2_even$Subject <- row.names(ranef_model_2_even)
ranef_model_3_odd = data.frame(ranef(model_3)$Subject)
ranef_model_3_odd$Subject <- row.names(ranef_model_3_odd)

Subject = merge(ranef_model_2_even, ranef_model_3_odd, by = "Subject",
suffixes = c("_even", "_odd"))
cor(Subject$Conditionunrelated_even, Subject $Conditionunrelated_odd)
#  [1] 0.849635





On Mon, Jun 12, 2023 at 1:36?AM Thierry Onkelinx
<thierry.onkelinx at inbo.be>  wrote:

Dear Timothy,

Add the interaction with item_num to every parameter and you should have the same parameterization for both models in a single model.

# gives similar parameters as both models
I(-1/RT) ~ item_num + item_num:Condition + (item_num + item_num:Condition|Subject) + (item_num + item_num:Condition|Item)
# same model fit, different parametrization
I(-1/RT) ~ item_num*Condition + (item_num*Condition|Subject) + (item_num*Condition|Item)

Best regards,

ir. Thierry Onkelinx
Statisticus / Statistician

Vlaamse Overheid / Government of Flanders
INSTITUUT VOOR NATUUR- EN BOSONDERZOEK / RESEARCH INSTITUTE FOR NATURE AND FOREST
Team Biometrie & Kwaliteitszorg / Team Biometrics & Quality Assurance
thierry.onkelinx at inbo.be
Havenlaan 88 bus 73, 1000 Brussel
www.inbo.be

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Op za 10 jun 2023 om 19:06 schreef Timothy MacKenzie<fswfswt at gmail.com>:

Hello All,

I'm hoping to clarify my prior post to elicit an informative response
from the experts on the list.

Currently, I'm running two models each using a subset of my data (below).

<Question>: Instead of running two separate models, is it possible to
create one model that captures both these separate models?

Thank you,
Tim M
################
d = read.csv("https://raw.githubusercontent.com/fpqq/w/main/d3.csv")
library(optimx)
library(blme)

# Subset 1:
model_2 = blmer(I(-1/RT) ~ Condition + (Condition|Subject) + (Condition|Item),
data = d, control=lmerControl(optimizer="optimx",optCtrl=list(method="nlminb")),
            subset = item_num == "Even")

# Subset 2:
model_3 = blmer(I(-1/RT) ~ Condition + (Condition|Subject) + (Condition|Item),
data = d, control=lmerControl(optimizer="optimx",optCtrl=list(method="nlminb")),
              subset = item_num == "Odd")