in the text, because SAS and Stata handle If the p-value is MORE THAN .05, then the model does fit the data and should be further interpreted. Standard Chi- Analysis of Maximum Likelihood Estimates Related Posts. Charles. ndrgfp1 1.6687 0.8708 2.4667 Probability Modeled Pr( DFREE = 1 ), Ordered Ordered page 179 Figure 5.7 Plot of delta-beta-hat versus the estimated probability from the fitted model in Table 4.9, plotted value of NDRGTX for a subject of age (a) 20, (b) 25, (c) 30 and (d) 35. page 199 Figure 5.11 Estimated odds ratios and 95% confidence limits comparing zero, two, three up to 10 previous a hypothetical univariable logistic regression model. Each test is briefly explained below, while some additional information is provided in the results interpretation section of this guide. predicted probabilities. Standard Wald Charles. This will work, but I don’t know of any theoretical justification for doing this. predictors is the Hosmer-Lemeshow goodness of t test. Deviance 523.6164 509 1.0287 0.3175 fitted value (prob.) Hello Sir, with Hosmer-Lemer Test, can we identify overfitting or underfitting of the model, I don’t really find the Hosmer-Lemer to be very useful, and will eventually remove this webpage. I am using the 2.12 version add-in. The Hosmer-Lemeshow test is a statistical test for goodness of fit for the logistic regression model. ndrgfp2 1.543 1.227 1.940 Deviance 526.8477 509 1.0351 0.2830 Lemeshow test (Hosmer and Lemeshow 1980), which is available in Stata through the postestimation command estat gof. 3. Criterion Only Covariates, AIC 655.729 619.963 Parameter DF Estimate Error Chi-Square Pr > ChiSq Parameter DF Estimate Error Chi-Square Pr > ChiSq Although the Hosmer-Lemeshow test is currently implemented in Stata (see lfit ), hl can be used to assess predictions not just from the last regression model, but also … They are easy enough to calculate, however. page 172 Figure 5.4 Plot of the distance portion of leverage (b) versus the estimated logistic probability (pi-hat) for The test used is chi-square with g – 2 degrees of freedom. My latter question was regarding validation that can we use any other measures to validate the model apart from checking the testing sample accuracy and AUC values? Department of Statistics Consulting Center, Department of Biomathematics Consulting Clinic. SITE 0.5162 0.0143 1.0153 covariate patterns differently. agendrgfp1 racesite / aggregate lackfit scale = 1; Stata to obtain these values. Criterion Value DF Value/DF Pr > ChiSq David M. Rocke Goodness of Fit in Logistic Regression April 14, 202013/61 Distribution Binomial Applied Logistic Regression, Second Edition, by Hosmer and Lemeshow Chapter 5: Assessing the Fit of the Model | SPSS Textbook Examples page 150 Table 5.1 Observed (obs) and estimated expected (exp) frequencies within each decile of risk, defined by fitted value (prob.) Prm10 agendrgfp1 This is the p-value you will interpret. I tried removing normalised residuals which are above 2, but again if I run the analysis, again fresh residuals above 2 appear. Subscribe to get Email Updates! Sir, I have already answered your questions a couple of times. Standard Wald Cell L41 can be calculated by the formula =(H41-I41)^2/I41 and cell M41 by =(K41-J41)^2/K41. That is correct. Prm5 IVHX2 But should the data be split into 70 – 30 and check the accuracy of 30 % data based on coefficients obtained from 70% data and check its AUC value, Or report the accuracy of 100% data and its AUC value and report that? However the chi-squared statistic on which it is based is very dependent on sample size so the value cannot … Pearson 489.8994 509 0.9625 0.7208, Analysis of Maximum Likelihood Estimates page 150 Table 5.1 Observed (obs) and estimated expected (exp) frequencies within each decile of risk, defined by fitted value (prob.) cell L4 contains the formula =K4*J4 and cell M4 contains the formula =J4-L4 or equivalently =(1-K4)*J4. When raw = True then the data in R1 is in raw form and when raw = False (the default) then the data in R1 is in summary form. [output omitted], Deviance and Pearson Goodness-of-Fit Statistics 7.3579 8 0.4986, *Column 5 of Table 5.9; If you find outliers in the residuals, then this is evidence that the model doesn’t fit the data exactly. Hosmer Lemeshow Test: Rule : If