Question on contr.equalprior function

[GiselaGovaart]

I have some questions regarding the contr.equalprior function, see the reprex below.

I run two brms models, m1 uses contr.equalprior and m2 uses contr.equalprior_pairs.

Question 1:
What is the exact difference between contr.equalprior_pairs and contr.equalprior, and based on which criteria should I choose one or the other? Both contr.equalprior and contr.equalprior_pairs give me equal priors - just with different values. However, these different values also mean that the BFs are different, so the choice seems important.

Question 2:

• A: For the custom contrasts combining Group and TestSpeaker: For both models, contrast 2,3 and 4 have similar priors. The first and last contrasts, however, have different priors. I think this is because for the first contrast we compare participants in two different Groups with two different TestSpeakers, whereas for contrast 2,3,4, only TestSpeaker differs and Group is the same. And for the last contrast, we look at a difference between two contrasts.\n
  My intuition is that it is completely fine that the priors on the contrasts differ, as long as I don't start comparing contrasts with different priors. In other words, I can test ((unfam2-unfam3)-(fam2-fam3)) and ((unfam2-unfam3)-(unfam1-unfam2), but I can't compare ((unfam2-unfam3)-(unfam2-fam1)) because these two contrast comparisons have different priors.
• B: The same hold for the custom contrasts with the sleepState factor: the priors are not the same, but I find that intuitive: for the first two contrasts, I combine two of the levels, whereas for the 3rd contrast, I only compare two separate levels. Thus, I assume that I can compare contrasts 1 and 2, but I can't compare contrast 1 and 3 or 2 and 3?

In summary, my question: is it okay that the priors for different contrasts are different, if that is caused my the fact that for these contrasts I am comparing different combinations of levels of my factors, and as long as I don't compare contrasts that have different priors? And if not, is there a way to force the priors to be the same for an entire custom contrast matrix?

Question 3
I have two additional questions:

• In the output of emmeans(), I always get the warning: NOTE: Results may be misleading due to involvement in interactions. Is this a problem for the contrasts I am comparing?
• The posterior distribution for the BF for model 2 has some weird bumps - do you know why they are there and whether it's a problem?

library(emmeans)
library(easystats)
#> # Attaching packages: easystats 0.7.0 (red = needs update)
#> ✖ bayestestR  0.13.1   ✔ correlation 0.8.4 
#> ✔ datawizard  0.9.1    ✔ effectsize  0.8.6 
#> ✔ insight     0.19.8   ✖ modelbased  0.8.6 
#> ✖ performance 0.10.8   ✖ parameters  0.21.4
#> ✔ report      0.5.8    ✖ see         0.8.1 
#> 
#> Restart the R-Session and update packages with `easystats::easystats_update()`.
library(brms)
#> Loading required package: Rcpp
#> Loading 'brms' package (version 2.18.0). Useful instructions
#> can be found by typing help('brms'). A more detailed introduction
#> to the package is available through vignette('brms_overview').
#> 
#> Attaching package: 'brms'
#> The following object is masked from 'package:stats':
#> 
#>     ar
library(tidyverse)
library(here)
#> here() starts at /private/var/folders/6h/zb056tz154712qv0hdv29h5w0000gn/T/RtmpzysS7l/reprex-339b529ac418-dopey-nyala
library(see)

