Returns structured data from an ackwards object in tidy format. The
default (what = "edges") returns the graph edge list that drives diagrams.
A factor is a summary variable standing in for a group of items that move
together, and a loading is the correlation between an item and a factor.
Arguments
- x
An
ackwardsobject.- what
What to extract:
"edges"(default): one row per directed between-level edge, with columnsfrom,to,level_from,level_to,r,beta,is_primary,above_cut. The columnris the correlation between the two factors' scores. The columnbetais the partialled coefficient. It is the standardized regression weight of thetofactor on all factors of thefromlevel together. It removes the part ofrthat the other factors at thefromlevel share. Under the default varimax rotation the factors within a level are uncorrelated, sobetaequalsr. The two come apart only when the factors within a level are correlated. When the within-level score correlation of thefromlevel cannot be inverted,betaisNAfor that level's edges and a warning names the level. That within-level score correlation always comes from the stored score weights and the fit's correlation matrix. This holds even whenrcame from materialised scores (edge_method = "scores", or the scores path under missing data). On those paths the two bases can differ slightly, sobetais then an approximation of the regression weight. Ifboot_edges()has been run on the object, four bootstrap columns are appended:se,lo,hi(bootstrap standard error and percentile confidence-interval endpoints), andn_boot_ok(usable replicates)."loadings": one row per item x factor x level, with columnslevel,factor,item,loading,se,ci_lower,ci_upper. The columnsse,ci_lower, andci_upperare populated only forengine = "esem". That engine produces loading SEs that account for the rotation, which is the step that turns the raw solution into a more interpretable one. They areNAfor PCA (principal component analysis) and EFA (exploratory factor analysis). The confidence level is controlled byconf_level."variance": one row per factor x level, with columnslevel,factor,proportion,cumulative,r2. The first two are proportions of total item variance on a 0-1 scale (multiply by 100 for a percentage). The columnr2is the share of the factor's score variance that all factors of the level just above account for together. It is also a proportion on a 0-1 scale, but of that factor's own score variance, not of total item variance, so it is not comparable withproportionorcumulative. It isNAat level 1, which has no level above. Under the default varimax rotationr2equals the sum of the squaredrvalues of that factor's edges from the level above. It isNA, with a warning, when the level above's within-level score correlation cannot be inverted."factor_cor": one row per pair of factors within a level, with columnslevel,factor_a,factor_b,cor. The columncoris the correlation between the two factors as the engine reports it, in the stored column order and sign. Level 1 has one factor and contributes no row. Under the default varimax rotation everycoris 0."fit": one row per fit statistic x level, with columnslevel,statistic,value. For PCA objects the statistics are eigenvalues. For EFA objects they arechi,dof,p_value,RMSEA,TLI, andBIC, wherechiis the likelihood-ratio chi-square (psych::fa()'sSTATISTIC). Sochi,dof,p_value,RMSEA, andTLIall share one statistical framing. (psych's residual-based empirical chi-square is a different statistic and is not reported.) For ESEM (exploratory structural equation modeling) they arechi,dof,p_value,CFI,TLI,RMSEA,SRMR,BIC. Three estimators run a scaled test:"WLSMV"and"ULSMV"for ordinal items (a few ordered categories, such as a 1 to 5 rating), and"MLR"for continuous ones. Under any of them the whole row reports lavaan's mean-and-variance-adjusted ("scaled") variant, so every quantity shares one scaling. That coverschi,dof, andp_valueandCFI,TLI, andRMSEA. This matters most for WLSMV and ULSMV. The naive chi-square has no valid reference distribution (lavaan's ownsummary()labels its p-value "Unknown"), and the naiveCFIandTLIare badly optimistic for ordinal data (Xia & Yang, 2019). The estimator"ML"has no scaled variant, so it reports the naive values (the correct ones for ML). The statisticSRMRhas no scaled variant and is reported as-is. The statisticBICisNAunder WLSMV and ULSMV, because a limited-information estimator has no proper log-likelihood, and it is populated under ML and MLR. Useformat = "wide"for one row per non-anchor level and one column per statistic. Non-anchor means k >= 2, because the saturated 1-factor anchor is dropped, matchingsummary()andautoplot(what = "fit"). Conventional fit cutoffs (Hu & Bentler 1999) are shown as reference lines inautoplot(what = "fit")and inline insummary(), but are not returned as a pass/fail column here. They are contested thresholds, report-only, and never gate anything (see those functions' docs). Theformatargument is oriented to the EFA and ESEM model-fit statistics. For PCA the "statistics" are per-component eigenvalues."nodes": Forbes-extension pruning annotations (requiresprune != "none"when the object was created). One row per factor across all levels, with columnsid,level,pruned,prune_reason. Returns an empty data frame with the same columns when no pruning was applied."scores": long-format per-observation factor scores, where a factor score is each person's estimated standing on a factor (requireskeep_scores = TRUEat fit time or useaugment.ackwards()for on-the-fly computation). Columns:obs(row index),level,factor,score.