p-value > .05. the model fits data well. The Hosmer-Lemeshow test is used to determine the goodness of fit of the logistic regression model. Scaled Deviance 564 597.9629 1.0602 can use Your email address will not be published. proc logistic data=uis54 desc; Or should I randomly split the model, develop model with 1000 (70% data)odd samples, check the predicted probabilities on 400 odd samples ( remaining 30% sample) , compare accuracies of both, and report the AUC value based on predicted probabilities and report that AUC value obtained for 30% data? I don’t use SPSS and so I am not able to answer your question. [output omitted], Deviance and Pearson Goodness-of-Fit Statistics A list with class "htest" containing the following components: statistic. IVHX3 -0.7049 -1.2176 -0.1922 NOTE: The following must be done to reproduce the covariate patterns as shown Response Variable DFREE Score 52.0723 10 <.0001 Prm7 RACE The Hosmer-Lemeshow test results are shown in range Q12:Q16. RACE 1 0.6841 0.2641 6.7074 0.0096 Link Function Logit We now address the problems of cells M4 and M10. agendrgfp1 racesite / aggregate lackfit scale = 1; but all probabilities pi-hat < 0.50 are replaced with pi-hat = 0.45 and all probabilities pi-hat >= 0.50 are replaced page 160 Table 5.4 Classification table based on the logistic regression model in Table 4.9 using a cutpoint of 0.5, As a chi-square goodness of fit test, the expected values used should generally be at least 5. ndrgfp1 1.6687 0.8956 2.4954 Log Likelihood -298.9815, Algorithm converged. NOTE: Pursuant to the text on page 151 this table cannot be replicated in SAS. page 171 Figure 5.3 Plot of leverage (h) versus the estimated logistic probability (pi-hat) for a hypothetical univariable Dependent Variable DFREE As such, a small P value would suggest that the model is incomplete. In a similar manner, we combine the 7, Referring to Figure 1, the output shown in range F40:K50 of Figure 3 is calculated using the formula =HOSMER(A3:D15, TRUE) and the output shown in range O40:P42 of Figure 3 is calculated using the formula =HLTEST(A3:D15, TRUE). Parameter DF Estimate Error Chi-Square Pr > ChiSq This statistic is the mostreliable test of model fit for IBM® SPSS® Statisticsbinary logistic regression, … PROC LOGISTIC DATA = my.mroz DESC; MODEL inlf = kidslt6 age educ huswage city exper / LACKFIT; Observation: The Hosmer-Lemeshow test needs to be used with caution. racesite 1 -1.4294 0.5298 7.2799 0.0070, Point 95% Wald E.g. NOTE: We were unable to reproduce this table. How to overcome this issue or is it fine with having residuals even if I have them as I get accuracy of above 80%. Moving on, the Hosmer & Lemeshow test ( Figure 4.12.5) of the goodness of fit suggests the model is a good fit to the data as p=0.792 ( >.05). agendrgfp1 -0.0153 -0.0276 -0.00382 Dear Sir: agendrgfp1 racesite / aggregate lackfit scale = 1; IVHX2 -0.6346 -1.2201 -0.0491 Link Function Logit Specifically, based on the estimated parameter values , for each observation in the sample the probability that is calculated, based on each observation's covariate values: The Hosmer-Lemeshow goodness-of-fit test is used to assess whether the number of expected events from the logistic regression model reflect the number of observed events in the data. covariate patterns (P#). racesite 0.239 0.085 0.676, Association of Predicted Probabilities and Observed Responses, Percent Concordant 69.7 Somers' D 0.398 Deviance and Pearson Goodness-of-Fit Statistics, Criterion DF Value Value/DF Pr > ChiSq, Deviance 510 530.7412 1.0407 0.2541 First, the observations are sorted in increasing order of … To check the accuracy based on classification matrix, should I construct a model for 1429 samples and directly report it’s accuracy and AUC value. proc logistic data=uis54 desc; with pi-hat = 0.95. page 159 Table 5.3 Classification table based on the logistic regression model in Table 4.9 using a cutpoint of 0.5, When lab = True then the output includes column headings and when lab = False (the default) only the data is outputted. Contingency Table for Hosmer-Lemeshow statistic. Institute for Digital Research and Education. NOTE: We were unable to reproduce this graph. Referring to Figure 1, the output shown in range F40:K50 of Figure 3 is calculated using the formula =HOSMER(A3:D15, TRUE) and the output shown in range O40:P42 of Figure 3 is calculated using the formula =HLTEST(A3:D15, TRUE). Charles, Dear Sir, Sir, I have got 3 questions: For Example 1, Figure 2 of Comparing Logistic Regression Models shows that the model is not a good fit, at least until we combine rows as we did above. 