# set-up:
project_seed = 2049
set.seed(project_seed) 

# Make df, with 12 subjects, with:
# Group (between subj factor): levels "fam" and "unfam"
# TestSpeaker (within): levels 1,2,3
# sleepState (between): levels awake, activesleep, quietsleep
# MMR: dependent variable
df = structure(list(Subj = structure(c(1L, 1L, 1L, 2L, 2L, 2L, 3L, 
                                       3L, 3L, 4L, 4L, 4L, 5L, 5L, 5L, 6L, 6L, 6L, 7L, 7L, 7L, 8L, 8L, 
                                       8L, 9L, 9L, 9L, 10L, 10L, 10L, 11L, 11L, 11L, 12L, 12L, 12L), 
                                     levels = c("Subj01","Subj02", "Subj03", "Subj04", "Subj05", "Subj06", 
                                                "Subj07", "Subj08","Subj09", "Subj10", "Subj11", "Subj12"), 
                                     class = "factor"),
                    Group = structure(c(1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
                                        1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 
                                        2L, 2L, 2L), levels = c("fam", "unfam"), class = "factor"), 
                    TestSpeaker = structure(c(1L, 2L, 3L, 1L, 2L, 3L, 1L, 2L, 3L, 1L, 2L, 3L, 1L, 2L, 3L, 1L, 2L, 
                                              3L, 1L, 2L, 3L, 1L, 2L, 3L, 1L, 2L, 3L, 1L, 2L, 3L, 1L, 2L, 3L, 
                                              1L, 2L, 3L), levels = c("1", "2", "3"), class = "factor"),
                    MMR = c(38.3193739833394,-26.3345733319488, -36.5391489690257, 17.6727210461579, 13.0723969801114, 
                            -4.24116674572545, 21.2481968372323, 11.4709975141478, 1.82856457361663, 
                            43.7294164718069, 20.3131479540544, 0.785675781481198, -2.15902787287105, 
                            -25.4903371611785, 61.873025266565, 9.06733331354276, -18.7574284113092, 
                            6.33216574768327, -34.9097027199614, -3.96327639212982, 15.9747552016853, 
                            -38.801070417319, -6.46518128748102, -22.630432474398, 21.9291933267653, 
                            24.4946719999554, -31.2847387815119, -8.04032285881707, 14.2321054924562, 
                            8.80183458992482, 18.9550435474235, 33.2621031208136, -11.4198082197363, 
                            -14.7150081652997, 29.2510483128696, -31.1494998323233), 
                    sleepState = structure(c(2L,2L, 2L, 3L, 3L, 3L, 2L, 2L, 2L, 2L, 2L, 2L, 3L, 3L, 3L, 1L, 1L, 
                                             1L, 1L, 1L, 1L, 1L, 1L, 1L, 3L, 3L, 3L, 1L, 1L, 1L, 2L, 2L, 2L, 
                                             1L, 1L, 1L), levels = c("awake", "activesleep", "quietsleep"), class = "factor")),
               row.names = c(NA,-36L), class = c("tbl_df", "tbl", "data.frame"))

### MODEL 1: With  contr.equalprior set globally
options(contrasts = c("contr.equalprior", "contr.poly"))

m1 = brm(MMR ~ 1 + TestSpeaker * Group +
        sleepState * TestSpeaker +
        (1 + TestSpeaker * Group | Subj),
      data = df,
      family = gaussian(),
      prior = c(set_prior("normal(5.97, 23.34)",
                          class = "Intercept"),
                set_prior("normal(0, 23.34)",
                          class = "b"),
                set_prior("normal(0, 23.34)",
                          class = "sigma")),
      init = "random",
      control = list(
        adapt_delta = .99,
        max_treedepth = 15
      ),
      chains = 4,
      iter = 4000,
      warmup = 2000,
      thin = 1,
      algorithm = "sampling",
      cores = 4,
      seed = project_seed,
      save_pars = save_pars(all = TRUE)
)
#> Compiling Stan program...
#> Start sampling
#> Warning: There were 31 divergent transitions after warmup. See
#> https://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
#> to find out why this is a problem and how to eliminate them.
#> Warning: There were 2 chains where the estimated Bayesian Fraction of Missing Information was low. See
#> https://mc-stan.org/misc/warnings.html#bfmi-low
#> Warning: Examine the pairs() plot to diagnose sampling problems
#> Warning: Bulk Effective Samples Size (ESS) is too low, indicating posterior means and medians may be unreliable.
#> Running the chains for more iterations may help. See
#> https://mc-stan.org/misc/warnings.html#bulk-ess
#> Warning: Tail Effective Samples Size (ESS) is too low, indicating posterior variances and tail quantiles may be unreliable.
#> Running the chains for more iterations may help. See
#> https://mc-stan.org/misc/warnings.html#tail-ess

