# hosmer and lemeshow test interpretation

*08 Aralık 2020 - 1 kez okunmuş*

If you reject the null, your model did not fit the data. Observation: the following functions can be used to perform the Hosmer-Lemeshow test with exactly 10 equal-sized data ranges. [output omitted], Deviance and Pearson Goodness-of-Fit Statistics how to find exp value for third variable. 5.2.2 The Hosmer-Lemeshow Tests . UIS J = 521 covariate patterns. First, the observations are sorted in increasing order of … Intercept and Optimization Technique Fisher's scoring, Ordered Total I am using the 2.12 version add-in. 4.4189 8 0.8175. Hosmer & Lemeshow (1980): Group data into 10 approximately equal sized groups, based on predicted values from the model. See the webpage Finding Logistic Regression Coefficients using Solver. Prm8 TREAT Number of Observations 575 IVHX2 -0.6346 -1.2201 -0.0491 Level Value Count, 1 0 428 As such, a small P value would suggest that the model is incomplete. The Hosmer-Lemeshow test is used to determine the goodness of fit of the logistic regression model. RACE 1 0.6841 0.2641 0.1664 1.2018 6.71 0.0096 Effect Estimate Confidence Limits, AGE 1.124 1.062 1.189 Charles. The observed values are given in columns H and I (duplicates of the input data columns C and D), while the expected values are given in columns L and M. E.g. Simply put, the test compares the expected and observed number of events in bins defined by the predicted probability of the outcome. Pearson 489.8994 509 0.9625 0.7208, Analysis of Maximum Likelihood Estimates I have already answered your questions a couple of times. Multinomial and Ordinal Logistic Regression, Linear Algebra and Advanced Matrix Topics, Finding Logistic Regression Coefficients using Solver, Finding Logistic Regression Coefficients using Excel’s Solver, Significance Testing of the Logistic Regression Coefficients, Testing the Fit of the Logistic Regression Model, Finding Logistic Regression Coefficients via Newton’s Method, Receiver Operating Characteristic (ROC) Curve, Real Statistics Functions for Logistic Regression. where covpat not in (31, 477, 105, 468); Calculate Hosmer Lemeshow Test with Excel. I would look at other indicators; if they look good then I wouldn’t worry too much about the Hosmer-Lemeshow result. model dfree = age ndrgfp1 ndrgfp2 ivhx2 ivhx3 race treat site 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of delta-chi-square versus the probability from the fitted model in Table 4.9 with size of the Your email address will not be published. My Hosmer Lemeshow value is coming almost zero thus suggesting poor model fit. This is a judgment call. Hosmer-Lemeshow test. proc logistic data=uis54 desc; Scale 0 1.0000 0.0000 1.0000 1.0000. Wald 47.2784 10 <.0001, Standard 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.) agendrgfp1 -0.0153 -0.0276 -0.00382 Standard Wald page 179 Figure 5.7 Plot of delta-beta-hat versus the estimated probability from the fitted model in Table 4.9, -2 Log L 653.729 597.963, Test Chi-Square DF Pr > ChiSq, Likelihood Ratio 55.7660 10 <.0001 The Hosmer-Lemeshow testsThe Hosmer-Lemeshow tests are goodness of fit tests for binary, multinomial and ordinal logistic regression models. 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. Prm10 agendrgfp1 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. page 150 Table 5.1 Observed (obs) and estimated expected (exp) frequencies within each decile of risk, defined by fitted value (prob.) Since the p-value > .05 (assuming α = .05) we conclude that the logistic regression model is a good fit. page 160 Table 5.4 Classification table based on the logistic regression model in Table 4.9 using a cutpoint of 0.5, Deviance and Pearson Goodness-of-Fit Statistics, Criterion DF Value Value/DF Pr > ChiSq, Deviance 510 530.7412 1.0407 0.2541 TREAT 0.4349 0.0373 0.8372 The HOSMER(R1, lab, raw, iter) function fails to calculate the last columns (HL-Suc and HL-Fail). Charles. Analysis of Maximum Likelihood Estimates AGE 1 0.1166 0.0289 16.3137 <.0001 See Lemeshow and Hosmer's American Journal of Epidemiology article for more details. Criterion Value DF Value/DF Pr > ChiSq 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. The Hosmer-Lemeshow statistic is then compared to a chi-square distribution. Response Variable DFREE Hosmer Lemeshow Test: Rule : If p-value > .05. the model fits data well. Thank you very much. Jessica, I don’t think it is such a good indicator, and the value produced by the Real Statistics software is really only a valid Homer-Lemeshow value when there are 10 summary rows. 