{"items": [{"author": "Bernadette", "source_link": "https://www.facebook.com/jefftk/posts/694069961112?comment_id=694070789452", "anchor": "fb-694070789452", "service": "fb", "text": "This is really interesting! Do you know what the time distribution of the different types of nap are? Rose seems to have times where she sleeps longer and more easily, and other times she has short, hard to settle naps. One theory (from two Dutch child development specialists) is that these are times preceding big developmental leaps, as the child's brain is adapting to new abilities. Does Lily's napping vary widely day to day, or does she have good and bad weeks?", "timestamp": "1414416876"}, {"author": "Mac", "source_link": "https://www.facebook.com/jefftk/posts/694069961112?comment_id=694071428172", "anchor": "fb-694071428172", "service": "fb", "text": "\"Might not seem good for her.\" Could be. Maybe the longer naps are from the stress of emotion and crying.", "timestamp": "1414417303"}, {"author": "Victor", "source_link": "https://www.facebook.com/jefftk/posts/694069961112?comment_id=694071787452", "anchor": "fb-694071787452", "service": "fb", "text": "I prefer allowing crying for increasing amounts of time, as first described by Ferber. Less crying, less trauma for parents and probably for infants as well.", "timestamp": "1414417616"}, {"author": "Mac", "source_link": "https://www.facebook.com/jefftk/posts/694069961112?comment_id=694073039942", "anchor": "fb-694073039942", "service": "fb", "text": "I cannot believe that regular trauma should be involved with infants falling asleep. After putting ourselves through the trauma of letting our first born cry, we quit that practice. We then rocked both our children (in arms, in a rocking chair), and sang them to sleep. So far, that has been the high point of my life.", "timestamp": "1414418691"}, {"author": "Jeff Kaufman", "source_link": "https://www.facebook.com/jefftk/posts/694069961112?comment_id=694074741532", "anchor": "fb-694074741532", "service": "fb", "text": "@Bernadette: \"Do you know what the time distribution of the different types of nap are?\"

I don't really see a pattern: http://jefftk.com/nap-length-by-time-of-day.png", "timestamp": "1414419890"}, {"author": "Ben", "source_link": "https://www.facebook.com/jefftk/posts/694069961112?comment_id=694074891232", "anchor": "fb-694074891232", "service": "fb", "text": "I actually got p-value = 8.997e-05, but w/e: both are super small. Different distribution plot here: http://imgur.com/9mM2sn7 Gist is here: https://gist.github.com/bwarren2/a1097ecc7106296afb7c Note: I hacked at your data a bit to square up the columns. I can provide that csv by request.", "timestamp": "1414420002"}, {"author": "Bernadette", "source_link": "https://www.facebook.com/jefftk/posts/694069961112?comment_id=694075470072", "anchor": "fb-694075470072", "service": "fb", "text": "Jeff ah sorry, I meant comparing nap length according to the day or week - so x axis would be calendar time.", "timestamp": "1414420362"}, {"author": "Jeff Kaufman", "source_link": "https://www.facebook.com/jefftk/posts/694069961112?comment_id=694075809392", "anchor": "fb-694075809392", "service": "fb", "text": "@Bernadette: Sure! http://jefftk.com/nap-length-by-datetime.png", "timestamp": "1414420631"}, {"author": "Bernadette", "source_link": "https://www.facebook.com/jefftk/posts/694069961112?comment_id=694076323362", "anchor": "fb-694076323362", "service": "fb", "text": "Interesting- it does look like she's become more likely to nap for two sleep cycles. Maybe this change could be seen as early as early October? I would agree that learning to self soothe could explain it. (Though so would a developmental change occurring at the same time). I am really appreciating you guys sharing your experience.", "timestamp": "1414421089"}, {"author": "Eloise", "source_link": "https://www.facebook.com/jefftk/posts/694069961112?comment_id=694077985032", "anchor": "fb-694077985032", "service": "fb", "text": "I had the impression that older children sleep more soundly than younger ones, which probably means being able to sleep for longer periods at a time. Part of the change you're seeing might just be from Lily getting older.", "timestamp": "1414422657"}, {"author": "Bronwyn", "source_link": "https://www.facebook.com/jefftk/posts/694069961112?comment_id=694078069862", "anchor": "fb-694078069862", "service": "fb", "text": "It looks to me like time (date) might be more of a driving factor here than the change in soothing. But they're pretty confounded, so who knows.", "timestamp": "1414422726"}, {"author": "Jeff Kaufman", "source_link": "https://www.facebook.com/jefftk/posts/694069961112?comment_id=694078593812", "anchor": "fb-694078593812", "service": "fb", "text": "@Eloise @Bronwyn: \"Part of the change you're seeing might just be from Lily getting older.\"