### MODEL 2: With  contr.equalprior_pairs set globally
options(contrasts = c("contr.equalprior_pairs", "contr.poly"))
m2 = brm(MMR ~ 1 + TestSpeaker * Group +
        sleepState * TestSpeaker +
        (1 + TestSpeaker * Group | Subj),
      data = df,
      family = gaussian(),
      prior = c(set_prior("normal(5.97, 23.34)",
                          class = "Intercept"),
                set_prior("normal(0, 23.34)",
                          class = "b"),
                set_prior("normal(0, 23.34)",
                          class = "sigma")),
      init = "random",
      control = list(
        adapt_delta = .99,
        max_treedepth = 15
      ),
      chains = 4,
      iter = 4000,
      warmup = 2000,
      thin = 1,
      algorithm = "sampling",
      cores = 4,
      seed = project_seed,
      save_pars = save_pars(all = TRUE)
  )
#> Compiling Stan program...
#> recompiling to avoid crashing R session
#> Start sampling
#> Warning: There were 52 divergent transitions after warmup. See
#> https://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
#> to find out why this is a problem and how to eliminate them.
#> Warning: There were 1 chains where the estimated Bayesian Fraction of Missing Information was low. See
#> https://mc-stan.org/misc/warnings.html#bfmi-low
#> Warning: Examine the pairs() plot to diagnose sampling problems
#> Warning: Bulk Effective Samples Size (ESS) is too low, indicating posterior means and medians may be unreliable.
#> Running the chains for more iterations may help. See
#> https://mc-stan.org/misc/warnings.html#bulk-ess
#> Warning: Tail Effective Samples Size (ESS) is too low, indicating posterior variances and tail quantiles may be unreliable.
#> Running the chains for more iterations may help. See
#> https://mc-stan.org/misc/warnings.html#tail-ess


## Question 1 -------
# The contrast matrices are different:
contrasts(df$TestSpeaker) <- contr.equalprior_pairs
contrasts(df$TestSpeaker)
#>   [,1]       [,2]
#> 1  0.0  0.5773503
#> 2 -0.5 -0.2886751
#> 3  0.5 -0.2886751
contrasts(df$TestSpeaker) <- contr.equalprior
contrasts(df$TestSpeaker)
#>         [,1]       [,2]
#> 1  0.0000000  0.8164966
#> 2 -0.7071068 -0.4082483
#> 3  0.7071068 -0.4082483

# Both contr.equalprior and contr.equalprior_pairs give me equal priors:
m_prior <- unupdate(m1, verbose=FALSE) # sample priors from model
m_prior_pairwise <-
  m_prior %>%
  emmeans(~ TestSpeaker)  %>%
  pairs()
#> NOTE: Results may be misleading due to involvement in interactions
# Priors for m1:
point_estimate(m_prior_pairwise, centr = "mean", disp = TRUE)
#> Point Estimate
#> 
#> Parameter                   | Mean |    SD
#> ------------------------------------------
#> TestSpeaker1 - TestSpeaker2 | 0.04 | 33.19
#> TestSpeaker1 - TestSpeaker3 | 0.24 | 33.47
#> TestSpeaker2 - TestSpeaker3 | 0.19 | 33.63

m_prior <- unupdate(m2, verbose=FALSE) # sample priors from model
m_prior_pairwise <-
  m_prior %>%
  emmeans(~ TestSpeaker)  %>%
  pairs()
#> NOTE: Results may be misleading due to involvement in interactions
# Priors for m2:
point_estimate(m_prior_pairwise, centr = "mean", disp = TRUE)
#> Point Estimate
#> 
#> Parameter                   |  Mean |    SD
#> -------------------------------------------
#> TestSpeaker1 - TestSpeaker2 |  0.11 | 23.58
#> TestSpeaker1 - TestSpeaker3 | -0.20 | 23.52
#> TestSpeaker2 - TestSpeaker3 | -0.32 | 23.01


## Question 2 --------
### Question 2A
# I compare some pairs of the interaction between TestSpeaker*Group. 
# create a custom contrast matrix:
MMR.emm1 = m2 %>%
  emmeans(~ Group:TestSpeaker) 
MMR.emm1 # to set the custom contrast correctly
#>  Group TestSpeaker emmean lower.HPD upper.HPD
#>  fam   1           14.095     -2.11      30.3
#>  unfam 1            0.595    -17.94      19.2
#>  fam   2           -1.025    -19.72      15.8
#>  unfam 2           12.887     -5.88      31.2
#>  fam   3            3.345    -15.58      22.2
#>  unfam 3           -6.456    -25.13      12.3
#> 
#> Results are averaged over the levels of: sleepState 
#> Point estimate displayed: median 
#> HPD interval probability: 0.95