- primary_only
For
what = "edges"only. WhenTRUE, returns just each factor's primary-parent edge (is_primary == TRUE). That is the lineage tree that the diagram draws as solid arrows. DefaultFALSE(all edges). Errors for any other value ofwhat.- sort
For
what = "edges"only. One of"none"(default, natural order) or"strength"(descending|r|). Ignored for all other values ofwhat.- format
For
what = "fit"only. One of"long"(default, one row per statistic x level) or"wide"(one row per level, one column per statistic). Errors for all other values ofwhat.- conf_level
For
what = "loadings"only. Confidence level for the loading intervals. Default0.95. The intervals are computed asloading ± qnorm((1 + conf_level) / 2) * seand areNAfor engines that carry no SEs (PCA, EFA). Errors for all other values ofwhat.- ...
Ignored.
Factor labels
If factor labels have been attached to the object, the
output gains display-only label columns: factor_label for what = "loadings", "variance", or "scores", from_label/to_label for
what = "edges", and factor_a_label/factor_b_label for what = "factor_cor". Each carries the label for a labeled factor and NA
otherwise. These columns are absent when no labels are set, so an
unlabeled object's output is unchanged. The ID columns (factor, from,
to) are never altered.
Examples
x <- ackwards(sim16, k_max = 5)
tidy(x) # edges in natural order
#> from to level_from level_to r beta is_primary
#> 1 m1f1 m2f1 1 2 0.7072961126 0.7072961126 TRUE
#> 2 m1f1 m2f2 1 2 0.7069173991 0.7069173991 TRUE
#> 3 m2f1 m3f1 2 3 -0.0113423946 -0.0113423946 FALSE
#> 4 m2f1 m3f2 2 3 0.6970929809 0.6970929809 TRUE
#> 5 m2f1 m3f3 2 3 0.7168910141 0.7168910141 TRUE
#> 6 m2f2 m3f1 2 3 0.9955932310 0.9955932310 TRUE
#> 7 m2f2 m3f2 2 3 0.0746157674 0.0746157674 FALSE
#> 8 m2f2 m3f3 2 3 -0.0568032178 -0.0568032178 FALSE
#> 9 m3f1 m4f1 3 4 -0.0164580578 -0.0164580578 FALSE
#> 10 m3f1 m4f2 3 4 -0.0048128349 -0.0048128349 FALSE
#> 11 m3f1 m4f3 3 4 0.6639134885 0.6639134885 TRUE
#> 12 m3f1 m4f4 3 4 0.7476127666 0.7476127666 TRUE
#> 13 m3f2 m4f1 3 4 0.9406477359 0.9406477359 TRUE
#> 14 m3f2 m4f2 3 4 0.0317352150 0.0317352150 FALSE
#> 15 m3f2 m4f3 3 4 0.2627656201 0.2627656201 FALSE
#> 16 m3f2 m4f4 3 4 -0.2124357359 -0.2124357359 FALSE
#> 17 m3f3 m4f1 3 4 0.0512578921 0.0512578921 FALSE
#> 18 m3f3 m4f2 3 4 0.9707784269 0.9707784269 TRUE
#> 19 m3f3 m4f3 3 4 -0.1715840980 -0.1715840980 FALSE
#> 20 m3f3 m4f4 3 4 0.1597522194 0.1597522194 FALSE
#> 21 m4f1 m5f1 4 5 0.9997725525 0.9997725525 TRUE
#> 22 m4f1 m5f2 4 5 0.0020429352 0.0020429352 FALSE
#> 23 m4f1 m5f3 4 5 -0.0043948033 -0.0043948033 FALSE
#> 24 m4f1 m5f4 4 5 0.0034107252 0.0034107252 FALSE
#> 25 m4f1 m5f5 4 5 -0.0204871256 -0.0204871256 FALSE