That does look like part of it, but if you look just at the week before/after the change it's pretty sharp: http://jefftk.com/nap-length-week-before-and-after-change...", "timestamp": "1414423111"}, {"author": "David Chudzicki", "source_link": "https://www.facebook.com/jefftk/posts/694069961112?comment_id=694079606782", "anchor": "fb-694079606782", "service": "fb", "text": "Jeff Bronwyn https://en.wikipedia.org/.../Regression_discontinuity_design", "timestamp": "1414423723"}, {"author": "Jeff Kaufman", "source_link": "https://www.facebook.com/jefftk/posts/694069961112?comment_id=694080050892", "anchor": "fb-694080050892", "service": "fb", "text": "@Toby: \"e.g. if you selected the time to change method based on frustration with a spate of short sleeps\"

Short sleeps weren't really something I found frustrating, so I don't think that was motivating, though I did worry they weren't good for her. The time spent comforting her to sleep was more of a motivation, especially as for Julia it involved leaning over the crib in a way that was building up stress on her back and getting painful (I think; that's my memory what she said.)", "timestamp": "1414424149"}, {"author": "Jeff Kaufman", "source_link": "https://www.facebook.com/jefftk/posts/694069961112?comment_id=694080195602", "anchor": "fb-694080195602", "service": "fb", "text": "@David: Is that the name for what my before/after chart [1] is looking at?

[1] http://www.jefftk.com/p/baby-sleep-ii...", "timestamp": "1414424264"}, {"author": "Jeff Kaufman", "source_link": "https://www.facebook.com/jefftk/posts/694069961112?comment_id=694080395202", "anchor": "fb-694080395202", "service": "fb", "text": "(We really should have randomized this switch. It feels like \"we just decided it was time\" (or \"we just got fed up with it\") but this lack of introspection is super frustrating.)", "timestamp": "1414424368"}, {"author": "David Chudzicki", "source_link": "https://www.facebook.com/jefftk/posts/694069961112?comment_id=694080495002", "anchor": "fb-694080495002", "service": "fb", "text": "Not quite Jeff. You'd want a model for the time series that's smooth except for allowing a discontinuity. Your estimate for the size of that discontinuity would be your estimate for the effect of the switch.", "timestamp": "1414424475"}, {"author": "David Chudzicki", "source_link": "https://www.facebook.com/jefftk/posts/694069961112?comment_id=694080589812", "anchor": "fb-694080589812", "service": "fb", "text": "When I say \"the time series\", I mean this: http://www.jefftk.com/nap-length-by-datetime.png", "timestamp": "1414424569"}, {"author": "David Chudzicki", "source_link": "https://www.facebook.com/jefftk/posts/694069961112?comment_id=694080924142", "anchor": "fb-694080924142", "service": "fb", "text": "... although you could also incorporate time of day into the model. It seems like you're right that there isn't much time-of-day trend, except the distribution of sleep durations does seem to be bimodal in non-evening times (and after 4pm you only get the lower mode). I don't know if the explanation for that is more likely to be intrinsic to Lily, or something about your late afternoon / evening routine.", "timestamp": "1414424800"}, {"author": "Jeff Kaufman", "source_link": "https://www.facebook.com/jefftk/posts/694069961112?comment_id=694080964062", "anchor": "fb-694080964062", "service": "fb", "text": "@David: The \"real\" time series is https://docs.google.com/.../1lt_UDOQEP4xgshH.../edit...", "timestamp": "1414424809"}, {"author": "David Chudzicki", "source_link": "https://www.facebook.com/jefftk/posts/694069961112?comment_id=694081188612", "anchor": "fb-694081188612", "service": "fb", "text": "\"Running a two-tailed t-test I got a p-value of 0.00025 which seems extreme enough that I'm really not sure I did the test right.\" Parametric tests like this can give absurd results when the assumptions are off (in this case maybe normality).", "timestamp": "1414424940"}, {"author": "Jeff Kaufman", "source_link": "https://www.facebook.com/jefftk/posts/694069961112?comment_id=694081263462", "anchor": "fb-694081263462", "service": "fb", "text": "@David: \"I don't know if the explanation for that is more likely to be intrinsic to Lily, or something about your late afternoon / evening routine.\"

There is a bit of a routine thing, in that I would often try to keep Lily up until Julia got home from work, if it wasn't stretching things too much. So she wouldn't typically go down in the late afternoon, and when she went down in the evening it was after having some time with Julia (including nursing instead of bottle-feeding).

Light levels wouldn't have been an issue because this whole time I had the windows blacked out with tinfoil.", "timestamp": "1414425014"}, {"author": "David Chudzicki", "source_link": "https://www.facebook.com/jefftk/posts/694069961112?comment_id=694081338312", "anchor": "fb-694081338312", "service": "fb", "text": "It sounds like your test was for a \"null hypothesis\" of zero effect. I think it's unlikely that you actually care whether the effect is zero. The things you are about are (a) your estimate of the effect size, and (b) your uncertainty around that estimate.", "timestamp": "1414425052"}, {"author": "Bronwyn", "source_link": "https://www.facebook.com/jefftk/posts/694069961112?comment_id=694081522942", "anchor": "fb-694081522942", "service": "fb", "text": "David Chudzicki I don't think that applies in this case.