fam1 = c(1,0,0,0,0,0)
unfam1 = c(0,1,0,0,0,0)
fam2 = c(0,0,1,0,0,0)
unfam2 = c(0,0,0,1,0,0)
fam3 = c(0,0,0,0,1,0)
unfam3 = c(0,0,0,0,0,1)

custom_contrasts <- list(
  list("unfam2-fam1" = unfam2 - fam1),
  list("unfam2-unfam3" = unfam2 - unfam3),
  list("unfam1-unfam2" = unfam1 - unfam2),
  list("fam2-fam3" = fam2-fam3),
  list("((unfam2-unfam3)-(fam2-fam3))" = ((unfam2 - unfam3) - (fam2 - fam3)))
) 

# Compute the BF for these contrasts
# For m1:
#  comparison of prior distributions
m1_prior <- unupdate(m1, verbose=FALSE) # sample priors from model
m1_prior_pairs <-
  m1_prior %>%
  emmeans(~ Group:TestSpeaker)
m1_prior_pairs = contrast(m1_prior_pairs, method = custom_contrasts)
#  comparison of posterior distributions
m1_post_pairs <-
  m1 %>%
  emmeans(~ TestSpeaker:Group) 
m1_post_pairs = contrast(m1_post_pairs, method = custom_contrasts)
# Bayes Factors (Savage-Dickey density ratio)
BF_m1 <-
  m1_post_pairs %>%
  bf_parameters(prior = m1_prior_pairs) %>%
  arrange(log_BF) # sort according to BF
#> Warning: Bayes factors might not be precise.
#>   For precise Bayes factors, sampling at least 40,000 posterior samples is
#>   recommended.
BF_m1
#> Bayes Factor (Savage-Dickey density ratio)
#> 
#> Parameter                     |    BF
#> -------------------------------------
#> unfam1-unfam2                 | 0.376
#> unfam2-unfam3                 | 0.475
#> fam2-fam3                     | 0.528
#> unfam2-fam1                   | 0.551
#> ((unfam2-unfam3)-(fam2-fam3)) | 0.840
#> 
#> * Evidence Against The Null: 0
plot(BF_m1)

# For m2:
#  comparison of prior distributions
m2_prior <- unupdate(m2, verbose=FALSE) # sample priors from model
m2_prior_pairs <-
  m2_prior %>%
  emmeans(~ Group:TestSpeaker)
m2_prior_pairs = contrast(m2_prior_pairs, method = custom_contrasts)
#  comparison of posterior distributions
m2_post_pairs <-
  m2 %>%
  emmeans(~ TestSpeaker:Group) 
m2_post_pairs = contrast(m2_post_pairs, method = custom_contrasts)
# Bayes Factors (Savage-Dickey density ratio)
BF_m2 <-
  m2_post_pairs %>%
  bf_parameters(prior = m2_prior_pairs) %>%
  arrange(log_BF) # sort according to BF
#> Warning: Bayes factors might not be precise.
#>   For precise Bayes factors, sampling at least 40,000 posterior samples is
#>   recommended.
BF_m2
#> Bayes Factor (Savage-Dickey density ratio)
#> 
#> Parameter                     |    BF
#> -------------------------------------
#> unfam1-unfam2                 | 0.503
#> unfam2-unfam3                 | 0.555
#> fam2-fam3                     | 0.661
#> unfam2-fam1                   | 0.679
#> ((unfam2-unfam3)-(fam2-fam3)) |  1.26
#> 
#> * Evidence Against The Null: 0
plot(BF_m2)

# Check priors on the contrasts:
point_estimate(m1_prior_pairs, centr = "mean", disp = TRUE)
#> Point Estimate
#> 
#> Parameter                     |     Mean |    SD
#> ------------------------------------------------
#> unfam2-fam1                   |    -0.08 | 48.58
#> unfam2-unfam3                 |    -0.37 | 40.04
#> unfam1-unfam2                 |    -0.31 | 40.55
#> fam2-fam3                     |    -0.37 | 39.75
#> ((unfam2-unfam3)-(fam2-fam3)) | 2.22e-03 | 46.38
point_estimate(m2_prior_pairs, centr = "mean", disp = TRUE)
#> Point Estimate
#> 
#> Parameter                     |  Mean |    SD
#> ---------------------------------------------
#> unfam2-fam1                   |  0.61 | 33.97
#> unfam2-unfam3                 | -0.08 | 26.04
#> unfam1-unfam2                 | -0.01 | 26.27
#> fam2-fam3                     | -0.43 | 25.77
#> ((unfam2-unfam3)-(fam2-fam3)) |  0.36 | 23.13