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? Prm5 IVHX2 predictors is the Hosmer-Lemeshow goodness of t test. ndrgfp2 0.4336 0.2088 0.6678, IVHX2 -0.6346 -1.2332 -0.0590 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. See the following article for further information. This works poorly if there are too many ties, but is useful when almost all the observations have distinct predictors. How to overcome this issue or is it fine with having residuals even if I have them as I get accuracy of above 80%. in the text, because SAS and Stata handle I am doing binary logistic regression with about 3000 data points. I have done step wise logistic regression based on Likelihood ratio in SPSS. Intercept 1 -7.0695 1.2399 32.5072 ChiSq p-value = 0.000016 and alpha = 0.05. with pi-hat = 0.55. Related Posts. c 2012 StataCorp LP st0269. 2007: Sep 35(9):2213 TREAT 0.4349 0.0356 0.8343 The GENMOD Procedure, Standard Wald 95% Confidence Chi- Number of Observations 575 This statistic is the mostreliable test of model fit for IBM® SPSS® Statisticsbinary logistic regression, … I am not using the true Hosmer-Lemeshow test and so there aren’t any deciles. IVHX3 -0.7049 -1.2176 -0.1922 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). a hypothetical univariable logistic regression model. IVHX2 1 -0.6346 0.2987 4.5134 0.0336 I have got a sample size of 1429 samples, if I split them as 70-30. This could be useful but is not essential. Is a low value of Hosmer is alone sufficient to discard the model? where g = the number of groups. NOTE: We cannot recreate this figure because we do have the hypothetical data that were used. RACE 1.982 1.181 3.326 You can ignore the Homer-L test; it is not a very indication of the validity of the regression. However the chi-squared statistic on which it is based is very dependent on sample size so the value cannot … 80% accuracy sounds pretty good to me. Distribution Binomial Prm11 racesite, Criterion DF Value Value/DF, Deviance 564 597.9629 1.0602 SC 660.083 667.861 IVHX3 0.494 0.296 0.825 model dfree = age ndrgfp1 ndrgfp2 ivhx2 ivhx3 race treat site RACE 1 0.6841 0.2641 6.7074 0.0096 Deviance 526.8477 509 1.0351 0.2830 Required fields are marked *, Everything you need to perform real statistical analysis using Excel .. … … .. © Real Statistics 2020. Pearson 482.6328 506 0.9538 0.7658, Analysis of Maximum Likelihood Estimates You can do a 70-30 split, but you need to select the test data randomly. The resulting curve NOTE: This graph looks slightly different than the one in the book because SAS and Stata use different methods of handling ndrgfp2 0.4336 0.2045 0.6627 We can eliminate the first of these by combining the first two rows, as shown in Figure 2. How to check the model validation other than split sample validation in SPSS? whereas in the example you gave in Figure 1, look for exp values for women in a 1-ppred * total way Log Likelihood -298.9815, Algorithm converged. Intercept I will consider adding these columns to the output of the function in the next release. proc logistic data=uis54 desc; They are easy enough to calculate, however. Deviance 511.1110 506 1.0101 0.4282 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. ndrgfp1 1.6687 0.8708 2.4667 2. Observation: We repeat Example 1 using these two functions, obtaining the results shown in Figure 3. Since this is a chi-square goodness of fit test, we need to calculate the HL statistic. As you can see from the comments following Figure 3, the HOSMER function does not calculate these last two columns. proc logistic data=uis54 desc; That is correct. 7.3579 8 0.4986, *Column 5 of Table 5.9; The HL stat is 24.40567 (as calculated in cell N16), We can eliminate the first of these by combining the first two rows, as shown in Figure 2. 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. I would be getting 1000 odd samples to develop a model. Value. SITE 1 0.5162 0.2549 4.1013 0.0429 Sir, I have got 3 questions: proc logistic data=uis54 desc; I apologize for repeatedly asking the question as I didn’t frame the question properly. This can be calculated in R and SAS. This test is available only for binary response models. Observation: The Real Statistics Logistic Regression data analysis tool automatically performs the Hosmer-Lemeshow test. page 157 Table 5.2 Classification table based on the logistic regression model in Table 4.9 using a cutpoint of 0.5. Convergence criterion (GCONV=1E-8) satisfied. Charles, Dear Sir, 1. NOTE: We were unable to reproduce this graph. Kindly help me sir, Sai, How to overcome this issue or is it fine with having residuals even if I have them as I get accuracy of above 80%. Prm6 IVHX3 The parameter iter determines the number of iterations used in the Newton method for calculating the logistic regression coefficients; the default value is 20. 