#> 26 m4f2 m5f1 4 5 -0.0019639857 -0.0019639857 FALSE
#> 27 m4f2 m5f2 4 5 0.9999850115 0.9999850115 TRUE
#> 28 m4f2 m5f3 4 5 -0.0025910717 -0.0025910717 FALSE
#> 29 m4f2 m5f4 4 5 -0.0012689323 -0.0012689323 FALSE
#> 30 m4f2 m5f5 4 5 0.0042184956 0.0042184956 FALSE
#> 31 m4f3 m5f1 4 5 0.0043781997 0.0043781997 FALSE
#> 32 m4f3 m5f2 4 5 0.0026035592 0.0026035592 FALSE
#> 33 m4f3 m5f3 4 5 0.9999840561 0.9999840561 TRUE
#> 34 m4f3 m5f4 4 5 0.0024297386 0.0024297386 FALSE
#> 35 m4f3 m5f5 4 5 -0.0001914960 -0.0001914960 FALSE
#> 36 m4f4 m5f1 4 5 -0.0016399230 -0.0016399230 FALSE
#> 37 m4f4 m5f2 4 5 0.0008901375 0.0008901375 FALSE
#> 38 m4f4 m5f3 4 5 -0.0023992589 -0.0023992589 FALSE
#> 39 m4f4 m5f4 4 5 0.9962530528 0.9962530528 TRUE
#> 40 m4f4 m5f5 4 5 0.0864327285 0.0864327285 TRUE
#> above_cut
#> 1 TRUE
#> 2 TRUE
#> 3 FALSE
#> 4 TRUE
#> 5 TRUE
#> 6 TRUE
#> 7 FALSE
#> 8 FALSE
#> 9 FALSE
#> 10 FALSE
#> 11 TRUE
#> 12 TRUE
#> 13 TRUE
#> 14 FALSE
#> 15 FALSE
#> 16 FALSE
#> 17 FALSE
#> 18 TRUE
#> 19 FALSE
#> 20 FALSE
#> 21 TRUE
#> 22 FALSE
#> 23 FALSE
#> 24 FALSE
#> 25 FALSE
#> 26 FALSE
#> 27 TRUE
#> 28 FALSE
#> 29 FALSE
#> 30 FALSE
#> 31 FALSE
#> 32 FALSE
#> 33 TRUE
#> 34 FALSE
#> 35 FALSE
#> 36 FALSE
#> 37 FALSE
#> 38 FALSE
#> 39 TRUE
#> 40 FALSE
tidy(x, sort = "strength") # strongest edges first
#> from to level_from level_to r beta is_primary
#> 1 m4f2 m5f2 4 5 0.9999850115 0.9999850115 TRUE
#> 2 m4f3 m5f3 4 5 0.9999840561 0.9999840561 TRUE
#> 3 m4f1 m5f1 4 5 0.9997725525 0.9997725525 TRUE
#> 4 m4f4 m5f4 4 5 0.9962530528 0.9962530528 TRUE
#> 5 m2f2 m3f1 2 3 0.9955932310 0.9955932310 TRUE
#> 6 m3f3 m4f2 3 4 0.9707784269 0.9707784269 TRUE
#> 7 m3f2 m4f1 3 4 0.9406477359 0.9406477359 TRUE
#> 8 m3f1 m4f4 3 4 0.7476127666 0.7476127666 TRUE
#> 9 m2f1 m3f3 2 3 0.7168910141 0.7168910141 TRUE
#> 10 m1f1 m2f1 1 2 0.7072961126 0.7072961126 TRUE
#> 11 m1f1 m2f2 1 2 0.7069173991 0.7069173991 TRUE
#> 12 m2f1 m3f2 2 3 0.6970929809 0.6970929809 TRUE
#> 13 m3f1 m4f3 3 4 0.6639134885 0.6639134885 TRUE
#> 14 m3f2 m4f3 3 4 0.2627656201 0.2627656201 FALSE
#> 15 m3f2 m4f4 3 4 -0.2124357359 -0.2124357359 FALSE
#> 16 m3f3 m4f3 3 4 -0.1715840980 -0.1715840980 FALSE
#> 17 m3f3 m4f4 3 4 0.1597522194 0.1597522194 FALSE
#> 18 m4f4 m5f5 4 5 0.0864327285 0.0864327285 TRUE
#> 19 m2f2 m3f2 2 3 0.0746157674 0.0746157674 FALSE
#> 20 m2f2 m3f3 2 3 -0.0568032178 -0.0568032178 FALSE
#> 21 m3f3 m4f1 3 4 0.0512578921 0.0512578921 FALSE
#> 22 m3f2 m4f2 3 4 0.0317352150 0.0317352150 FALSE
#> 23 m4f1 m5f5 4 5 -0.0204871256 -0.0204871256 FALSE
#> 24 m3f1 m4f1 3 4 -0.0164580578 -0.0164580578 FALSE
#> 25 m2f1 m3f1 2 3 -0.0113423946 -0.0113423946 FALSE
#> 26 m3f1 m4f2 3 4 -0.0048128349 -0.0048128349 FALSE
#> 27 m4f1 m5f3 4 5 -0.0043948033 -0.0043948033 FALSE
