On Graphically Checking Goodness-of-fit of Binary Logistic Regression Models

OBJECTIVES: This paper is concerned with checking goodness-of-fit of binary logistic regression models. For the practitioners of data analysis, the broad classes of procedures for checking goodness-of-fit available in the literature are described. The challenges of model checking in the context of binary logistic regression are reviewed. As a viable solution, a simple graphical procedure for checking goodness-of-fit is proposed. METHODS: The graphical procedure proposed relies on pieces of information available from any logistic analysis; the focus is on combining and presenting these in an informative way. RESULTS: The information gained using this approach is presented with three examples. In the discussion, the proposed method is put into context and compared with other graphical procedures for checking goodness-of-fit of binary logistic models available in the literature. CONCLUSION: A simple graphical method can significantly improve the understanding of any logistic regression analysis and help to prevent faulty conclusions.

In vitro precision of fit of computer-aided design and computer-aided manufacturing titanium and zirconium dioxide bars

OBJECTIVES Optical scanners combined with computer-aided design and computer-aided manufacturing (CAD/CAM) technology provide high accuracy in the fabrication of titanium (TIT) and zirconium dioxide (ZrO) bars. The aim of this study was to compare the precision of fit of CAD/CAM TIT bars produced with a photogrammetric and a laser scanner. METHODS Twenty rigid CAD/CAM bars were fabricated on one single edentulous master cast with 6 implants in the positions of the second premolars, canines and central incisors. A photogrammetric scanner (P) provided digitized data for TIT-P (n=5) while a laser scanner (L) was used for TIT-L (n=5). The control groups consisted of soldered gold bars (gold, n=5) and ZrO-P with similar bar design. Median vertical distance between implant and bar platforms from non-tightened implants (one-screw test) was calculated from mesial, buccal and distal scanning electron microscope measurements. RESULTS Vertical microgaps were not significantly different between TIT-P (median 16μm; 95% CI 10-27μm) and TIT-L (25μm; 13-32μm). Gold (49μm; 12-69μm) had higher values than TIT-P (p=0.001) and TIT-L (p=0.008), while ZrO-P (35μm; 17-55μm) exhibited higher values than TIT-P (p=0.023). Misfit values increased in all groups from implant position 23 (3 units) to 15 (10 units), while in gold and TIT-P values decreased from implant 11 toward the most distal implant 15. SIGNIFICANCE CAD/CAM titanium bars showed high precision of fit using photogrammetric and laser scanners. In comparison, the misfit of ZrO bars (CAM/CAM, photogrammetric scanner) and soldered gold bars was statistically higher but values were clinically acceptable.

In vitro precision of fit of computer-aided designed and computer-aided manufactured titanium screw-retained fixed dental prostheses before and after ceramic veneering

OBJECTIVE To compare the precision of fit of full-arch implant-supported screw-retained computer-aided designed and computer-aided manufactured (CAD/CAM) titanium-fixed dental prostheses (FDP) before and after veneering. The null-hypothesis was that there is no difference in vertical microgap values between pure titanium frameworks and FDPs after porcelain firing. MATERIALS AND METHODS Five CAD/CAM titanium grade IV frameworks for a screw-retained 10-unit implant-supported reconstruction on six implants (FDI tooth positions 15, 13, 11, 21, 23, 25) were fabricated after digitizing the implant platforms and the cuspid-supporting framework resin pattern with a laser scanner (CARES(®) Scan CS2; Institut Straumann AG, Basel, Switzerland). A bonder, an opaquer, three layers of porcelain, and one layer of glaze were applied (Vita Titankeramik) and fired according to the manufacturer's preheating and fire cycle instructions at 400-800°C. The one-screw test (implant 25 screw-retained) was applied before and after veneering of the FDPs to assess the vertical microgap between implant and framework platform with a scanning electron microscope. The mean microgap was calculated from interproximal and buccal values. Statistical comparison was performed with non-parametric tests. RESULTS All vertical microgaps were clinically acceptable with values <90 μm. No statistically significant pairwise difference (P = 0.98) was observed between the relative effects of vertical microgap of unveneered (median 19 μm; 95% CI 13-35 μm) and veneered FDPs (20 μm; 13-31 μm), providing support for the null-hypothesis. Analysis within the groups showed significantly different values between the five implants of the FDPs before (P = 0.044) and after veneering (P = 0.020), while a monotonous trend of increasing values from implant 23 (closest position to screw-retained implant 25) to 15 (most distant implant) could not be observed (P = 0.169, P = 0.270). CONCLUSIONS Full-arch CAD/CAM titanium screw-retained frameworks have a high accuracy. Porcelain firing procedure had no impact on the precision of fit of the final FDPs. All implant microgap measurements of each FDP showed clinically acceptable vertical misfit values before and after veneering. Thus, the results do not only show accurate performance of the milling and firing but show also a reproducible scanning and designing process.