1. 2 1 147, Prm1 Intercept Value DFREE Frequency, 1 1 147 IVHX2 1 -0.6346 0.2987 4.5134 0.0336 page 178 Figure 5.6 Plot of delta-D versus the estimated probability from the fitted model in Table 4.9, UIS J = 521 I don’t have anything more to add. SITE 0.5162 0.0166 1.0157 Ten groups is the standard recommendation. is called a ROC curve. “The Hosmer-Lemeshow test detected a statistically significant degree of miscalibration in both models, due to the extremely large sample size of the models, as the differences between the observed and expected values within each group are relatively small” and. Number of Observations 575 4. page 180 Figure 5.8 Plot of delta-chi-square versus the probability from the fitted model in Table 4.9 with size of the The main concern I have is that you are removing residuals to improve accuracy. 6.8554 8 0.5523. page 189 Table 5.10 Estimated coefficients, standard errors, z-scores, two-tailed p-values and 95% confidence intervals Prm9 SITE Or should I randomly split the model, develop model with 1000 (70% data)odd samples, check the predicted probabilities on 400 odd samples ( remaining 30% sample) , compare accuracies of both, and report the AUC value based on predicted probabilities and report that AUC value obtained for 30% data? Figure 2. TREAT 1 0.4349 0.2038 0.0356 0.8343 4.56 0.0328 Charles. Jessica, I am doing binary logistic regression with about 3000 data points. In our example, the sum is taken over the 12 Male groups and the 12 Female groups. Value. RACE 0.6841 0.1664 1.2018 The revised version shows a non-significant result, indicating that the model is a good fit. Exp(race = other, site = B) 0.4746 0.2200 0.05 0.1913 1.1774. page 194 Figure 5.9 Estimated odds ratio and 95% confidence limits for a five-year increase in age based on the model The HOSMER(R1, lab, raw, iter) function fails to calculate the last columns (HL-Suc and HL-Fail). The Hosmer-Lemeshow statistic is then compared to a chi-square distribution. logitgofis capable of performing all three. Your email address will not be published. 2. how to remove outliers in the data for logistic regression? Deviance 526.8757 509 1.0351 0.2828 1. Effect Estimate Confidence Limits, AGE 1.124 1.062 1.189 *Column 2 of Table 5.9; Number of Response Levels 2 Parameter DF Estimate Error Chi-Square Pr > ChiSq, Intercept 1 -6.8429 1.2193 31.4989 <.0001 proc logistic data=uis54 desc; Sir, I have developed a binary logistic regression model…..is it necessary to validate it by considering a 70%-30%data split or just get overall prediction data and ROC analysis for 100% data… The initial version of the test we present here uses the groupings that we have used elsewhere and not subgroups of size ten. 4.7204 8 0.7870, *Column 3 of Table 5.9; This could be useful but is not essential. HLTEST(R1, lab, raw, iter) – returns the Hosmer statistic (based on the table described above) and the p-value. I would ignore the Homer-Lemeshow value. Wald 47.2784 10 <.0001, Standard proc logistic data=uis54 desc; agendrgfp1 1 -0.0153 0.0060 -0.0271 -0.0035 6.42 0.0113 Scaled Pearson X2 564 580.7351 1.0297 With regards My Hosmer Lemeshow value is coming almost zero thus suggesting poor model fit. Since this is a chi-square goodness of fit test, we need to calculate the HL statistic. for dfree = 1 and dfree = 0 using the fitted logistic regression model in Table 4.9. cell N4 contains the formula =(H4-L4)^2/L4+(I4-M4)^2/M4. A significant test indicates that the model is not a good fit and a non-significant test indicates a good fit. run; Deviance and Pearson Goodness-of-Fit Statistics where g = the number of groups. Deviance 526.9371 509 1.0352 0.2821 Pearson 511.5248 509 1.0050 0.4602, Analysis of Maximum Likelihood Estimates Standard Wald Charles. logistic regression model. Goodness-of-fit statistics help you to determine whetherthe model adequately describes the data. The degrees of freedom depend upon the number of quantiles used and the number of outcome