regression-demos

--- title: regression-demos tags: statistical-software-demos, statistical-software robots: noindex, nofollow --- Regression Demonstrations ========================= This file demonstrates the application of [rOpenSci](https://ropensci.org) ’s [standards for statistical software](https://ropenscilabs.github.io/statistical-software-review-book/standards.html) to one [Regression software](https://ropenscilabs.github.io/statistical-software-review-book/standards.html#regression-and-supervised-learning) package. These applications are not intended to represent or reflect evaluations or assessment of the packages, and particularly not of the extent to which they fail to meet standards. Rather, the demonstrations are intended to highlight aspects of the software which could be productively improved by adhering to the standards, and thereby more generally to demonstrate the general usefulness of these standards in advancing and improving software quality. [lme4](https://github.com/lme4/lme4) ------------------------------------ ### 1 [General Standards](https://ropenscilabs.github.io/statistical-software-review-book/standards.html#general-standards-for-statistical-software) #### 1.1 Documentation - [x] **G1.0** primary reference provided **Statistical Terminology** - [x] **G1.1** Statistical terminology clarified and defined. **Function-level Documentation** - [x] **G1.2** [`roxygen`](https://roxygen2.r-lib.org/) is (conditionally and appropriately) used to document all functions. - [ ] **G1.2a** Internal functions generally not appropriately documented **Supplementary Documentation** - [x] **G1.3** Code necessary to reproduce performance claims is provided. - [x] **G1.4** Code necessary to compare performance with alternative implementations in other R packages is provided. #### 1.2 Input Structures **Uni-variate (Vector) Input** - [x] **G2.0** Expected lengths of inputs generally documented and asserted. - [x] **G2.1** Expected types of inputs generally documented and asserted. - [x] **G2.2** Parameters expected to be univariate do not accept multivariate input - [ ] **G2.3** *For univariate character input:* - [x] **G2.3a** `match.arg()` is used to only permit expected values. - [ ] **G2.3b** `tolower()` is not used, and character parameters are case-dependent - [x] **G2.4** Mechanisms provided to convert between different data types - [x] **G2.5** `factor` type inputs appropriate documented and processed. **Tabular Input** - [x] **G2.6** Software accepts standard tabular inputs - [x] **G2.7** Software appropriately converts inputs to a single defined class or type. - [ ] **G2.8** Software does not issue diagnostic messages for type conversion in which information is lost or added Main routines assume data to have a “grouping factor”, yet where or not the relevant column is a `factor` or not, or whether or not it is ordered, makes no difference. Thus submitting data in which the “grouping factor” is, for example, a simple integer, lead to that being interpreted as a `factor`, which is equivalent to the addition of information describing the factor levels. Conversely, submitting as an ordered factor makes no difference, thereby effectively removing the information that the `factor` variable is ordered. - [x] **G2.9** Extraction or filtering of single columns from tabular is appropriately performed regardless of input class. **Missing or Undefined Values** - [x] **G2.10**–**G2.12** Missing values appropriately handled throughout, with ability for user control - [ ] **G2.13** No options are provided for handling undefined values, rather routines simply error with informative messages. #### 1.3 Output Structures - [x] **G4.0** No local files produced, so not relvant #### 1.4 Testing **Test Data Sets** - [x] **G5.0** Tests use standard data sets with known properties - [x] **G5.1** Data sets created within package are exported **Responses to Unexpected Input** - [ ] **G5.2** The package issues numerous error and warning messages, neither the triggering conditions nor values of which are explicitly tested. - [x] **G5.2a** Messages produced by `stop()`, `warning()`, `message()`are unique. - [ ] **G5.2b** Tests do not trigger