#> 28 m4f3 m5f1 4 5 0.0043781997 0.0043781997 FALSE
#> 29 m4f2 m5f5 4 5 0.0042184956 0.0042184956 FALSE
#> 30 m4f1 m5f4 4 5 0.0034107252 0.0034107252 FALSE
#> 31 m4f3 m5f2 4 5 0.0026035592 0.0026035592 FALSE
#> 32 m4f2 m5f3 4 5 -0.0025910717 -0.0025910717 FALSE
#> 33 m4f3 m5f4 4 5 0.0024297386 0.0024297386 FALSE
#> 34 m4f4 m5f3 4 5 -0.0023992589 -0.0023992589 FALSE
#> 35 m4f1 m5f2 4 5 0.0020429352 0.0020429352 FALSE
#> 36 m4f2 m5f1 4 5 -0.0019639857 -0.0019639857 FALSE
#> 37 m4f4 m5f1 4 5 -0.0016399230 -0.0016399230 FALSE
#> 38 m4f2 m5f4 4 5 -0.0012689323 -0.0012689323 FALSE
#> 39 m4f4 m5f2 4 5 0.0008901375 0.0008901375 FALSE
#> 40 m4f3 m5f5 4 5 -0.0001914960 -0.0001914960 FALSE
#> above_cut
#> 1 TRUE
#> 2 TRUE
#> 3 TRUE
#> 4 TRUE
#> 5 TRUE
#> 6 TRUE
#> 7 TRUE
#> 8 TRUE
#> 9 TRUE
#> 10 TRUE
#> 11 TRUE
#> 12 TRUE
#> 13 TRUE
#> 14 FALSE
#> 15 FALSE
#> 16 FALSE
#> 17 FALSE
#> 18 FALSE
#> 19 FALSE
#> 20 FALSE
#> 21 FALSE
#> 22 FALSE
#> 23 FALSE
#> 24 FALSE
#> 25 FALSE
#> 26 FALSE
#> 27 FALSE
#> 28 FALSE
#> 29 FALSE
#> 30 FALSE
#> 31 FALSE
#> 32 FALSE
#> 33 FALSE
#> 34 FALSE
#> 35 FALSE
#> 36 FALSE
#> 37 FALSE
#> 38 FALSE
#> 39 FALSE
#> 40 FALSE
tidy(x, primary_only = TRUE) # just the primary-parent lineage
#> from to level_from level_to r beta is_primary above_cut
#> 1 m1f1 m2f1 1 2 0.70729611 0.70729611 TRUE TRUE
#> 2 m1f1 m2f2 1 2 0.70691740 0.70691740 TRUE TRUE
#> 3 m2f1 m3f2 2 3 0.69709298 0.69709298 TRUE TRUE
#> 4 m2f1 m3f3 2 3 0.71689101 0.71689101 TRUE TRUE
#> 5 m2f2 m3f1 2 3 0.99559323 0.99559323 TRUE TRUE
#> 6 m3f1 m4f3 3 4 0.66391349 0.66391349 TRUE TRUE
#> 7 m3f1 m4f4 3 4 0.74761277 0.74761277 TRUE TRUE
#> 8 m3f2 m4f1 3 4 0.94064774 0.94064774 TRUE TRUE
#> 9 m3f3 m4f2 3 4 0.97077843 0.97077843 TRUE TRUE
#> 10 m4f1 m5f1 4 5 0.99977255 0.99977255 TRUE TRUE
#> 11 m4f2 m5f2 4 5 0.99998501 0.99998501 TRUE TRUE
#> 12 m4f3 m5f3 4 5 0.99998406 0.99998406 TRUE TRUE
#> 13 m4f4 m5f4 4 5 0.99625305 0.99625305 TRUE TRUE
#> 14 m4f4 m5f5 4 5 0.08643273 0.08643273 TRUE FALSE
tidy(x, what = "loadings")
#> level factor item loading se ci_lower ci_upper
#> 1 1 m1f1 i1 0.461752431 NA NA NA
#> 2 1 m1f1 i2 0.485041500 NA NA NA
#> 3 1 m1f1 i3 0.514249968 NA NA NA
#> 4 1 m1f1 i4 0.515548605 NA NA NA
#> 5 1 m1f1 i5 0.575053347 NA NA NA
#> 6 1 m1f1 i6 0.568480393 NA NA NA
#> 7 1 m1f1 i7 0.589789932 NA NA NA
#> 8 1 m1f1 i8 0.508096441 NA NA NA
#> 9 1 m1f1 i9 0.563485394 NA NA NA
#> 10 1 m1f1 i10 0.551924658 NA NA NA
#> 11 1 m1f1 i11 0.546706411 NA NA NA
#> 12 1 m1f1 i12 0.563394632 NA NA NA
#> 13 1 m1f1 i13 0.519943165 NA NA NA
#> 14 1 m1f1 i14 0.525582317 NA NA NA
#> 15 1 m1f1 i15 0.502500732 NA NA NA
#> 16 1 m1f1 i16 0.481206189 NA NA NA
#> 17 2 m2f1 i1 0.670505125 NA NA NA