### Question 2B
# Contrasts for the factor sleepState:
# make custom contrast:
MMR.emm2 = m2 %>%
  emmeans(~ sleepState) 
#> NOTE: Results may be misleading due to involvement in interactions
MMR.emm2 # to set the custom contrast correctly
#>  sleepState  emmean lower.HPD upper.HPD
#>  awake        -3.95    -16.08      8.57
#>  activesleep   8.89     -5.07     21.39
#>  quietsleep    6.61     -8.93     20.95
#> 
#> Results are averaged over the levels of: TestSpeaker, Group 
#> Point estimate displayed: median 
#> HPD interval probability: 0.95
# set custom contrast sleep
custom_contrasts_sleep <- list(
  list("awake - activesleep and quietsleep" = c(1, -1/2, -1/2)),
  list("quietsleep - awake and activesleep" = c(-1/2, -1/2, 1)),
  list("quietsleep vs activesleep" =c(0, 1, -1))
)

# Compute BFs (only for model 2)
#  comparison of prior distributions
m2_prior <- unupdate(m2, verbose=FALSE) # sample priors from model
m2_prior_sleep <-
  m2_prior %>%
  emmeans(~ sleepState)
#> NOTE: Results may be misleading due to involvement in interactions
m2_prior_sleep = contrast(m2_prior_sleep, method = custom_contrasts_sleep)
#  comparison of posterior distributions
m2_post_sleep <-
  m2 %>%
  emmeans(~ sleepState) 
#> NOTE: Results may be misleading due to involvement in interactions
m2_post_sleep = contrast(m2_post_sleep, method = custom_contrasts_sleep)
# Bayes Factors (Savage-Dickey density ratio)
BF_m2_sleep <-
  m2_post_sleep %>%
  bf_parameters(prior = m2_prior_sleep) %>%
  arrange(log_BF) # sort according to BF
#> Warning: Bayes factors might not be precise.
#>   For precise Bayes factors, sampling at least 40,000 posterior samples is
#>   recommended.
BF_m2_sleep
#> Bayes Factor (Savage-Dickey density ratio)
#> 
#> Parameter                          |    BF
#> ------------------------------------------
#> quietsleep vs activesleep          | 0.400
#> quietsleep - awake and activesleep | 0.488
#> awake - activesleep and quietsleep |  1.21
#> 
#> * Evidence Against The Null: 0
plot(BF_m2_sleep)

# Check the priors:
point_estimate(m2_prior_sleep, centr = "mean", disp = TRUE)
#> Point Estimate
#> 
#> Parameter                          |  Mean |    SD
#> --------------------------------------------------
#> awake - activesleep and quietsleep | -0.30 | 20.20
#> quietsleep - awake and activesleep |  0.34 | 20.20
#> quietsleep vs activesleep          | -0.25 | 23.61

^{Created on 2024-03-08 with reprex v2.0.2}

[mattansb]

Question 1

As specified in the docs, the bayestestR::contr.equalprior() all give the same prior structure, but with different scaling. Specifically, bayestestR::contr.equalprior_pairs() allow to specify priors on all the pairwise differences.

For example, if you have a categorical predictor with 3 levels ($A_1$, $A_2$, $A_3$), and you use bayestestR::contr.equalprior_pairs() to generate 2 contrasts ($C_1$, $C_2$), and you set the following prior:

$$ \begin{bmatrix} C_1 \\ C_2 \end{bmatrix} \sim Normal(0, 10) $$

This is the same as setting the same scaled prior (only when the prior above is centered on 0!):

$$ \begin{bmatrix} A1 - A2 \\ A_1 - A3 \\ A_2 - A3 \\ \end{bmatrix} \sim Normal(0, 10) $$

bayestestR::contr.equalprior() is the same, but the priors on the pairwise differences are scaled by $\sqrt{2}$ (which I find less helpfull...).