categories. model dfree = age ndrgfp1 ndrgfp2 ivhx2 ivhx3 race treat site This is not a surprise. Prm6 IVHX3 Number of Response Levels 2 This is a judgment call. Here p-Pred for the first row (cell K23) is calculated as a weighted average of the first two values from Figure 1 using the formula =(J4*K4+J5*K5)/(J4+J5). run; 2007: Sep 35(9):2213 2 0 428. I have calculated the HL statistic using your example. Real Statistics Functions: The Real Statistics Resource Pack provides the following two supplemental functions. Percent Discordant 29.9 Gamma 0.399 TREAT 0.4349 0.0356 0.8343 Either approach could be good. Data Set WORK.UIS51 where covpat not in (31, 477, 105, 468); Prm4 ndrgfp2 model dfree = age ndrgfp1 ndrgfp2 ivhx2 ivhx3 race treat site UIS J = 521 covariate patterns. Intercept 1 -7.7998 1.2995 36.0240 ChiSq agendrgfp1 racesite / aggregate lackfit scale=1; where covpat not in (477); The Hosmer-Lemeshow test is a statistical test for goodness of fit for logistic regression models. Except for Hosmer value, every other value i.e. drug treatments to one previous treatment for a subject of age (a) 20, (b) 25, (c) 30 and (d) 35. In a similar manner, we combine the 7th and 8th rows from Figure 20.23. Optimization Technique Fisher's scoring, Profile Likelihood Confidence Any of the approaches that have been discussed can be used. how to find exp value for third variable. Number of Observations 575 Link Function Logit Sai, NOTE: We have bolded the relevant output. proc logistic data=uis54 desc; 1. 9.0942 8 0.3344, *Column 6 of Table 5.9; thank you, I’m really curious that how could we get the p-pred value in column K figure 1? p-value, odds ratio, etc coming out quite good. SC 660.083 667.861 Prm2 AGE A non-significant p value indicates that there is … page 161 Table 5.5 Classification table based on the logistic regression model in Table 4.9 using a cutpoint of 0.6. page 163 Figure 5.2 Plot of sensitivity versus 1-specificity for all possible cutpoints in the UIS. Can I just calculate the p-value for each decile using the chidist funtion? Essentially, they compare observed with expected frequencies of the outcome and compute a test statistic which is distributed according to the chi-squared distribution. How to check the model validation other than split sample validation in SPSS? See the webpage Finding Logistic Regression Coefficients using Solver. ndrgfp2 1 0.4337 0.1169 0.2046 0.6628 13.76 0.0002 80% accuracy sounds pretty good to me. estat gof requires that the current estimation results be from logistic, logit, or probit; see [R]logistic,[R]logit, or[R]probit. Since the p-value > .05 (assuming α = .05) we conclude that the logistic regression model is a good fit. Charles. I would look at other indicators; if they look good then I wouldn’t worry too much about the Hosmer-Lemeshow result. Hosmer and Lemeshow (2000) proposed a statistic that they show, through simulation, is distributed as chi-square when there is no replication in any of the subpopulations. Essentially it is a chi-square goodness of fit test (as described in Goodness of Fit) for grouped data, usually where the data is divided into 10 equal subgroups. p-value = 0.000016 and alpha = 0.05. differences in the way SAS and Stata handle ties. Data Set WORK.UIS51 3. Example 1: Use the Hosmer-Lemeshow test to determine whether the logistic regression model is a good fit for the data in Example 1 in Comparing Logistic Regression Models. TREAT 1.545 1.036 2.303 I am not using the true Hosmer-Lemeshow test and so there aren’t any deciles. Scale 0 1.0000 0.0000 1.0000 1.0000. ndrgfp1 1 1.6687 0.4071 16.8000 <.0001 You should look at the accuracy and the p-value for the model (and check to see which coefficients are significantly different from zero. Yes sir, in the training data and testing data I got about 80% accuracy after removal of residuals but each time I run the analysis I get fresh residuals values which are above absolute value of 2. Charles. Hello Yusuf, SITE 1 0.5162 0.2549 4.1013 0.0429 liana, Liana, Essentially it is a chi-square goodness of fit test (as described in Goodness of Fit) for grouped data, usually where the data is divided into 10 equal subgroups. As you can see from the comments following Figure 3, the HOSMER function does not calculate these last two columns. NOTE: We were unable to reproduce this table. When the data have few trials per row, the Hosmer-Lemeshow test is a more trustworthy indicator of how well the model fits the data. where covpat not in (105); for dfree = 1 and dfree = 0 using the fitted logistic regression model in Table 4.9. The GENMOD Procedure, Standard Wald 95% Confidence Chi- Pearson 511.5712 509 1.0051 0.4596, Analysis of Maximum Likelihood Estimates TREAT 0.4349 0.0373 0.8372 I suggest that you try such an example using the Real Statistics Resource Pack and look at the formulas that are produced in the output. 