#> 18 2 m2f1 i2 0.688261361 NA NA NA
#> 19 2 m2f1 i3 0.666960388 NA NA NA
#> 20 2 m2f1 i4 0.695694541 NA NA NA
#> 21 2 m2f1 i5 0.677994613 NA NA NA
#> 22 2 m2f1 i6 0.671411581 NA NA NA
#> 23 2 m2f1 i7 0.688528565 NA NA NA
#> 24 2 m2f1 i8 0.646831586 NA NA NA
#> 25 2 m2f1 i9 0.142480573 NA NA NA
#> 26 2 m2f1 i10 0.106321144 NA NA NA
#> 27 2 m2f1 i11 0.099785669 NA NA NA
#> 28 2 m2f1 i12 0.132520254 NA NA NA
#> 29 2 m2f1 i13 0.045302307 NA NA NA
#> 30 2 m2f1 i14 0.056844031 NA NA NA
#> 31 2 m2f1 i15 0.027746191 NA NA NA
#> 32 2 m2f1 i16 0.002718709 NA NA NA
#> 33 2 m2f2 i1 -0.017672839 NA NA NA
#> 34 2 m2f2 i2 -0.002494047 NA NA NA
#> 35 2 m2f2 i3 0.060136416 NA NA NA
#> 36 2 m2f2 i4 0.033223911 NA NA NA
#> 37 2 m2f2 i5 0.135108279 NA NA NA
#> 38 2 m2f2 i6 0.132396786 NA NA NA
#> 39 2 m2f2 i7 0.145414946 NA NA NA
#> 40 2 m2f2 i8 0.071571268 NA NA NA
#> 41 2 m2f2 i9 0.654545268 NA NA NA
#> 42 2 m2f2 i10 0.674370338 NA NA NA
#> 43 2 m2f2 i11 0.673527623 NA NA NA
#> 44 2 m2f2 i12 0.664382532 NA NA NA
#> 45 2 m2f2 i13 0.690181088 NA NA NA
#> 46 2 m2f2 i14 0.686610283 NA NA NA
#> 47 2 m2f2 i15 0.683072674 NA NA NA
#> 48 2 m2f2 i16 0.677990466 NA NA NA
#> 49 3 m3f1 i1 0.018282326 NA NA NA
#> 50 3 m3f1 i2 0.030497878 NA NA NA
#> 51 3 m3f1 i3 0.088799850 NA NA NA
#> 52 3 m3f1 i4 0.065163580 NA NA NA
#> 53 3 m3f1 i5 0.088559024 NA NA NA
#> 54 3 m3f1 i6 0.085162586 NA NA NA
#> 55 3 m3f1 i7 0.100894156 NA NA NA
#> 56 3 m3f1 i8 0.021040215 NA NA NA
#> 57 3 m3f1 i9 0.635370326 NA NA NA
#> 58 3 m3f1 i10 0.654349429 NA NA NA
#> 59 3 m3f1 i11 0.656287051 NA NA NA
#> 60 3 m3f1 i12 0.643589738 NA NA NA
#> 61 3 m3f1 i13 0.702820782 NA NA NA
#> 62 3 m3f1 i14 0.704046359 NA NA NA
#> 63 3 m3f1 i15 0.701468675 NA NA NA
#> 64 3 m3f1 i16 0.697838670 NA NA NA
#> 65 3 m3f2 i1 0.132996558 NA NA NA
#> 66 3 m3f2 i2 0.167151079 NA NA NA
#> 67 3 m3f2 i3 0.189869691 NA NA NA
#> 68 3 m3f2 i4 0.181206856 NA NA NA
#> 69 3 m3f2 i5 0.775819255 NA NA NA
#> 70 3 m3f2 i6 0.776938349 NA NA NA
#> 71 3 m3f2 i7 0.767129561 NA NA NA
#> 72 3 m3f2 i8 0.784709189 NA NA NA
#> 73 3 m3f2 i9 0.260572503 NA NA NA
#> 74 3 m3f2 i10 0.245798186 NA NA NA
#> 75 3 m3f2 i11 0.220477487 NA NA NA
#> 76 3 m3f2 i12 0.267289841 NA NA NA
#> 77 3 m3f2 i13 -0.040980546 NA NA NA
#> 78 3 m3f2 i14 -0.070825420 NA NA NA
#> 79 3 m3f2 i15 -0.096078981 NA NA NA
#> 80 3 m3f2 i16 -0.122682914 NA NA NA
#> 81 3 m3f3 i1 0.806261359 NA NA NA
#> 82 3 m3f3 i2 0.798011727 NA NA NA
#> 83 3 m3f3 i3 0.747129970 NA NA NA
#> 84 3 m3f3 i4 0.795261223 NA NA NA
#> 85 3 m3f3 i5 0.192750257 NA NA NA
#> 86 3 m3f3 i6 0.182425580 NA NA NA
#> 87 3 m3f3 i7 0.216089072 NA NA NA
#> 88 3 m3f3 i8 0.139567888 NA NA NA
#> 89 3 m3f3 i9 -0.044575909 NA NA NA
