ReaderBench Model 1e Variable Importance - shmercer/writeAlizer GitHub Wiki

Relative Importance of Each Metric

ReaderBench Model 1e

This model used ReaderBench scores from 7 min narrative writing samples ("I once had a magic pencil and ...") from 131 students in the winter of Grades 2-5 (Mercer et al., 2019) to predict holistic writing quality on the samples (elo ratings calculated from paired comparisons).

Principal component scores were generated during data pre-processing (see section on Scoring Model Development for more details).

Mercer, S. H., Keller-Margulis, M. A., Faith, E. L., Reid, E. K., & Ochs, S. (2019). The potential for automated text evaluation to improve the technical adequacy of written expression curriculum-based measurement. Learning Disability Quarterly, 42, 117-128. https://doi.org/10.1177/0731948718803296

Algorithm Weightings in Ensemble

Abbreviations:

  • all = ensemble model
  • gbm = stochastic gradient boosted trees
  • pls = partial least squares regression
  • svm = support vector machines
  • enet = elastic net regression
  • rf = random forest regression
  • mars = bagged multivariate adaptive regression splines
  • cube = cubist regression

The table below presents the linear weightings of each algorithm for the ensemble model.

Intercept gbm pls svm enet rf mars cube
-8.0185 0.0573 0.5839 0.5269 -0.3984 0.1184 0.1066 0.0459

Metric Importance in Each Algorithm and Ensemble

Each column sums to 100 (so values can be interpreted as % contribution to the model).

PC1 = scores on 1st principal component extracted, ...

Note: Importance is unavailable for support vector machines when PCA-based pre-processing is used (so all values for svm are 0).

Metric all gbm pls svm enet rf mars cube
PC2 32.8 53 47.34 0 9.95 26.16 39.14 22.22
PC1 7.63 1.98 13.73 0 1.84 4.83 0 11.11
PC39 4.81 1.96 1.08 0 7.68 2.76 17.37 8.89
PC5 4.35 2.14 4.78 0 4.24 3.9 0 13.33
PC11 4.33 1.43 3.55 0 5.85 1.52 4.87 11.11
PC37 4.21 1.94 1.15 0 7.47 1.75 12.15 6.67
PC6 3.45 3.05 3.87 0 3.53 2.17 0 8.89
PC26 3.28 2.41 1.25 0 4.41 1.69 14.49 0
PC38 3.13 0.57 1.08 0 7.55 0.99 0 6.67
PC14 2.89 4.55 1.94 0 3.33 6.23 0 6.67
PC24 2.2 1.36 1.07 0 3.24 0.49 8.2 0
PC40 2.12 0.85 0.72 0 5.11 1.28 0 2.22
PC9 1.75 0.72 2.06 0 2.21 0.62 0 2.22
PC33 1.63 0.91 0.67 0 2.86 2.41 2.5 0
PC45 1.61 0.26 0.5 0 4.33 0.63 0 0
PC44 1.51 0.65 0.49 0 3.6 1.94 0 0
PC32 1.3 0.87 0.67 0 2.61 1.92 0 0
PC20 1.29 1.94 1 0 2.28 0.76 0 0
PC4 1.16 1.23 1.61 0 0.82 1.5 0 0
PC19 1.07 1.79 0.78 0 1.41 2.19 0 0
PC34 0.98 1.11 0.5 0 1.9 1.2 0.26 0
PC43 0.97 0.27 0.42 0 2.53 0 0 0
PC8 0.95 0.61 1.17 0 0.8 1.73 0 0
PC15 0.94 1.05 0.88 0 1.21 1.47 0 0
PC23 0.9 0.73 0.64 0 1.33 1.89 0 0
PC17 0.9 0.77 0.85 0 1.41 0.6 0 0
PC35 0.86 1.17 0.46 0 1.61 1.24 0 0
PC3 0.81 0.64 1.28 0 0.16 1.75 0 0
PC12 0.76 0.42 0.78 0 0.71 1.86 0 0
PC28 0.73 0.92 0.48 0 1.01 1.9 0 0
PC16 0.69 0.41 0.71 0 0.86 0.92 0 0
PC25 0.59 0.21 0.47 0 0.73 1.59 0 0
PC30 0.42 1.15 0.31 0 0.25 1.74 0 0
PC42 0.41 0.61 0.22 0 0.34 1.92 0 0
PC36 0.36 0.14 0.29 0 0.51 0.88 0 0
PC27 0.35 0.38 0.35 0 0.34 0.77 0 0
PC7 0.34 1.67 0.06 0 0 1.66 1.01 0
PC13 0.28 0.89 0.01 0 0 2.56 0 0
PC29 0.28 0.97 0.05 0 0 2.36 0 0
PC10 0.27 0.54 0.27 0 0 1.27 0 0
PC18 0.24 0.52 0.14 0 0 1.68 0 0
PC31 0.18 0.35 0.08 0 0 1.51 0 0
PC46 0.11 0.43 0.15 0 0 0.24 0 0
PC21 0.07 0.18 0 0 0 0.64 0 0
PC22 0.07 0.25 0.09 0 0 0.27 0 0
PC41 0.06 0 0 0 0 0.6 0 0