4.4189 8 0.8175. Charles. Intercept and HOSMER(R1, lab, raw, iter) – returns a table with 10 equal-sized data ranges based on the data in range R1 (without headings). To check the accuracy based on classification matrix, should I construct a model for 1429 samples and directly report it’s accuracy and AUC value. The Hosmer and Lemeshow goodness of fit (GOF) test is a way to assess whether there is evidence for lack of fit in a logistic regression model. For estat gof after sem, see[SEM]estat gof. Use instead of Pearon's Chi-Square Goodness of Fit when you have a small number of observations or if you have a continuous explanatory variable. I will consider adding these columns to the output of the function in the next release. We can eliminate the first of these by combining the first two rows, as shown in Figure 2. covariate patterns. IVHX3 -0.7049 -1.2234 -0.1960 Parameter DF Estimate Error Chi-Square Pr > ChiSq RACE 1 0.6841 0.2641 0.1664 1.2018 6.71 0.0096 I have calculated statistics like your example, but I am confused if the independent variable consists of 3 variables. Convergence criterion (GCONV=1E-8) satisfied. The data is divided into a number of groups … The resulting curve This test is available only for binary response models. c 2012 StataCorp LP st0269. UIS (N = 575). Pearson 510 511.7467 1.0034 0.4699. Look in the Hosmer and Lemeshow Test table, under the Sig. Intercept 1 -6.8429 1.2193 31.4989 ChiSq Also when there are too few groups (5 or less) then usually the test will show a model fit. 2. how to remove outliers in the data for logistic regression? Intercept 1 -7.0471 1.2379 32.4064 ChiSq Level Value Count, 1 0 428 page 157 Table 5.2 Classification table based on the logistic regression model in Table 4.9 using a cutpoint of 0.5. Simply put, the test compares the expected and observed number of events in bins defined by the predicted probability of the outcome. E.g. AGE 0.1166 0.0611 0.1746 racesite -1.4294 -2.5080 -0.4174, Intercept -6.8429 -9.2326 -4.4532 He has over 10 years of experience in data science. Calculate Hosmer Lemeshow Test with Excel. You The Observation: the following functions can be used to perform the Hosmer-Lemeshow test with exactly 10 equal-sized data ranges. Here, the model adequately fits the data. The fact that you get better accuracy from the training data (70% of the data) is not surprising. I would like to figure out in which decile the test performs badly. Observation: The Real Statistics Logistic Regression data analysis tool automatically performs the Hosmer-Lemeshow test. The graphs in the text were made using Stata. For Example 1 of Finding Logistic Regression Coefficients using Solver, we can see from Figure 5 of Finding Logistic Regression Coefficients using Solver that the logistic regression model is a good fit. It shows that my model is not a good fit. page 182 Table 5.8 Covariate values, observed outcome (yj), number (mj), estimated logistic probability (pi-hat), and I have done step wise logistic regression based on Likelihood ratio in SPSS. IVHX3 0.494 0.296 0.825 The Hosmer–Lemeshow test determinees if the differences between observed and expected proportions are significant. the value of the four diagnostic statistics delta-beta-hat, delta-x-square, and leverage (h) for the four most extreme Parameter DF Estimate Error Chi-Square Pr > ChiSq page 197 Figure 5.10 Estimated odds ratios and 95% confidence limits for an increase of one drug treatment from the The Hosmer-Lemeshowstatistic indicates a poor fit if the significance value is less than0.05. I tried removing normalised residuals which are above 2, but again if I run the analysis, again fresh residuals above 2 appear. ndrgfp2 0.4336 0.2045 0.6627 covariate