#> 90 3 m3f3 i10 -0.080348554 NA NA NA
#> 91 3 m3f3 i11 -0.064812882 NA NA NA
#> 92 3 m3f3 i12 -0.064871464 NA NA NA
#> 93 3 m3f3 i13 0.114161326 NA NA NA
#> 94 3 m3f3 i14 0.159301070 NA NA NA
#> 95 3 m3f3 i15 0.143227502 NA NA NA
#> 96 3 m3f3 i16 0.134128155 NA NA NA
#> 97 4 m4f1 i1 0.128686176 NA NA NA
#> 98 4 m4f1 i2 0.149030299 NA NA NA
#> 99 4 m4f1 i3 0.143394315 NA NA NA
#> 100 4 m4f1 i4 0.164542205 NA NA NA
#> 101 4 m4f1 i5 0.802597931 NA NA NA
#> 102 4 m4f1 i6 0.810490299 NA NA NA
#> 103 4 m4f1 i7 0.791631093 NA NA NA
#> 104 4 m4f1 i8 0.832623843 NA NA NA
#> 105 4 m4f1 i9 0.082991593 NA NA NA
#> 106 4 m4f1 i10 0.069135718 NA NA NA
#> 107 4 m4f1 i11 0.049095872 NA NA NA
#> 108 4 m4f1 i12 0.101317088 NA NA NA
#> 109 4 m4f1 i13 0.090878291 NA NA NA
#> 110 4 m4f1 i14 0.058515420 NA NA NA
#> 111 4 m4f1 i15 0.037287536 NA NA NA
#> 112 4 m4f1 i16 0.005030840 NA NA NA
#> 113 4 m4f2 i1 0.813408272 NA NA NA
#> 114 4 m4f2 i2 0.814344929 NA NA NA
#> 115 4 m4f2 i3 0.782025429 NA NA NA
#> 116 4 m4f2 i4 0.809823496 NA NA NA
#> 117 4 m4f2 i5 0.165603797 NA NA NA
#> 118 4 m4f2 i6 0.150442425 NA NA NA
#> 119 4 m4f2 i7 0.190612643 NA NA NA
#> 120 4 m4f2 i8 0.098061225 NA NA NA
#> 121 4 m4f2 i9 0.067952773 NA NA NA
#> 122 4 m4f2 i10 0.031112689 NA NA NA
#> 123 4 m4f2 i11 0.043242680 NA NA NA
#> 124 4 m4f2 i12 0.039067952 NA NA NA
#> 125 4 m4f2 i13 0.010228110 NA NA NA
#> 126 4 m4f2 i14 0.057767882 NA NA NA
#> 127 4 m4f2 i15 0.039026995 NA NA NA
#> 128 4 m4f2 i16 0.034210703 NA NA NA
#> 129 4 m4f3 i1 -0.015409920 NA NA NA
#> 130 4 m4f3 i2 0.025695304 NA NA NA
#> 131 4 m4f3 i3 0.126581449 NA NA NA
#> 132 4 m4f3 i4 0.046794854 NA NA NA
#> 133 4 m4f3 i5 0.099123172 NA NA NA
#> 134 4 m4f3 i6 0.084120174 NA NA NA
#> 135 4 m4f3 i7 0.108694221 NA NA NA
#> 136 4 m4f3 i8 0.018603667 NA NA NA
#> 137 4 m4f3 i9 0.800528531 NA NA NA
#> 138 4 m4f3 i10 0.810953636 NA NA NA
#> 139 4 m4f3 i11 0.796816493 NA NA NA
#> 140 4 m4f3 i12 0.784529901 NA NA NA
#> 141 4 m4f3 i13 0.162504347 NA NA NA
#> 142 4 m4f3 i14 0.161065367 NA NA NA
#> 143 4 m4f3 i15 0.148774737 NA NA NA
#> 144 4 m4f3 i16 0.154760740 NA NA NA
#> 145 4 m4f4 i1 0.046208286 NA NA NA
#> 146 4 m4f4 i2 0.026498312 NA NA NA
#> 147 4 m4f4 i3 0.014558967 NA NA NA
#> 148 4 m4f4 i4 0.054441870 NA NA NA
#> 149 4 m4f4 i5 0.049164544 NA NA NA
#> 150 4 m4f4 i6 0.058020972 NA NA NA
#> 151 4 m4f4 i7 0.057083956 NA NA NA
#> 152 4 m4f4 i8 0.030583096 NA NA NA
#> 153 4 m4f4 i9 0.141224932 NA NA NA
#> 154 4 m4f4 i10 0.156811061 NA NA NA
#> 155 4 m4f4 i11 0.171594148 NA NA NA
#> 156 4 m4f4 i12 0.166644111 NA NA NA
#> 157 4 m4f4 i13 0.797841995 NA NA NA
#> 158 4 m4f4 i14 0.800352794 NA NA NA
#> 159 4 m4f4 i15 0.807231575 NA NA NA
#> 160 4 m4f4 i16 0.796319167 NA NA NA