Proportion of Variance by Varimax Rotated Component (RC)

Due to space limitations, loadings for only the first five principal components are displayed. The full PCA results are available here

Variable RC1 RC2 RC3 RC4 RC5
SS loadings 46.99 34.24 14.94 7.95 6.95
Proportion Var 0.23 0.17 0.07 0.04 0.03
Cumulative Var 0.23 0.40 0.48 0.52 0.55
Proportion Explained 0.42 0.31 0.13 0.07 0.06
Cumulative Proportion 0.42 0.73 0.87 0.94 1.00

Varimax Rotated Loadings

Abbreviated ReaderBench metric names can be found here.

Metric RC1 RC2 RC3 RC4 RC5
Sentences -0.66 0.48 -0.05 -0.04 -0.26
Words 0.07 0.97 0 -0.08 -0.05
Content.words -0.05 0.94 0.07 0.07 -0.11
RdbltyFlesch -0.82 -0.19 -0.02 -0.12 0.09
RdbltyFog 0.91 0.17 0.01 0.04 0.01
RdbltyKincaid 0.91 0.18 0.01 0.05 0
RdbltyDaleChall 0.5 -0.34 0.11 -0.06 -0.22
AvgBlLen -0.11 0.91 0.08 0.13 -0.16
AvgCommaBl -0.23 0.38 0.06 -0.1 -0.1
AvgSenLen 0.9 0.26 0.08 0.15 0.03
AvgSenBl -0.66 0.48 -0.05 -0.04 -0.26
AvgUnqWdBl -0.08 0.91 0.05 0.12 -0.15
AvgUnqWdSen 0.93 0.22 0.08 0.12 0.05
AvgWdLen -0.21 0.26 -0.17 0.25 -0.46
AvgWdBl -0.05 0.94 0.07 0.07 -0.11
AvgWdSen 0.93 0.23 0.07 0.09 0.06
CharEnt -0.14 0.54 0.11 -0.02 -0.03
SenStDevUnqWd -0.23 0.5 0.04 0.09 0.41
SenStdDevWd -0.16 0.48 0.04 0.07 0.45
WdEnt 0.03 0.86 0.04 0.1 -0.13
WdLettStdDev -0.09 0.4 0.37 0.24 0.04
LxcDiv 0 0.81 0.09 0.2 -0.07
LxcSoph 0.36 0.09 -0.28 0.11 -0.35
SynSoph 0.82 0.44 0.12 0.14 0.12
AvgNounBl 0.01 0.76 0.11 0.03 -0.35
AvgPronounBl 0.1 0.79 -0.1 -0.13 0.18
AvgVerbBl 0.03 0.91 -0.05 -0.02 0.05
AvgAdverbBl 0.09 0.63 -0.01 -0.22 0.11
AvgAdjectiveBl -0.06 0.55 0.12 -0.07 -0.09
AvgPrepositionBl 0.11 0.75 -0.04 0.27 -0.1
AvgNounSen 0.9 0.06 0.06 0.06 -0.14
AvgPronounSen 0.91 0.1 -0.08 -0.02 0.15
AvgVerbSen 0.94 0.16 -0.01 0.04 0.09
AvgAdverbSen 0.77 0.15 -0.02 -0.13 0.18
AvgAdjectiveSen 0.71 0.11 0.13 -0.13 0.1
AvgPrepositionSen 0.85 0.2 -0.07 0.26 -0.04
AvgUnqNoundBl 0.02 0.71 0.05 0.02 -0.36
AvgUnqPronounBl 0.09 0.66 -0.01 -0.09 0.02
AvgUnqVerbBl 0.03 0.85 -0.05 0.01 0.04
AvgUnqAdverbBl -0.01 0.61 -0.02 -0.13 0.05
AvgUnqAdjectiveBl -0.06 0.57 0.12 -0.09 -0.13
AvgUnqPrepositionBl 0.09 0.71 0 0.3 -0.14
AvgPronBl_first_person 0.09 0.69 -0.05 -0.14 0.12
AvgPronBl_indefinite -0.05 0.45 0.01 0.24 -0.04
AggPronSen_indefinite 0.62 0.17 0.05 0.23 0.02