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. Hello Sir, 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. 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 IVHX2 1 -0.6346 0.2987 -1.2201 -0.0492 4.51 0.0336 The HL stat is 24.40567 (as calculated in cell N16), df = g – 2 = 12 – 2 = 10 and p-value = CHIDIST(24.40567, 10) = .006593 < .05 = α, and so the test is significant, which indicates that the model is not a good fit. TREAT 1.545 1.036 2.303 Percent Discordant 29.9 Gamma 0.399 proc logistic data=uis54 desc; It shows that my model is not a good fit. agendrgfp1 racesite / aggregate lackfit scale = 1; drug treatments to one previous treatment for a subject of age (a) 20, (b) 25, (c) 30 and (d) 35. Calculate observed and expected frequencies in the 10 x 2 table, and compare them with Pearson’s chi -square (with 8 df). run; agendrgfp1 racesite / aggregate lackfit scale=1; In a similar manner, we combine the 7th and 8th rows from Figure 20.23. run; page 171 Figure 5.3 Plot of leverage (h) versus the estimated logistic probability (pi-hat) for a hypothetical univariable 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. The graphs in the text were made using Stata. ndrgfp2 1 0.4336 0.1169 13.7585 0.0002 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. If the p-value for the regression is significant, then it seems like you have a good result. Observations Used 575 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. Parameter DF Estimate Error Chi-Square Pr > ChiSq, Intercept 1 -6.8429 1.2193 31.4989 <.0001 1. Goodness-of-fit statistics help you to determine whetherthe model adequately describes the data. TREAT 1 0.4349 0.2038 0.0356 0.8343 4.56 0.0328 E.g. If the p-value is MORE THAN .05, then the model does fit the data and should be further interpreted. I tried removing normalised residuals which are above 2, but again if I run the analysis, again fresh residuals above 2 appear. The In Example 1 the cells L9, L15, M4 and M10 all have values less than 5, with cells M4 and M10 especially troubling with values less than 1. 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. Link Function Logit With regards 9.2002 8 0.3257, *Column 4 of Table 5.9; 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. When lab = True then the output includes column headings and when lab = False (the default) only the data is outputted. Look in the Hosmer and Lemeshow Test table, under the Sig. Sir, I have got 3 questions: Parameter DF Estimate Error Chi-Square Pr > ChiSq UIS J = 521 covariate patterns. Can I just calculate the p-value for each decile using the chidist funtion? Data Set WORK.UIS54 This is the p-value you will interpret. I have calculated statistics like your example, but I am confused if the independent variable consists of 3 variables. for dfree = 1 and dfree = 0 using the fitted logistic regression model in Table 4.9. Number of Response Levels 2 racesite 1 -1.4294 0.5298 7.2799 0.0070, Point 95% Wald NOTE: Pursuant to the text on page 151 this table cannot be replicated in SAS. The Hosmer-Lemeshow test results are shown in range Q12:Q16. Contingency Table for Hosmer-Lemeshow statistic. model dfree = age ndrgfp1 ndrgfp2 ivhx2 ivhx3 race treat site Conduct a Hosmer-Lemeshow Goodness of Fit to test the fit of the logistic regression model. 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. Use the following SAS code at the end of your logistic regression code to test the fit of the model. IVHX2 0.530 0.295 0.952 covariate patterns differently. Score 52.0723 10 <.0001 Scaled Pearson X2 564 580.7351 1.0297 Deviance 523.6164 509 1.0287 0.3175 racesite 1 -1.4295 0.5298 -2.4678 -0.3911 7.28 0.0070 NOTE: This graph looks slightly different than the one in the book because SAS and Stata use different methods of handling Value DFREE Frequency, 1 1 147 Department of Statistics Consulting Center, Department of Biomathematics Consulting Clinic. 