#> 161 5 m5f1 i1 0.125845182 NA NA NA
#> 162 5 m5f1 i2 0.146281625 NA NA NA
#> 163 5 m5f1 i3 0.141457000 NA NA NA
#> 164 5 m5f1 i4 0.166373116 NA NA NA
#> 165 5 m5f1 i5 0.802636385 NA NA NA
#> 166 5 m5f1 i6 0.805601696 NA NA NA
#> 167 5 m5f1 i7 0.794174370 NA NA NA
#> 168 5 m5f1 i8 0.834242419 NA NA NA
#> 169 5 m5f1 i9 0.079330358 NA NA NA
#> 170 5 m5f1 i10 0.071440903 NA NA NA
#> 171 5 m5f1 i11 0.053199270 NA NA NA
#> 172 5 m5f1 i12 0.111309787 NA NA NA
#> 173 5 m5f1 i13 0.088459037 NA NA NA
#> 174 5 m5f1 i14 0.055792727 NA NA NA
#> 175 5 m5f1 i15 0.032789698 NA NA NA
#> 176 5 m5f1 i16 0.011575744 NA NA NA
#> 177 5 m5f2 i1 0.813880739 NA NA NA
#> 178 5 m5f2 i2 0.814971814 NA NA NA
#> 179 5 m5f2 i3 0.782834508 NA NA NA
#> 180 5 m5f2 i4 0.809628684 NA NA NA
#> 181 5 m5f2 i5 0.167503047 NA NA NA
#> 182 5 m5f2 i6 0.153331666 NA NA NA
#> 183 5 m5f2 i7 0.192001129 NA NA NA
#> 184 5 m5f2 i8 0.099430502 NA NA NA
#> 185 5 m5f2 i9 0.071729201 NA NA NA
#> 186 5 m5f2 i10 0.033692262 NA NA NA
#> 187 5 m5f2 i11 0.045365102 NA NA NA
#> 188 5 m5f2 i12 0.040036629 NA NA NA
#> 189 5 m5f2 i13 0.011914118 NA NA NA
#> 190 5 m5f2 i14 0.059428222 NA NA NA
#> 191 5 m5f2 i15 0.040979436 NA NA NA
#> 192 5 m5f2 i16 0.033839573 NA NA NA
#> 193 5 m5f3 i1 -0.018210287 NA NA NA
#> 194 5 m5f3 i2 0.022847977 NA NA NA
#> 195 5 m5f3 i3 0.123874092 NA NA NA
#> 196 5 m5f3 i4 0.043893857 NA NA NA
#> 197 5 m5f3 i5 0.095050271 NA NA NA
#> 198 5 m5f3 i6 0.079955315 NA NA NA
#> 199 5 m5f3 i7 0.104624657 NA NA NA
#> 200 5 m5f3 i8 0.014647210 NA NA NA
#> 201 5 m5f3 i9 0.799531025 NA NA NA
#> 202 5 m5f3 i10 0.810165899 NA NA NA
#> 203 5 m5f3 i11 0.796079656 NA NA NA
#> 204 5 m5f3 i12 0.783678485 NA NA NA
#> 205 5 m5f3 i13 0.160134023 NA NA NA
#> 206 5 m5f3 i14 0.158704883 NA NA NA
#> 207 5 m5f3 i15 0.146512650 NA NA NA
#> 208 5 m5f3 i16 0.152849170 NA NA NA
#> 209 5 m5f4 i1 0.049869940 NA NA NA
#> 210 5 m5f4 i2 0.030875158 NA NA NA
#> 211 5 m5f4 i3 0.018057780 NA NA NA
#> 212 5 m5f4 i4 0.039945216 NA NA NA
#> 213 5 m5f4 i5 0.050944187 NA NA NA
#> 214 5 m5f4 i6 0.080103321 NA NA NA
#> 215 5 m5f4 i7 0.048270051 NA NA NA
#> 216 5 m5f4 i8 0.025018104 NA NA NA
#> 217 5 m5f4 i9 0.171116784 NA NA NA
#> 218 5 m5f4 i10 0.162190188 NA NA NA
#> 219 5 m5f4 i11 0.168862429 NA NA NA
#> 220 5 m5f4 i12 0.139322561 NA NA NA
#> 221 5 m5f4 i13 0.802972834 NA NA NA
#> 222 5 m5f4 i14 0.806163196 NA NA NA
#> 223 5 m5f4 i15 0.820241598 NA NA NA
#> 224 5 m5f4 i16 0.763490591 NA NA NA
#> 225 5 m5f5 i1 -0.046701926 NA NA NA
#> 226 5 m5f5 i2 -0.054283683 NA NA NA
#> 227 5 m5f5 i3 -0.041636964 NA NA NA
#> 228 5 m5f5 i4 0.165490526 NA NA NA
#> 229 5 m5f5 i5 -0.002239278 NA NA NA
#> 230 5 m5f5 i6 -0.236088047 NA NA NA
#> 231 5 m5f5 i7 0.120061811 NA NA NA