AvgPronBl_third_person 0.13 0.48 -0.08 -0.12 0.14
AggPronSen_third_person 0.84 -0.02 -0.09 -0.09 0.12
AvgSemDep 0.97 0.12 -0.01 -0.06 0.06
WdDiffLemmaStem -0.11 0.06 -0.23 -0.01 -0.24
WdDiffWdStem -0.28 0.19 0.03 0.16 -0.28
WdMaxDpthHypernymTree -0.02 -0.26 -0.09 0.14 -0.23
WdAvgDpthHypernymTree 0 -0.27 -0.11 0.13 -0.24
WdPathCntHypernymTree -0.1 -0.26 -0.17 0.16 -0.09
WdPolysemyCnt 0.06 0.11 -0.09 -0.09 0.35
WdSylCnt -0.1 0.05 -0.26 0.11 -0.46
AvgAOADoc_Shock 0.03 0.43 0.12 0.27 -0.28
AvgAOABl_Shock 0.03 0.43 0.12 0.27 -0.28
AvgAOASen_Shock 0.46 0.21 0.05 0.31 -0.27
AvgAOADoc_Cortese -0.17 0.07 0.69 0.22 0.19
AvgAOABl_Cortese -0.17 0.07 0.69 0.22 0.19
AvgAOASen_Cortese 0.14 0.01 0.55 0.3 0.17
AvgAOADoc_Kuperman -0.22 -0.03 0.43 0.31 -0.38
AvgAOABl_Kuperman -0.22 -0.03 0.43 0.31 -0.38
AvgAOASen_Kuperman -0.03 -0.04 0.42 0.41 -0.3
AvgAOADoc_Bird -0.12 0.17 0.55 0.32 0.21
AvgAOABl_Bird -0.12 0.17 0.55 0.32 0.21
AvgAOASen_Bird 0.23 0.12 0.43 0.36 0.21
AvgAOADoc_Bristol -0.06 0.24 0.54 0.25 -0.04
AvgAOABl_Bristol -0.06 0.24 0.54 0.25 -0.04
AvgAOASen_Bristol 0.37 0.08 0.34 0.26 0
AvgAOEDoc_IndexPolyFAT.3 -0.02 -0.07 0.77 -0.22 -0.14
AvgAOEBl_IndexPolyFAT.3 -0.02 -0.07 0.77 -0.22 -0.14
AvgAOESen_IndexPolyFAT.3 0.02 -0.02 0.74 -0.12 -0.17
AvgAOEDoc_InvLinRegSlo 0 -0.1 0.82 -0.22 -0.09
AvgAOEBl_InvLinRegSlo 0 -0.1 0.82 -0.22 -0.09
AvgAOESen_InvLinRegSlo 0.17 -0.02 0.67 -0.02 -0.11
AvgAOEDoc_InfPointPoly -0.1 0.01 0.86 -0.15 0.1
AvgAOEBl_InfPointPoly -0.1 0.01 0.86 -0.15 0.1
AvgAOESen_InfPointPoly 0.07 0.03 0.73 0.02 0.05
AvgAOEDoc_InvAverage -0.11 0 0.88 -0.14 0.06
AvgAOEBl_InvAverage -0.11 0 0.88 -0.14 0.06
AvgAOESen_InvAverage 0.06 0.02 0.74 0.03 0.02
AvgAOEDoc_IndexAbThr.0.3. 0.03 -0.04 0.77 -0.12 -0.21
AvgAOEBl_IndexAbThr.0.3. 0.03 -0.04 0.77 -0.12 -0.21
AvgAOESen_IndexAbThr.0.3. 0.05 0 0.75 -0.04 -0.27
AvgNmdEntBl -0.07 0.32 0.15 -0.11 -0.44
AvgNounNmdEntBl -0.02 0.24 0.24 -0.13 -0.43
AvgUnqNmdEntBl -0.07 0.34 0.12 -0.09 -0.48
AvgNmdEntSen 0.59 0.01 0.19 -0.09 -0.26
TCorefChainDoc 0.04 0.69 0.06 -0.2 -0.01
AvgCorefChain 0.02 0.46 -0.18 0 0.11
AvgChainSpan 0.06 0.73 -0.03 0.07 -0.1
AvgInferenceDistChain 0.45 0.31 -0.02 0.31 0.07
TActCorefChainWd -0.02 -0.25 -0.04 -0.19 0.04
TCorefChainBigSpan 0.19 0.52 -0.02 -0.09 -0.01
AvgConnBl_addition 0.1 0.53 0.1 -0.58 -0.08