every one of those messages - [x] **G5.3** Absence of missing values form return results is explicitly tested. **Algorithm Tests** - [x] **G5.4** Correctness tests are implemented. - [x] **G5.5** Correctness tests are run with a fixed random seed - [x] **G5.6** Parameter recovery tests implemented - [ ] **G5.6a** Many, but not all, parameter recovery tests are expected to succeed within a defined tolerance - [ ] **G5.6b** Parameter recovery are generally only run with one single random seeds when algorithm contains a random component. - [ ] **G5.7** There appear to be no algorithm performance tests - [x] **G5.8** Edge condition appropriately tested - [ ] **G5.9** There appear to be no noise susceptibility tests, neither tests of the effect of adding trivial noise, nor tests running under different random seeds. **Extended tests** - [x] **G5.10**–**G5.12** The `lme4` package provides exemplary use of exactly such an environmental variable, carefully documented in a `tests/README.md` file. ------------------------------------------------------------------------ ### 2 [Regression and Supervised Learning Standards](https://ropenscilabs.github.io/statistical-software-review-book/standards.html#regression-and-supervised-learning) #### 2.1 Input data structures and validation - [x] **RE1.0** Models are specified via a formula interface - [x] **RE1.1** Documentation is provided for how formula interfaces are converted to matrix representations of input data. The main [package vignette](https://cran.r-project.org/web/packages/lme4/vignettes/lmer.pdf) provides a particularly exemplary demonstration (in Section 2.3) of the relationship between the package’s formula interface and the underlying matrix representations. - [ ] **RE1.2** Expected input formats are documented, but errors from other formats are not informative. Documentation of the primary function (`lmer`) states that the main `data` parameter is, “*an optional data frame containing the variables named in `formula`*”. This function fails with equivalent `matrix` input with the uninformative error, ``` r s <- sleepstudy s$Subject <- as.integer (s$Subject) s <- as.matrix (s) m <- lmer(Reaction ~ Days + (Days | Subject), data = s) ``` ## Error in list2env(data) : first argument must be a named list The function nevertheless accepts any generic rectangular input, including `tibble`, and `data.table` formats. Rectification to this standard would require only (i) updating the documentation to explicate that the function accepts any objects able to be coerced to `data.frame` representation; and (ii) ensuring that passing non-compliant `data` objects generates informative messages. - [x] **RE1.3** All relevant aspects of input data are transferred to return objects - [x] **RE1.4** Assumptions made with regard to input data are clearly documented. #### 2.2 Pre-processing and Variable Transformation - [ ] **RE2.0** Not all transformations applied to input data are documented `lme4` implicitly converts all columns of input data specified in a model formula as grouping factors (through being on the right-side of a vertical bar, `|`, in the formula) to `factor`, yet this is not explicitly stated in documentation. Avoiding such conversion would make no sense here. - [x] **RE2.1**–**RE2.2** Appropriate processing of missing values is implemented. `lme4` provides exemplary handling of this case, as illustrated by the following code: ``` r set.seed (1) s <- sleepstudy s$Reaction [ceiling (runif (1, max = nrow (s)))] <- NA # random NA value in response variable m <- lmer(Reaction ~ Days + (Days | Subject), data = s) nobs (m) ``` ## [1] 179 ``` r length (predict (m)) ``` ## [1] 179 ``` r length (predict (m, s)) ``` ## [1] 180 - [x] **RE2.3** Centering of data is appropriately diagnosed and implemented. - [ ] **RE2.4** *Regression Software should implement pre-processing routines to identify whether aspects of input data are perfectly collinear, notably including:* - [ ] **RE2.4a** *Perfect collinearity among predictor variables* - [ ] **RE2.4b** *Perfect collinearity between independent and dependent variables* These conditions are neither pre-identified nor appropriately processed, with the first