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POInterpolate product attributes
 

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    <p>I have a set of data from a set of <a href="http://en.wikipedia.org/wiki/Discrete_choice">discrete choice tasks</a> which included two alternatives with three attributes (brand, price, performance). From this data, I have taken 1000 draws from the posterior distribution which I'll then use to calculate utility and eventually preference share for each individual and each draw. </p> <p>Price and performance were tested at discrete levels (-.2, 0, .2) and (-.25, 0, .25) respectively. I need to be able to interpolate utility between attribute levels tested. Let's assume for now that a linear interpolation is a reasonable thing to do statistically. In other words, what is the most efficient way to interpolate the utility for price if I wanted to test a scenario with price @ 10% lower? I have not been able to think of a slick or efficient way to do the interpolation. I've resorted to an mapply() approach with the mdply function from plyr</p> <p>Here's some data and my current approach:</p> <pre><code>library(plyr) #draws from posterior, 2 respondents, 2 draws each draw &lt;- list(structure(c(-2.403, -2.295, 3.198, 1.378, 0.159, 1.531, 1.567, -1.716, -4.244, 0.819, -1.121, -0.622, 1.519, 1.731, -1.779, 2.84), .Dim = c(2L, 8L), .Dimnames = list(NULL, c("brand_1", "brand_2", "price_1", "price_2", "price_3", "perf_1", "perf_2", "perf_3"))), structure(c(-4.794, -2.147, -1.912, 0.241, 0.084, 0.31, 0.093, -0.249, 0.054, -0.042, 0.248, -0.737, -1.775, 1.803, 0.73, -0.505), .Dim = c(2L, 8L), .Dimnames = list(NULL, c("brand_1", "brand_2", "price_1", "price_2", "price_3", "perf_1", "perf_2", "perf_3")))) #define attributes for each brand: brand constant, price, performance b1 &lt;- c(1, .15, .25) b2 &lt;- c(2, .1, .2) #Create data.frame out of attribute lists. Wil use mdply to go through each interpolateCombos &lt;- data.frame(xout = c(b1,b2), atts = rep(c("Brand", "Price", "Performance"), 2), i = rep(1:2, each = 3), stringsAsFactors = FALSE) #Find point along line. Tried approx(), but too slow findInt &lt;- function(x1,x2,y1,y2,reqx) { range &lt;- x2 - x1 diff &lt;- reqx - x1 out &lt;- y1 + ((y2 - y1)/range) * diff return(out) } calcInterpolate &lt;- function(xout, atts, i){ if (atts == "Brand") { breaks &lt;- 1:2 cols &lt;- 1:2 } else if (atts == "Price"){ breaks &lt;- c(-.2, 0, .2) cols &lt;- 3:5 } else { breaks &lt;- c(-.25, 0, .25) cols &lt;- 6:8 } utils &lt;- draw[[i]][, cols] if (atts == "Brand" | xout %in% breaks){ #Brand can't be interpolated or if level matches a break out &lt;- data.frame(out = utils[, match(xout, breaks)]) } else{ #Must interpolate mi &lt;- min(which(breaks &lt;= xout)) ma &lt;- max(which(breaks &gt;= xout)) out &lt;- data.frame(out = findInt(breaks[mi], breaks[ma], utils[, mi], utils[,ma], xout)) } out$draw &lt;- 1:nrow(utils) return(out) } out &lt;- mdply(interpolateCombos, calcInterpolate) </code></pre> <p>To provide context on what I'm trying to accomplish without interpolating attribute levels, here's how I'd do that. Note the brands are now defined in terms of their column reference. p1 &amp; p2 refer to the product definition, u1 &amp; u2 are the utility, and s1, s2 are the preference shares for that draw. </p> <p>Any nudge in the right direction would be appreciated. My real case has 10 products with 8 attributes each. At 10k draws, my 8gb of ram are crapping out, but I can't get out of this rabbit hole I've dug myself.</p> <pre><code>p1 &lt;- c(1,2,1) p2 &lt;- c(2,1,2) FUN &lt;- function(x, p1, p2) { bases &lt;- c(0,2,5) u1 &lt;- rowSums(x[, bases + p1]) u2 &lt;- rowSums(x[, bases + p2]) sumExp &lt;- exp(u1) + exp(u2) s1 &lt;- exp(u1) / sumExp s2 &lt;- exp(u2) / sumExp return(cbind(s1,s2)) } lapply(draw, FUN, p1 = p1, p2 = p2) [[1]] s1 s2 [1,] 0.00107646039 0.9989235 [2,] 0.00009391749 0.9999061 [[2]] s1 s2 [1,] 0.299432858 0.7005671 [2,] 0.004123175 0.9958768 </code></pre>
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    1. COWhat do you wish to improve? Speed? Memory? Statistical convergence? (All of the above? :)) I can sort of grok your code, but I don't understand the statistical problem you're trying to solve. Humor me: why wouldn't this simply be ordinary least squares regression? `lm()` is okay with categorical factors, and (unless I'm mistaken) ordered factors as well.
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    2. CO@Iterator - I'll take option 3 for 500 please! The main issues I am running into are both speed and memory based. The statistical problem, if I were to even classify it as such, is simply needing to perform a linear interpolation for 80+ attributes for a matrix containing somewhere around 0.5M rows. Two easy changes I've made proved quite significant. Namely: 1) moving to `mapply()`from `mdply()`. 2) Changing all data.frames to matrices. I'm still not convinced that the whole approach is as efficient computationally as it could be, but it's sufficient for now. When I get to a stopping point
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    3. COI'll update / answer my own question for posterity. I gather you do a fair amount of related work (with the namesake and all), so can talk in more detail offline if it's of interest!
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