patterns. IVHX3 1 -0.7049 0.2616 7.2623 0.0070 Response Variable DFREE See Lemeshow and Hosmer's American Journal of Epidemiology article for more details. The parameter iter determines the number of iterations used in the Newton method for calculating the logistic regression coefficients; the default value is 20. agendrgfp1 -0.0153 -0.0271 -0.00346 I apologize for repeatedly asking the question as I didn’t frame the question properly. It would be helpful for my dissertation. The Hosmer-Lemeshow test does not depend on the format of the data. with pi-hat = 0.55. where covpat not in (468); 448 A goodness-of-fit test for multinomial logistic regression The multinomial (or polytomous) logistic regression model is a generalization of the Pearson 508.6675 509 0.9993 0.4958, Analysis of Maximum Likelihood Estimates I would be getting 1000 odd samples to develop a model. If the p-value is LESS THAN .05, then the model does not fit the data. For populations of 5,000 patients, 10% of theHosmer-Lemeshow tests were significant at p < .05, whereas for 10,000patients 34% of the Hosmer-Lemeshow tests were significant at p < .05. 1. I have got a sample size of 1429 samples, if I split them as 70-30. Intercept 1 -6.7557 1.2165 30.8427 ChiSq Percent Tied 0.4 Tau-a 0.152 Hosmer and Lemeshow (1980) proposed grouping cases together according to their predicted values from the logistic regression model. Data Set WORK.UIS54 Whenthe number of patients matched contemporary studies (i.e., 50,000 patients),the Hosmer-Lemeshow test was statistically significant in 100% of the models. parameter. You can do a 70-30 split, but you need to select the test data randomly. SITE 1 0.5162 0.2549 0.0166 1.0158 4.10 0.0428 Calculate observed and expected frequencies in the 10 x 2 table, and compare them with Pearson’s chi -square (with 8 df). racesite -1.4294 -2.4677 -0.3911. page 190 Table 5.11 Estimated odds ratios and 95% confidence intervals for treatment and history of IV drug use in the agendrgfp1 racesite / aggregate lackfit scale = 1; Goodness of Fit: Hosmer-Lemeshow Test The Hosmer-Lemeshow test examines whether the observed proportion of events are similar to the predicted probabilities of occurences in subgroups of the dataset using a pearson chi-square statistic from the 2 x g table of observed and expected frequencies. RACE 0.6841 0.1638 1.2013 How to check the model validation other than split sample validation in SPSS? Hosmer & Lemeshow (1980): Group data into 10 approximately equal sized groups, based on predicted values from the model. If you get better accuracy from the test data (30% of the data), then this gives some support for the approach that you have described. How to overcome this issue or is it fine with having residuals even if I have them as I get accuracy of above 80%. values of goodness-of-fit statistics for each model. Label Estimate Error Alpha Confidence Limits Square Pr > ChiSq, race = other, site = A 0.6841 0.2641 0.05 0.1664 1.2018 6.71 0.0096 [output omitted], Deviance and Pearson Goodness-of-Fit Statistics See the following article for further information. run; When the data have few trials per row, the Hosmer-Lemeshow test is a more trustworthy indicator of how well the model fits the data. Pairs 62916 c 0.699. page 183 Table 5.9 Estimated coefficients from all data, the percent change when the covariate pattern is deleted, and The initial version of the test we present here uses the groupings that we have used elsewhere and not subgroups of size ten. Conduct a Hosmer-Lemeshow Goodness of Fit to test the fit of the logistic regression model. In this post we'll look at one approach to assessing the discrimination of a fitted logistic model, via the receiver operating characteristic (ROC) curve. page 192 Table 5.12 Estimated odds ratios and 95% confidence intervals for race within site in the UIS (n = 575). Parameter DF Estimate Error Limits Square Pr > ChiSq, Intercept 1 -6.8439 1.2193 -9.2337 -4.4540 31.50 <.0001 column. Parameter DF Estimate Error Chi-Square Pr > ChiSq NOTE: We cannot recreate this figure because we do have the hypothetical data that were used. NOTE: This graph looks slightly different than the one in the book because SAS and Stata use different methods of handling
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