Question 2

If you have priors on those custom contrasts, you might want to set priors on them directly instead of using bayestestR::contr.equalprior().

But generally the answer to any "is it okay if..." is always it depends.

Question 3

In the output of emmeans(), I always get the warning: NOTE: Results may be misleading due to involvement in interactions. Is this a problem for the contrasts I am comparing?

This is related to emmeans, not anything easystats related. It just reminding you that you are marginalizing over some variable(s) that (in the model) interact with the focal predictor. In your example, you are comparing marginal mean of TestSpeaker over the levels of Group and sleepstate that interact with it.

See emmeans docs for more.

The posterior distribution for the BF for model 2 has some weird bumps - do you know why they are there and whether it's a problem?

Adding chains/samples will smooth those out.
If you are computing BFs, you should probably be using more chains/samples any way (the current suggestion is to get 10 times more overall samples than what you would normally).

[GiselaGovaart]

Hi Matt,

Thanks for your (superfast!) response, it's very helpful! I am sorry for not specifying better what I’d already learned from the documentation.

Question 1
I do get that the different contrasts are just differently scaled to allow for different contrasts to be tested. I did not get from the docs, however, how the scalings for contr.equalprior and contr.equalprior_pairs differ (which you now clarified!) and how to choose one or the other.
I think that’s because in the documentation, contr.equalprior is not described as a contrast by itself, such that I got the feeling it was just the “overarching function” that you’d not use (because you’d always use either *_pairs or *_deviations). But then in the examples, contr.equalprior is used to show the matrices, so I got the feeling maybe I should use contr.equalprior after all.
I then tried testing their differences by trying:
contr.equalprior(3)
contr.equalprior_pairs(3)
contr.equalprior_deviations(3)
However,
contr.equalprior(3) and contr.equalprior_deviations(3) both give me the corresponding contrast structure, whereas contr.equalprior_pairs(3) does not output anything, which confused me. However, I now figured out that if I just save the output in a variable, I do actually get the output matrix, which already clarified a lot!

So that’s where my question came from. And since the BF changed because of the different prior contrasts (of course, because the prior specifications changed), I got a bit confused how to know which one to pick:)

I would be happy to contribute to updating the documentation on this issue, by the way. For me as a newbie, it would be helpful to add:

1. In which case one would use contr.equalprior instead of one of the other two (I don’t know the answer to that yet though:) ).
2. An example that shows that if you save the output of contr.equalprior_pairs(n), you can inspect the matrix

Question 2
Thanks! Yes, setting the priors directly on the custom contrasts was actually what I meant with my question “is there a way to force the priors to be the same for an entire custom contrast matrix?” :)
I tried a lot to figure out how to do this, but the only solution I came up with, was specifying each separate contrast as a new variable and set a prior on this variable.

So for the first contrast in the custom contrast matrix, like this:

# create a variable with the contrast
df$CustomContrast <- with(df, ifelse(Group == “unfam” & TestSpeaker == 2, 1,
                               ifelse(Group == “fam” & TestSpeaker == 1, -1, 0)))

# And then set a prior for the contrast: 
prior = c(set_prior("normal(5.97, 23.34)", class = "Intercept"),
                     set_prior("normal(0, 23.34)", class = "b"),
                     set_prior("normal(0, 23.34)", class = "sigma"),
                     set_prior("normal(0, 25)", class = "b", coef = "CustomContrast"))

However, this seems a bit excessive to me.. Was this also the way you meant it?

Question 3
Thanks a lot for taking the time to clarify this. Just as a sidenote, I should have also added that in my first entry: this was just a toy example. I have more data so that the models will actually converge, and will also use more chains :) Good to know that this would fix the bumps!

[mattansb]

Q1

Honestly I'm not sure why you'd want to use contr.equalprior() - it doesn't seem that useful to me, but we provide it for completeness.

I'm not getting the printing issue you describe ...

Q2

I'm not familiar with your data, but yes - that is exactly what I'd do.
I don't think this is excessive - you are exerting fine-tune control of your model.

[GiselaGovaart]

Q1: Okay, thanks, then it's clear. I don't know why that issue comes up for me, but it's also not important for now..
Q2: Thanks for your input - good to know it sounds sound to you:)