AvgConnSen_addition 0.74 0.04 0.05 -0.4 -0.02
AvgConnBl_conjunctions 0.15 0.59 0.09 -0.57 0.06
AvgConnSen_conjunctions 0.83 0.04 0.06 -0.36 0.06
AvgConnBl_contrasts 0.19 0.37 0 -0.11 0.28
AvgConnSen_contrasts 0.63 0.11 0.04 -0.11 0.22
AvgConnBl_coord_conjs 0.17 0.47 -0.17 0.14 0.23
AvgConnSen_coord_conjs 0.63 0.25 -0.14 0.21 0.25
AvgConnBl_coord_connects 0.21 0.7 -0.02 -0.4 0.18
AvgConnSen_coord_connects 0.88 0.1 -0.02 -0.23 0.17
AvgConnBl_logical_conn 0.09 0.5 0.07 -0.64 0.05
AvgConnSen_logical_conn 0.67 -0.02 0.03 -0.5 0.1
AvgConnBl_oppositions 0.19 0.37 0.05 0.02 0.22
AvgConnSen_oppositions 0.6 0.16 0.07 0.12 0.11
AvgConnBl_order 0.12 0.38 0.05 -0.29 -0.16
AvgConnSen_order 0.57 0.14 0.02 -0.07 -0.1
AvgConnBl_reas_purp 0.18 0.58 -0.07 -0.03 0.09
AvgConnSen_reas_purp 0.73 0.25 -0.06 0.08 0.09
AvgConnBl_semi_coords 0.17 0.47 -0.17 0.14 0.23
AvgConnSen_semi_coords 0.63 0.25 -0.14 0.21 0.25
AvgConnBl_sentence_link 0.2 0.77 -0.01 -0.33 0.13
AvgConnSen_sentence_link 0.92 0.14 -0.03 -0.13 0.12
AvgConnBl_simp_subords -0.02 0.41 -0.05 0.27 0.11
AvgConnSen_simp_subords 0.52 0.18 -0.09 0.34 0.16
AvgConnBl_temp_conn -0.14 0.36 0.05 -0.23 0.08
AvgConnSen_temp_conn 0.36 0.06 0.04 -0.25 0.27
LexChainAvgSpan 0.07 0.49 0.03 -0.01 0.16
LexChainMaxSp 0 0.72 0 -0.02 0.08
AvgBlScore 0.14 0.82 0.01 0 0.13
AvgSenScore 0.9 0.22 0.02 0.04 0.14
SenScoreStDev -0.27 0.5 0.04 0.05 0.45
AvgIntraBlCoh_LeackChod -0.73 0.44 0.16 0.2 0.17
AvgSenAdjCoh_LeackChod -0.7 0.43 0.19 0.22 0.17
AvgSenBlCoh_LeackChod 0.77 -0.38 -0.13 -0.08 0.09
AvgIntraBlCoh_WuPalmer -0.74 0.44 0.16 0.2 0.18
AvgSenAdjCoh_WuPalmer -0.7 0.43 0.19 0.22 0.17
AvgSenBlCoh_WuPalmer 0.79 -0.39 -0.13 -0.09 0.08
AvgIntraBlCoh_Path -0.73 0.43 0.16 0.2 0.19
AvgSenAdjCoh_Path -0.7 0.42 0.19 0.22 0.2
AvgSenBlCoh_Path 0.82 -0.42 -0.12 -0.13 0.08
AvgIntraBlCoh_LSA -0.73 0.46 0.16 0.18 0.18
AvgSenAdjCoh_LSA -0.7 0.44 0.2 0.22 0.18
AvgSenBlCoh_LSA 0.8 -0.35 -0.11 -0.12 0.11
AvgIntraBlCoh_LDA -0.73 0.48 0.16 0.18 0.15
AvgSenAdjCoh_LDA -0.7 0.47 0.2 0.2 0.15
AvgSenBlCoh_LDA 0.75 -0.21 -0.13 -0.11 0.08
AvgIntraBlCoh_word2vec -0.73 0.45 0.16 0.19 0.18
AvgSenAdjCoh_word2vec -0.7 0.44 0.2 0.22 0.18
AvgSenBlCoh_word2vec 0.8 -0.39 -0.1 -0.11 0.11
AvgBlVoiceCoOcc 0.03 0.63 -0.05 -0.04 -0.01
AvgVoice -0.01 0.6 -0.08 -0.05 0