case returning an empty model, and the second initially issuing an appropriate message (“dropping 1 column / coefficient”), yet failing to subsequently fit an appropriate model. The following code demonstrates: ``` r s1 <- s2 <- sleepstudy s1$Reaction <- s1$Days lmer(Reaction ~ Days + (Days | Subject), data = s1) ``` ## Linear mixed model fit by REML ['lmerMod'] ## Formula: Reaction ~ Days + (Days | Subject) ## Data: s1 ## REML criterion at convergence: -Inf ## Random effects: ## Groups Name Std.Dev. Corr ## Subject (Intercept) 0 ## Days 0 NaN ## Residual 0 ## Number of obs: 180, groups: Subject, 18 ## Fixed Effects: ## (Intercept) Days ## 0 1 ## optimizer (nloptwrap) convergence code: 0 (OK) ; 0 optimizer warnings; 1 lme4 warnings ``` r s2$Days2 <- 2 * s2$Days m <- lmer(Reaction ~ Days + Days2 + (Days | Subject) + (Days2 | Subject), data = s2) ``` ## fixed-effect model matrix is rank deficient so dropping 1 column / coefficient ## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, : ## unable to evaluate scaled gradient ## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, : ## Model failed to converge: degenerate Hessian with 2 negative eigenvalues #### 2.3 Algorithms - [x] **RE3.0**–**RE3.3** Control over algorithmic convergence in `lme4` is exemplarily handled through the `lmerControl()` function and associated extensive documentation. #### 2.4 Return Results - [ ] **RE4.0**–**RE4.13** All accessor methods for model data provided by the `stats` package, and all model parameters, are also implemented for `lmerMod` objects. **Prediction, Extrapolation, and Forecasting** - [ ] **RE4.14** *Where possible, values should also be provided for extrapolation or forecast *errors*.* - [ ] **RE4.15** *Sufficient documentation and/or testing should be provided to demonstrate that forecast errors, confidence intervals, or equivalent values increase with forecast horizons.* The `lme4` package does not explicitly implement forecasting or extrapolation algorithms, rather it is a generic model fitting package, the results of which can be used with methods such as `predict()` to generate forecast values beyond the ranges of input data. There are nevertheless no explicit methods to use a model to generate confidence intervals on forecasts in the ways offered by the `stats` package: ``` r x <- data.frame (x = 1:10, y = runif (10)) m0 <- lm (y ~ x, data = x) predict (m0, newdata = data.frame (x = 11:16), se.fit = TRUE) ``` ## $fit ## 1 2 3 4 5 6 ## 0.3774055 0.3468319 0.3162582 0.2856846 0.2551110 0.2245373 ## ## $se.fit ## 1 2 3 4 5 6 ## 0.2235715 0.2560541 0.2893782 0.3232838 0.3576055 0.3922340 ## ## $df ## [1] 8 ## ## $residual.scale ## [1] 0.3272751 ``` r predict (m0, newdata = data.frame (x = 11:16), interval = "confidence") ``` ## fit lwr upr ## 1 0.3774055 -0.1381512 0.8929622 ## 2 0.3468319 -0.2436299 0.9372936 ## 3 0.3162582 -0.3510492 0.9835656 ## 4 0.2856846 -0.4598092 1.0311784 ## 5 0.2551110 -0.5695287 1.0797506 ## 6 0.2245373 -0.6799558 1.1290305 ``` r predict (m0, newdata = data.frame (x = 11:16), interval = "prediction") ``` ## fit lwr upr ## 1 0.3774055 -0.5365789 1.291390 ## 2 0.3468319 -0.6114029 1.305067 ## 3 0.3162582 -0.6911483 1.323665 ## 4 0.2856846 -0.7751310 1.346500 ## 5 0.2551110 -0.8627438 1.372966 ## 6 0.2245373 -0.9534595 1.402534 The three calls to `precict()` illustrate different ways of using the model to generate estimates of uncertainty involved in using that model to make forecasts. No such equivalent methods exist for objects of class `lmerMod`: ``` r m <- lmer(Reaction ~ Days + (Days | Subject), data = sleepstudy) predict (m, data.frame (Days = 0:12, Subject = 308)) ``` ## 1 2 3 4 5 6 7 8 ## 253.6637 273.3299 292.9962 312.6624 332.3287 351.9950 371.6612 391.3275 ## 9 10 11 12 13 ## 410.9937 430.6600 450.3263 469.9925 489.6588 ``` r predict (m, data.frame (Days = 0:12, Subject = 308), se.fit = TRUE) ``` ## Warning in predict.merMod(m, data.frame(Days = 0:12, Subject = 308), se.fit = ## TRUE): unused arguments ignored ## 1 2 3 4 5 6 7 8 ## 253.6637 273.3299 292.9962 312.6624 332.3287 351.9950 371.6612 391.3275 ## 9 10 11 12 13 ## 410.9937 430.6600 450.3263 469.9925 489.6588 ``` r predict (m, data.frame (Days = 0:12, Subject = 308), interval = "confidence") ``` ## Warning in predict.merMod(m, data.frame(Days = 0:12, Subject = 308), interval = ## "confidence"): unused arguments ignored ## 1 2 3 4 5 6 7 8 ## 253.6637 273.3299 292.9962 312.6624 332.3287 351.9950 371.6612 391.3275 ## 9 10 11 12 13 ## 410.9937 430.6600 450.3263 469.9925 489.6588 ``` r predict (m, data.frame (Days = 0:12, Subject = 308), interval = "prediction") ``` ## Warning in predict.merMod(m, data.frame(Days = 0:12, Subject = 308), interval = ## "prediction"): unused arguments ignored ## 1 2 3 4 5 6 7 8 ## 253.6637 273.3299 292.9962 312.6624 332.3287 351.9950 371.6612 391.3275 ## 9 10 11 12 13 ## 410.9937 430.6600 450.3263 469.9925 489.6588 Similar comments apply to objects of class `glmerMod` returned by the `glmer` function: ``` r gm <- glmer(cbind(incidence, size - incidence) ~ period + (1 |herd), data = cbpp, family = binomial) p <- predict (gm, type = "response", se.fit = TRUE) ``` ## Warning in predict.merMod(gm, type = "response", se.fit = TRUE): unused ## arguments ignored ``` r p <- predict (gm, type = "response", interval = "confidence") ``` ## Warning in predict.merMod(gm, type = "response", interval = "confidence"): ## unused arguments ignored ``` r p <- predict (gm, type = "response", interval = "prediction") ``` ## Warning in predict.merMod(gm, type = "response", interval = "prediction"): ## unused arguments ignored ``` r p # numeric values only ``` ## 1 2 3 4 5 6 7 ## 0.30816472 0.14177337 0.12598556 0.08405701 0.15480041 0.06360406 0.05595361 ## 8 9 10 11 12 13 14 ## 0.27042309 0.12085036 0.10710175 0.07094767 0.20435088 0.08696688 0.07673659 ## 15 16 17 18 19 20 21 ## 0.05025587 0.16957699 0.07040052 0.06198670 0.04037338 0.14199540 0.05782664 ## 22 23 24 25 26 27 28 ## 0.05083338 0.03297227 0.37533879 0.18223092 0.16279236 0.11015824 0.31019619 ## 29 30 31 32 33 34 35 ## 0.16299384 0.06735522 0.05928214 0.03857306 0.12570809 0.05062411 0.04446079 ## 36 37 38 39 40 41 42 ## 0.02877092 0.18492941 0.07761332 0.06840089 0.04465757 0.18795612 0.07905396 ## 43 44 45 46 47 48 49 ## 0.06968345 0.04551668 0.11022977 0.04392632 0.03854533 0.02488860 0.39460615 ## 50 51 52 53 54 55 56 ## 0.19467475 0.17419155 0.11839303 0.12686730 0.05113143 0.04490927 0.02906595 - [x] **RE4.16** It is possible to submit new groups to `predict()` methods.\* **Reporting Return Results** - [x] **RE4.17**–**RE4.18** Default `print` and `summary` methods for model objects are implemented. #### 2.5 Documentation - [ ] **RE5.0** `lme4` does not explicitly document scaling of model fitting algorithms #### 2.6 Visualization - [x] **RE6.0** Default plot methods provided for model objects - [x] **RE6.3** It is not possible to use `lme4` to distinguish *extrapolated* from *interpolated* predicted values, and thus no visual distinction is possible. See preceding comments regarding prediction methods under 4.2. #### 2.7 Testing **Input Data** - [ ] **RE7.0** *Tests with noiseless, exact relationships between predictor (independent) data.* - [ ] **RE7.0a** In particular, these tests should confirm ability to reject perfectly noiseless input data. - [ ] **RE7.1** *Tests with noiseless, exact relationships between predictor (independent) and response (dependent) data.* - [ ] **RE7.1a** *In particular, these tests should confirm that model fitting is at least as fast or (preferably) faster than testing with equivalent noisy data (see RE2.4b).* These tests do not appear to explicitly exist, although the test suite is quite large, and they could nevertheless be present somewhere. **Diagnostic Messages** - [ ] **RE7.2** Not all error and warning messages are explicitly triggered in tests **Return Results** - [x] **RE7.3** Tests demonstrate that output objects retain aspects of input data such as row or case names. - [x] **RE7.4** Tests demonstrate expected behaviour when return objects are submitted to the accessor methods of **RE4.2**–**RE4.7**. - [ ] **RE7.5** Test do not demonstrate that forecast errors, confidence intervals, or equivalent values increase with forecast horizons, although that could readily be argued to be inappropriate here.

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