\"Regression discontinuity design requires that treatment assignment is \"as good as random\" at the threshold for treatment.\"

If we are thinking of \"naps\" as the unit here, the naps with soothing and the naps without are not determined based on any threshold of a characteristic of the nap itself. The whole technique is based upon the assumption that you get essentially random assignment in a subset of the population near the threshold (eg grade threshold for getting a scholarship). I don't think that makes sense here.", "timestamp": "1414425150"}, {"author": "Bronwyn", "source_link": "https://www.facebook.com/jefftk/posts/694069961112?comment_id=694082286412", "anchor": "fb-694082286412", "service": "fb", "text": "Jeff Kaufman, the two-week plot is a little misleading, I think. Those two weeks are pretty different, but if you plot all the weeks in that way, you get the plot here.

It looks more like week 5 (the one right before the change) is actually the odd one out. The other weeks are generally increasing from one to the next.

For what it's worth, a simple linear regression with time and soothing status as predictors finds time to be significant and soothing status not to be. But since soothings status can be perfectly determined by time, that's not actually terribly meaningful.

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -7.989e+03 3.463e+03 -2.307 0.0229 *
Date 5.692e-06 2.454e-06 2.320 0.0221 *
self 8.394e+00 7.750e+00 1.083 0.2811", "timestamp": "1414425604"}, {"author": "Bronwyn", "source_link": "https://www.facebook.com/jefftk/posts/694069961112?comment_id=694082471042", "anchor": "fb-694082471042", "service": "fb", "text": "(Facebook comments don't allow enough formatting to make that chart terribly readable. Sorry.)", "timestamp": "1414425733"}, {"author": "David Chudzicki", "source_link": "https://www.facebook.com/jefftk/posts/694069961112?comment_id=694082790402", "anchor": "fb-694082790402", "service": "fb", "text": "Bronwyn, that sentence in the article is pretty confusing. I should have found a better link. I think they just mean that everything else that matters (besides the treatment itself) is random in the period around the threshhold. (Which is likely to be satisfied here.)", "timestamp": "1414425878"}, {"author": "David Chudzicki", "source_link": "https://www.facebook.com/jefftk/posts/694069961112?comment_id=694083074832", "anchor": "fb-694083074832", "service": "fb", "text": "It's possible I'm getting the terms a little wrong, but I think Bronwyn's linear regression is an example of what I mean when I talk about regression discontinuity:

The model should be interpreted as a linearly increasing duration, with a possible jump at the threshold.", "timestamp": "1414426047"}, {"author": "David Chudzicki", "source_link": "https://www.facebook.com/jefftk/posts/694069961112?comment_id=694083429122", "anchor": "fb-694083429122", "service": "fb", "text": "I'd also say that I think fancy analysis is sometimes overused compared with just looking at the data [edit: ...and I was probably guilty of that in suggesting \"regression discontinuity\"]. Both Bronwyn's chart with a line for each week, and Jeff's scatter plot of time vs. nap duration both tell us that if this change made any difference to nap durations, that difference is very small compared with the other variation in durations.", "timestamp": "1414426266"}, {"author": "Bronwyn", "source_link": "https://www.facebook.com/jefftk/posts/694069961112?comment_id=694084581812", "anchor": "fb-694084581812", "service": "fb", "text": "David Chudzicki, \"everything else that matters (besides the treatment itself) is random in the period around the threshhold\"

Yes, that's what they mean. But in this case, assuming that everything else that could impact the outcome is random in the (say) week before and after the switch seems pretty strong. I think most of the problem comes from the fact that these naps are not actually at all independent since they are measured in the same individual. If there is something different about Lily before and after the switch (eg getting older, some kind of stress) or even just dependency in the nap time series (how well she sleeps depends on how well she's been sleeping), all the assumptions of these models (including the linear regression I fit) are sort of out the window.

But yes, I think my regression with an indicator for soothing is probably what you're getting at. It fits a regression with a different intercept for the two conditions but the same slope for the impact of time.

However, that model is actually a pretty horrible fit to the data, so I wouldn't read too much into it. If you add a treatment:date interaction (different slope for the two conditions as well as different intercept), everything becomes significant but the fit is still horrible.", "timestamp": "1414427045"}, {"author": "David Chudzicki", "source_link": "https://www.facebook.com/jefftk/posts/694069961112?comment_id=694088254452", "anchor": "fb-694088254452", "service": "fb", "text": "I see -- if other things vary on a time scale that's too long to be treated as independent noise but too short to be captured by a model of the time trend, then I think any inference about the effect of the switch is probably impossible.", "timestamp": "1414429352"}, {"author": "David Chudzicki", "source_link": "https://www.facebook.com/jefftk/posts/694069961112?comment_id=694088329302", "anchor": "fb-694088329302", "service": "fb", "text": "So I could have been more explicit in pointing to regression discontinuity models. I meant something like: This might be the sort of model with the weakest assumptions under which you could make any inference about the effect of the switch.", "timestamp": "1414429416"}]}