448 A goodness-of-ﬁt test for multinomial logistic regression The multinomial (or polytomous) logistic regression model is a generalization of the predicted probabilities. Prm2 AGE You can try both approaches and see whether there is much of a difference. Standard Chi- 4.7204 8 0.7870, *Column 3 of Table 5.9; A list with class "htest" containing the following components: statistic. Link Function Logit Dependent Variable DFREE Criterion Value DF Value/DF Pr > ChiSq I have got a sample size of 1429 samples, if I split them as 70-30. HOSMER(R1, lab, raw, iter) – returns a table with 10 equal-sized data ranges based on the data in range R1 (without headings). 3. agendrgfp1 -0.0153 -0.0271 -0.00346 Given that all other results are good? for dfree = 1 and dfree = 0 using the fitted logistic regression model in Table 4.9. thank you, race = other, site = B -0.7454 0.4636 0.05 -1.6540 0.1633 2.58 0.1079 racesite 0.239 0.085 0.676, Association of Predicted Probabilities and Observed Responses, Percent Concordant 69.7 Somers' D 0.398 If the p-value is LESS THAN .05, then the model does not fit the data. Parameter DF Estimate Error Chi-Square Pr > ChiSq covariate patterns (P#). ndrgfp2 1 0.4337 0.1169 0.2046 0.6628 13.76 0.0002 plotting symbol proportional to delta-beta-hat, UIS J = 521 covariate patterns. A significant test indicates that the model is not a good fit and a non-significant test indicates a good fit. The HL statistic is calculated in cell N16 via the formula =SUM(N4:N15). but all probabilities pi-hat < 0.50 are replaced with pi-hat = 0.45 and all probabilities pi-hat >= 0.50 are replaced Also when there are too few groups (5 or less) then usually the test will show a model fit. 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 … AGE 0.1166 0.0600 0.1732 This test uses the null hypothesis that the specified model is correct. 9.0942 8 0.3344, *Column 6 of Table 5.9; SITE 0.5162 0.0166 1.0157 Stata to obtain these values. The Hosmer-Lemeshow test results are shown in range Q12:Q16. logitgofis capable of performing all three. RACE 0.6841 0.1664 1.2018 logistic regression model. 2 1 147, Prm1 Intercept For estat gof after poisson, see[R]poisson postestimation. Prm4 ndrgfp2 IVHX3 -0.7049 -1.2234 -0.1960 The test used is chi-square with g – 2 degrees of freedom. This will work, but I don’t know of any theoretical justification for doing this. [output omitted], Deviance and Pearson Goodness-of-Fit Statistics where covpat not in (468); 3. where covpat not in (105); NOTE: The Hosmer and Lemeshow goodness-of-fit statistic is different than that shown in the text because of the agendrgfp1 1 -0.0153 0.00603 6.4177 0.0113 p-value, odds ratio, etc coming out quite good. I would be getting 1000 odd samples to develop a model. Sir, You NOTE: We were unable to reproduce this table. agendrgfp1 0.985 0.973 0.997 agendrgfp1 racesite / aggregate lackfit scale = 1; for the final logistic regression model for the UIS (n=575). with pi-hat = 0.95. Charles. 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. agendrgfp1 racesite / aggregate lackfit scale = 1; model dfree = age ndrgfp1 ndrgfp2 ivhx2 ivhx3 race treat site You should look at the accuracy and the p-value for the model (and check to see which coefficients are significantly different from zero. Sai, Data Set WORK.UIS51 Intercept 1 -7.7998 1.2995 36.0240 ChiSq Institute for Digital Research and Education. The Hosmer–Lemeshow test determinees if the differences between observed and expected proportions are significant. 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 NOTE: We have bolded the relevant output. SITE 0.5162 0.0143 1.0153 Hello Yusuf, 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). IVHX3 1 -0.7049 0.2616 -1.2176 -0.1923 7.26 0.0070 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. Parameter DF Estimate Error Limits Square Pr > ChiSq, Intercept 1 -6.8439 1.2193 -9.2337 -4.4540 31.50 <.0001 This is not a surprise. page 172 Figure 5.4 Plot of the distance portion of leverage (b) versus the estimated logistic probability (pi-hat) for Either approach could be good. Criterion Value DF Value/DF Pr > ChiSq In our example, the sum is taken over the 12 Male groups and the 12 Female groups. Charles. Hosmer and Lemeshow (1980) proposed grouping cases together according to their predicted values from the logistic regression model. About Author: Deepanshu founded ListenData with a simple objective - Make analytics easy to understand and follow. Essentially, they compare observed with expected frequencies of the outcome and compute a test statistic which is distributed according to the chi-squared distribution. 2 0 428. 