AvgSenSyll 0.98 0.12 0.01 0.02 0.02
AvgSenStressedSyll 0.94 0.22 0.07 0.08 0.05
AvgRhythmUnits 0.23 0.26 0.15 0.01 0.28
AvgRhythmUnitSyll 0.84 0.01 -0.09 0.02 -0.09
AvgRhythmUnitStreesSyll 0.81 0.11 -0.01 0.08 -0.05
LangRhythmCoeff 0.39 -0.1 -0.21 -0.17 -0.06
LangRhythmId -0.11 -0.02 -0.4 -0.27 -0.14
FrqRhythmId 0.72 -0.3 0.01 -0.12 0.04
LangRhythmDiameter 0.27 -0.01 -0.34 -0.25 -0.19
SenAsson 0.13 0.25 0.12 -0.11 -0.17
AvgDepsBl_acl -0.03 0.24 0.15 0.19 -0.16
AvgDepsSen_acl 0.44 0.03 0.26 0.09 -0.13
AvgDepsBl_advcl 0.23 0.52 -0.05 0.1 0.16
AvgDepsSen_advcl 0.67 0.21 -0.08 0.2 0.09
AvgDepsBl_advmod 0.07 0.67 0.03 -0.25 0.13
AvgDepsSen_advmod 0.78 0.15 0.02 -0.17 0.2
AvgDepsBl_amod -0.07 0.39 0.16 0.06 -0.2
AvgDepsSen_amod 0.62 0.1 0.17 0 -0.01
AvgDepsBl_aux 0.13 0.37 -0.13 0.13 0.24
AvgDepsSen_aux 0.56 0.02 -0.14 -0.01 0.27
AvgDepsBl_auxpass 0.06 0.26 0.08 0.05 0.03
AvgDepsBl_case 0.06 0.69 0.01 0.15 -0.26
AvgDepsSen_case 0.84 0.13 -0.02 0.15 -0.17
AvgDepsBl_cc 0.17 0.59 0.08 -0.61 0.09
AvgDepsSen_cc 0.8 0.02 0.05 -0.42 0.11
AvgDepsBl_ccomp 0.37 0.51 -0.03 -0.01 0.32
AvgDepsSen_ccomp 0.78 0.16 -0.01 -0.01 0.19
AvgDepsBl_compound 0.17 0.16 0.19 -0.05 -0.36
AvgDepsSen_compound 0.61 -0.12 0.18 -0.07 -0.27
AvgDepsBl_conj 0.23 0.52 0.06 -0.58 0.14
AvgDepsSen_conj 0.77 0.02 0.04 -0.4 0.13
AvgDepsBl_cop 0.04 0.49 0.09 0.03 -0.1
AvgDepsSen_cop 0.71 0.16 0.14 0.04 -0.03
AvgDepsBl_dep 0.2 0.22 0.08 -0.34 0.07
AvgDepsSen_dep 0.56 -0.05 0.1 -0.31 0.11
AvgDepsBl_det -0.09 0.58 -0.03 0.05 -0.28
AvgDepsSen_det 0.86 0.1 -0.02 0.04 -0.16
AvgDepsBl_dobj 0 0.73 0.03 -0.2 0.01
AvgDepsSen_dobj 0.91 0.07 -0.01 -0.04 0.1
AvgDepsBl_mark 0.22 0.63 -0.11 0.28 0.09
AvgDepsSen_mark 0.78 0.25 -0.1 0.28 0.05
AvgDepsBl_mwe -0.07 0.19 0.06 0 -0.02
AvgDepsSen_mwe 0.3 0 0.03 -0.09 0.05
AvgDepsBl_neg 0.03 0.37 -0.08 -0.03 0.25
AvgDepsSen_neg 0.38 0.12 -0.04 0.05 0.28
AvgDepsBl_nmod 0.05 0.64 -0.01 0.17 -0.27
AvgDepsSen_nmod 0.83 0.07 -0.06 0.14 -0.18
AvgDepsBl_nsubj 0.03 0.9 -0.1 -0.1 0.08
AvgDepsSen_nsubj 0.94 0.14 -0.07 0.01 0.14
AvgDepsBl_nsubjpass 0.05 0.2 0.03 0.08 0.16
AvgDepsBl_nummod -0.09 0.17 -0.05 0.04 -0.2
AvgDepsBl_punct -0.53 0.52 -0.01 -0.06 -0.17
AvgDepsSen_punct -0.13 0.35 0.14 0.12 0.26
AvgDepsBl_xcomp 0.08 0.49 -0.03 0.01 -0.11
AvgDepsSen_xcomp 0.63 0.15 0.02 -0.06 -0.1