Regression Demonstrations

This file demonstrates the application of rOpenSci ’s standards for statistical software to one Regression software 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

1 General Standards

1.1 Documentation

  • G1.0 primary reference provided

Statistical Terminology

  • G1.1 Statistical terminology clarified and defined.

Function-level Documentation

  • G1.2 roxygen is (conditionally and appropriately) used to document all functions.
    • G1.2a Internal functions generally not appropriately documented

Supplementary Documentation

  • G1.3 Code necessary to reproduce performance claims is provided.
  • G1.4 Code necessary to compare performance with alternative implementations in other R packages is provided.

1.2 Input Structures

Uni-variate (Vector) Input

  • G2.0 Expected lengths of inputs generally documented and asserted.
  • G2.1 Expected types of inputs generally documented and asserted.
  • G2.2 Parameters expected to be univariate do not accept multivariate input
  • G2.3 For univariate character input:
  • G2.3a match.arg() is used to only permit expected values.
  • G2.3b tolower() is not used, and character parameters are case-dependent
  • G2.4 Mechanisms provided to convert between different data types
  • G2.5 factor type inputs appropriate documented and processed.

Tabular Input

  • G2.6 Software accepts standard tabular inputs
  • 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.

  • G2.9 Extraction or filtering of single columns from tabular is appropriately performed regardless of input class.

Missing or Undefined Values

  • 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

  • G4.0 No local files produced, so not relvant

1.4 Testing

Test Data Sets

  • G5.0 Tests use standard data sets with known properties
  • 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.
    • G5.2a Messages produced by stop(), warning(), message()are unique.
    • G5.2b Tests do not trigger every one of those messages
  • G5.3 Absence of missing values form return results is explicitly tested.

Algorithm Tests

  • G5.4 Correctness tests are implemented.
  • G5.5 Correctness tests are run with a fixed random seed
  • 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
  • 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

  • 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

2.1 Input data structures and validation

  • RE1.0 Models are specified via a formula interface
  • RE1.1 Documentation is provided for how formula interfaces are converted to matrix representations of input data.

The main package vignette 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,

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.

  • RE1.3 All relevant aspects of input data are transferred to return objects
  • 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.

  • RE2.1–RE2.2 Appropriate processing of missing values is implemented.

lme4 provides exemplary handling of this case, as illustrated by the following code:

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

length (predict (m))

​​​​## [1] 179

length (predict (m, s))

​​​​## [1] 180
  • 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:

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

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

  • 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:

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

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

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:

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

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

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

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:

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

p <- predict (gm, type = "response", interval = "confidence")

​​​​## Warning in predict.merMod(gm, type = "response", interval = "confidence"):
​​​​## unused arguments ignored

p <- predict (gm, type = "response", interval = "prediction")

​​​​## Warning in predict.merMod(gm, type = "response", interval = "prediction"):
​​​​## unused arguments ignored

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
  • RE4.16 It is possible to submit new groups to predict() methods.*

Reporting Return Results

  • 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

  • RE6.0 Default plot methods provided for model objects
  • 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

  • RE7.3 Tests demonstrate that output objects retain aspects of input data such as row or case names.
  • 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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