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). Before the removal of residuals I had a sample size of 1479 with a accuracy of 73% and after removal of residuals I had a accuracy of 80%, there is slight change in the coefficients of the variables. ndrgfp1 1.6687 0.8956 2.4954 Shirley, Shirley, For estat gof after sem, see[SEM]estat gof. fitted value (prob.) Real Statistics Functions: The Real Statistics Resource Pack provides the following two supplemental functions. It tends to be highly dependent on the groupings chosen, i.e. 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. 1. The Hosmer-Lemeshowstatistic indicates a poor fit if the significance value is less than0.05. This was the question I wanted to ask. Dear Sir: SITE 1.676 1.017 2.761 ndrgfp1 1 1.6687 0.4071 16.8000 <.0001 Observation: The Hosmer-Lemeshow test needs to be used with caution. Parameter DF Estimate Error Chi-Square Pr > ChiSq page 192 Table 5.12 Estimated odds ratios and 95% confidence intervals for race within site in the UIS (n = 575). Whenthe number of patients matched contemporary studies (i.e., 50,000 patients),the Hosmer-Lemeshow test was statistically significant in 100% of the models. Percent Tied 0.4 Tau-a 0.152 Parameter DF Estimate Error Chi-Square Pr > ChiSq AGE 0.1166 0.0611 0.1746 NOTE: We were unable to reproduce this table. Data Set WORK.UIS51 We now address the problems of cells M4 and M10. I have calculated the HL statistic using your example. cell N4 contains the formula =(H4-L4)^2/L4+(I4-M4)^2/M4. Link Function Logit Exp(race = other, site = A) 1.9820 0.5235 0.05 1.1811 3.3261 UIS (N = 575). The Hosmer-Lemeshow test is used to determine the goodness of fit of the logistic regression model. The main concern I have is that you are removing residuals to improve accuracy. In a previous post we looked at the popular Hosmer-Lemeshow test for logistic regression, which can be viewed as assessing whether the model is well calibrated. The degrees of freedom depend upon the number of quantiles used and the number of outcome categories. Pearson Chi-Square 564 580.7351 1.0297 Intercept 1 -7.0471 1.2379 32.4064 ChiSq column. Pearson 508.6675 509 0.9993 0.4958, Analysis of Maximum Likelihood Estimates 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. It would be helpful for my dissertation. NOTE: The covariance matrix has been multiplied by the heterogeneity factor (square of SCALE=1) page 178 Figure 5.6 Plot of delta-D versus the estimated probability from the fitted model in Table 4.9, UIS J = 521 Charles. but all probabilities pi-hat < 0.50 are replaced with pi-hat = 0.05 and all probabilities pi-hat >= 0.50 are replaced 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. run; Standard Wald Another calibration statistic for logistic regression is the Hosmer-Lemeshow goodness-of-fit test (Hosmer & Lemeshow, 1980). Lemeshow test (Hosmer and Lemeshow 1980), which is available in Stata through the postestimation command estat gof. NOTE: The following must be done to reproduce the covariate patterns as shown The Hosmer-Lemeshow test does not depend on the format of the data. agendrgfp1 1 -0.0153 0.0060 -0.0271 -0.0035 6.42 0.0113 [output omitted], Deviance and Pearson Goodness-of-Fit Statistics liana, Liana, Hosmer-Lemeshow: The Hosmer-Lemeshow test does not depend on the number of trials per row in the data as the other goodness-of-fit tests do. page 177 Figure 5.5 Plot of delta-x-square versus the estimated probability from the fitted model in Table 4.9, The Hosmer-Lemeshow goodness of fit test is based on dividing the sample up according to their predicted probabilities, or risks. 4. The initial version of the test we present here uses the groupings that we have used elsewhere and not subgroups of size ten. I’m really curious that how could we get the p-pred value in column K figure 1? 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). Charles. 1. where covpat not in (31); 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. Probability Modeled Pr( DFREE = 1 ), Ordered Ordered The revised version shows a non-significant result, indicating that the model is a good fit. agendrgfp1 racesite / aggregate lackfit scale = 1; The fact that you get better accuracy from the training data (70% of the data) is not surprising. Pearson 511.5248 509 1.0050 0.4602, Analysis of Maximum Likelihood Estimates In general, you shouldn’t remove sample data outliers, especially with large samples where “outliers” are not unusual.

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