#> 232 5 m5f5 i8 0.080680811 NA NA NA
#> 233 5 m5f5 i9 -0.315461030 NA NA NA
#> 234 5 m5f5 i10 -0.031706091 NA NA NA
#> 235 5 m5f5 i11 0.061565807 NA NA NA
#> 236 5 m5f5 i12 0.345595171 NA NA NA
#> 237 5 m5f5 i13 -0.018551750 NA NA NA
#> 238 5 m5f5 i14 -0.027424572 NA NA NA
#> 239 5 m5f5 i15 -0.110696540 NA NA NA
#> 240 5 m5f5 i16 0.417028618 NA NA NA
tidy(x, what = "variance")
#> level factor proportion cumulative r2
#> 1 1 m1f1 0.28172978 0.2817298 NA
#> 2 2 m2f1 0.23251408 0.2325141 0.500267791
#> 3 2 m2f2 0.23246133 0.4649754 0.499732209
#> 4 3 m3f1 0.23028614 0.2302861 0.991334532
#> 5 3 m3f2 0.17522787 0.4055140 0.491506137
#> 6 3 m3f3 0.16924345 0.5747575 0.517159332
#> 7 4 m4f1 0.17155300 0.1715530 0.887716402
#> 8 4 m4f2 0.16895577 0.3405088 0.943441041
#> 9 4 m4f3 0.16846890 0.5089777 0.539267994
#> 10 4 m4f4 0.16753770 0.6765154 0.629574562
#> 11 5 m5f1 0.17147388 0.1714739 0.999570872
#> 12 5 m5f2 0.16935421 0.3408281 0.999981768
#> 13 5 m5f3 0.16774286 0.5085710 0.999999897
#> 14 5 m5f4 0.16695127 0.6755222 0.992539292
#> 15 5 m5f5 0.03262035 0.7081426 0.007908171
tidy(x, what = "factor_cor") # all 0 under varimax
#> level factor_a factor_b cor
#> 1 2 m2f1 m2f2 0
#> 2 3 m3f1 m3f2 0
#> 3 3 m3f1 m3f3 0
#> 4 3 m3f2 m3f3 0
#> 5 4 m4f1 m4f2 0
#> 6 4 m4f1 m4f3 0
#> 7 4 m4f1 m4f4 0
#> 8 4 m4f2 m4f3 0
#> 9 4 m4f2 m4f4 0
#> 10 4 m4f3 m4f4 0
#> 11 5 m5f1 m5f2 0
#> 12 5 m5f1 m5f3 0
#> 13 5 m5f1 m5f4 0
#> 14 5 m5f1 m5f5 0
#> 15 5 m5f2 m5f3 0
#> 16 5 m5f2 m5f4 0
#> 17 5 m5f2 m5f5 0
#> 18 5 m5f3 m5f4 0
#> 19 5 m5f3 m5f5 0
#> 20 5 m5f4 m5f5 0
tidy(x, what = "fit")
#> level statistic value
#> 1 1 eigenvalue.m1f1 4.5076765
#> 2 2 eigenvalue.m2f1 4.5076765
#> 3 2 eigenvalue.m2f2 2.9319301
#> 4 3 eigenvalue.m3f1 4.5076765
#> 5 3 eigenvalue.m3f2 2.9319301
#> 6 3 eigenvalue.m3f3 1.7565127
#> 7 4 eigenvalue.m4f1 4.5076765
#> 8 4 eigenvalue.m4f2 2.9319301
#> 9 4 eigenvalue.m4f3 1.7565127
#> 10 4 eigenvalue.m4f4 1.6281266
#> 11 5 eigenvalue.m5f1 4.5076765
#> 12 5 eigenvalue.m5f2 2.9319301
#> 13 5 eigenvalue.m5f3 1.7565127
#> 14 5 eigenvalue.m5f4 1.6281266
#> 15 5 eigenvalue.m5f5 0.5060352
tidy(x, what = "fit", format = "wide")
#> level eigenvalue.m2f1 eigenvalue.m2f2 eigenvalue.m3f1 eigenvalue.m3f2
#> 1 2 4.507677 2.93193 NA NA
#> 2 3 NA NA 4.507677 2.93193
#> 3 4 NA NA NA NA
#> 4 5 NA NA NA NA
#> eigenvalue.m3f3 eigenvalue.m4f1 eigenvalue.m4f2 eigenvalue.m4f3
#> 1 NA NA NA NA
#> 2 1.756513 NA NA NA
#> 3 NA 4.507677 2.93193 1.756513
#> 4 NA NA NA NA
#> eigenvalue.m4f4 eigenvalue.m5f1 eigenvalue.m5f2 eigenvalue.m5f3
#> 1 NA NA NA NA
#> 2 NA NA NA NA
#> 3 1.628127 NA NA NA
#> 4 NA 4.507677 2.93193 1.756513
#> eigenvalue.m5f4 eigenvalue.m5f5
#> 1 NA NA
#> 2 NA NA
#> 3 NA NA
#> 4 1.628127 0.5060352