Gender-fair language in the context of leadership: Preventing the lack of fit for women

Women are still underrepresented in leadership due to a perceived a ‘lack of fit’. Thus, women are hired less likely, evaluated unfavorably or are less willing to take over a leadership role than their male counterparts. Because gender-fair language (e.g., feminine-masculine word pairs, German: ‘Geschäftsführerin/Geschäftsführer’, CEO, fem./CEO, masc.) leads to a higher mental inclusion of women compared to generic masculine forms (German: ‘Geschäftsführer’, CEO,masc.), we argue that masculine forms endorse the ‘lack of fit’ for women in leadership, whereas gender-fair language reduces it. Three studies support our assumption. Masculine forms led to a ‘lack of fit’ for women in leader selection: they were hired less likely (Study 1) and evaluated less favorably (Study 2) than their male counterparts. Moreover, women showed less willingness to apply when masculine forms were used in the advertisement for a leadership position. Contrary, no such gender-bias was obtained in case of gender-fair language.

Precision of fit and retention force of cast non-precious-crowns on standard titanium implant-abutment with different design and height

OBJECTIVE The cost-effectiveness of cast nonprecious frameworks has increased their prevalence in cemented implant crowns. The purpose of this study was to assess the effect of the design and height of the retentive component of a standard titanium implant abutment on the fit, possible horizontal rotation and retention forces of cast nonprecious alloy crowns prior to cementation. MATERIALS AND METHODS Two abutment designs were examined: Type A with a 6° taper and 8 antirotation planes (Straumann Tissue-Level RN) and Type B with a 7.5° taper and 1 antirotation plane (SICace implant). Both types were analyzed using 60 crowns: 20 with a full abutment height (6 mm), 20 with a medium abutment height (4 mm), and 20 with a minimal (2.5 mm) abutment height. The marginal and internal fit and the degree of possible rotation were evaluated by using polyvinylsiloxane impressions under a light microscope (magnification of ×50). To measure the retention force, a custom force-measuring device was employed. STATISTICAL ANALYSIS one-sided Wilcoxon rank-sum tests with Bonferroni-Holm corrections, Fisher's exact tests, and Spearman's rank correlation coefficient. RESULTS Type A exhibited increased marginal gaps (primary end-point: 55 ± 20 μm vs. 138 ± 59 μm, P < 0.001) but less rotation (P < 0.001) than Type B. The internal fit was also better for Type A than for Type B (P < 0.001). The retention force of Type A (2.49 ± 3.2 N) was higher (P = 0.019) than that of Type B (1.27 ± 0.84 N). Reduction in abutment height did not affect the variables observed. CONCLUSION Less-tapered abutments with more antirotation planes provide an increase in the retention force, which confines the horizontal rotation but widens the marginal gaps of the crowns. Thus, casting of nonprecious crowns with Type A abutments may result in clinically unfavorable marginal gaps.

Precision of fit of implant-supported screw-retained 10-unit computer-aided-designed and computer-aided-manufactured frameworks made from zirconium dioxide and titanium: an in vitro study

OBJECTIVE To analyze the precision of fit of implant-supported screw-retained computer-aided-designed and computer-aided-manufactured (CAD/CAM) zirconium dioxide (ZrO) frameworks. MATERIALS AND METHODS Computer-aided-designed and computer-aided-manufactured ZrO frameworks (NobelProcera) for a screw-retained 10-unit implant-supported reconstruction on six implants (FDI positions 15, 13, 11, 21, 23, 25) were fabricated using a laser (ZrO-L, N = 6) and a mechanical scanner (ZrO-M, N = 5) for digitizing the implant platform and the cuspid-supporting framework resin pattern. Laser-scanned CAD/CAM titanium (TIT-L, N = 6) and cast CoCrW-alloy frameworks (Cast, N = 5) fabricated on the same model and designed similar to the ZrO frameworks were the control. The one-screw test (implant 25 screw-retained) was applied to assess the vertical microgap between implant and framework platform with a scanning electron microscope. The mean microgap was calculated from approximal and buccal values. Statistical comparison was performed with non-parametric tests. RESULTS No statistically significant pairwise difference was observed between the relative effects of vertical microgap between ZrO-L (median 14 μm; 95% CI 10-26 μm), ZrO-M (18 μm; 12-27 μm) and TIT-L (15 μm; 6-18 μm), whereas the values of Cast (236 μm; 181-301 μm) were significantly higher (P < 0.001) than the three CAD/CAM groups. A monotonous trend of increasing values from implant 23 to 15 was observed in all groups (ZrO-L, ZrO-M and Cast P < 0.001, TIT-L P = 0.044). CONCLUSIONS Optical and tactile scanners with CAD/CAM technology allow for the fabrication of highly accurate long-span screw-retained ZrO implant-reconstructions. Titanium frameworks showed the most consistent precision. Fit of the cast alloy frameworks was clinically inacceptable.

Multinomial goodness-of-fit: large sample tests with survey design correction and exact tests for small samples

I introduce the new mgof command to compute distributional tests for discrete (categorical, multinomial) variables. The command supports largesample tests for complex survey designs and exact tests for small samples as well as classic large-sample x2-approximation tests based on Pearson’s X2, the likelihood ratio, or any other statistic from the power-divergence family (Cressie and Read, 1984, Journal of the Royal Statistical Society, Series B (Methodological) 46: 440–464). The complex survey correction is based on the approach by Rao and Scott (1981, Journal of the American Statistical Association 76: 221–230) and parallels the survey design correction used for independence tests in svy: tabulate. mgof computes the exact tests by using Monte Carlo methods or exhaustive enumeration. mgof also provides an exact one-sample Kolmogorov–Smirnov test for discrete data.

Reducing women’s lack of fit with leadership? Effects of the wording of job advertisements

Linguistic forms which refer to individuals impact mental representations of these individuals: When masculine generics are used, women tend to be cognitively underrepresented, whereas feminine–masculine word pairs are associated with a higher cognitive inclusion of women. The present research investigates whether linguistic forms affect women’s perceived lack of fit with leadership positions, which is particularly pronounced for high-status leadership positions. In a hiring-simulation experiment (N = 363), we tested the effects of different linguistic forms used in German-language job advertisements: (1) masculine forms (e.g., Geschäftsführer, ‘CEO, masc.’); (2) masculine forms with (m/f) (e.g., Geschäftsführer (m/w), ‘CEO, masc. (m/f)’); and (3) word pairs (e.g., Geschäftsführerin/Geschäftsführer, ‘CEO, fem./CEO, masc.’). The job ads announced either a high- or low-status leadership position. Results showed that female applicants were perceived to fit less well with the high-status position than male applicants when either the masculine or the masculine form with (m/f) was used––even though they were perceived to be equally competent. However, female and male applicants were perceived as fitting the high-status leadership position similarly well when word pairs were used.

MGOF: Stata module to perform goodness-of-fit tests for multinomial data

mgof computes goodness-of-fit tests for the distribution of a discrete (categorical, multinomial) variable. The default is to perform classical large sample chi-squared approximation tests based on Pearson's X2 statistic and the log likelihood ratio (G2) statistic or a statistic from the Cressie-Read family. Alternatively, mgof computes exact tests using Monte Carlo methods or exhaustive enumeration. A Kolmogorov-Smirnov test for discrete data is also provided. The moremata package, also available from SSC, is required.

Multinomial goodness-of-fit: large sample tests with survey design correction and exact tests for small samples

A new Stata command called -mgof- is introduced. The command is used to compute distributional tests for discrete (categorical, multinomial) variables. Apart from classic large sample $\chi^2$-approximation tests based on Pearson's $X^2$, the likelihood ratio, or any other statistic from the power-divergence family (Cressie and Read 1984), large sample tests for complex survey designs and exact tests for small samples are supported. The complex survey correction is based on the approach by Rao and Scott (1981) and parallels the survey design correction used for independence tests in -svy:tabulate-. The exact tests are computed using Monte Carlo methods or exhaustive enumeration. An exact Kolmogorov-Smirnov test for discrete data is also provided.