I conducted binary logistic regression analysis (DV is measured in yes, no). Among my IVs, One IV is about partnership measured in dichotomous (yes, no) and another IV is population density and measured as (Low=1, average =2, high (reference group) =3).  The output shows that:   For partnership: $\beta$ value of partnership(1) is .795 while it is significant.  For population density: $\beta$ values are: low(1) = -.976, average = -.641   I need your help on how to interpret beta values especially the negative signs
122317
I am currently reading a  concerning voting location and voting preference in the 2000 and 2004 election. In it, there is a chart which displays logistic regression coefficients.  From courses years back and a little , I understand logistic regression to be a way of describing the relationship between multiple independent variables and a binary response variable. What I'm confused about is, given the table below, because the South has a logistic regression coefficient of .903, does that mean that 90.3% of Southerners vote republican? Because of the logistical nature of the metric, that this direct correlation does not exist. Instead, I assume that you can only say that the south, with .903, votes Republican more than the Mountains/plains, with the regression of .506.  Given the latter to be the case, how do I know what is significant and what is not and is it possible to extrapolate a percentage of republican votes given this logistic regression coefficient.  As a side note, please edit my post if anything is stated incorrectly
29773
I like Peter Flom's answer to an earlier question about multicollinearity in logistic regression, but David Garson's Logistic Binomial Regression states that there is no valid test for multicollinearity for binary-dependent logistic regression, even if the independent variables are ratio scale. Can anyone supply one or more references? My own experience is that OLS correlation matrices and VIF worked for me, as my logistic coefficients went haywire before removing entangled independent variables based on the OLS tests for multicollinearity. But I have to publish my results and methods, and would like a reputable way to cite the practice, if one or more exist.
27542
We usually get an estimate of $\beta$ in the logistic regression by finding the $MLE$ of the observed random samples of $X_1,X_2....,X_N$. Then we use Wald's test i.e. ${[\hat \beta / S.E.(\hat \beta)]}^2$ to test whether that variable is significant or not.   From what I have read, this Wald's test is based on two facts (or assumptions, I am not sure).    $\hat \beta$ follows a normal distribution Standard Deviation of this normal distribution is given by the inverse of Fisher's Matrix   Can someone explain the proofs behind these two facts/ (or assumptions). I have read this  but most of the intuition went over my head.
3668
I have a question regarding interpretation of regression results based on data where I have some negative values. Since the residuals were positively skewed I needed to log-transform my data, and because of negative values my log transformation looked like $\ln(Y-\min(Y)+1)$. Normally, if we have $\ln$ in both sides of the equation, then our $b$ coefficient means a percentage change of DV for 1 % change of IV. But I have big doubts whether the same is valid for such log-transformed data, where I added a constant to my DV in order to make the minimum value equal to 1. I can't also find any literature on this topic. Does anyone know for sure what would be the correct interpretation in such a situation?
64582
I have built a logistic regression where the outcome variable is being cured after receiving treatment (Cure vs. No Cure). All patients in this study received treatment. I am interested in seeing if having diabetes is associated with this outcome.   In R my logistic regression output looks as follows:   Call: glm(formula = Cure ~ Diabetes, family = binomial(link = "logit"), data = All_patients) ... Coefficients:             Estimate Std. Error z value Pr(&gt;|z|)     (Intercept)   1.2735     0.1306   9.749   &lt;2e-16 *** Diabetes     -0.5597     0.2813  -1.990   0.0466 *   ...     Null deviance: 456.55  on 415  degrees of freedom Residual deviance: 452.75  on 414  degrees of freedom   (2 observations deleted due to missingness) AIC: 456.75   However, the confidence interval for the odds ratio includes 1:                     OR     2.5 %   97.5 % (Intercept) 3.5733333 2.7822031 4.646366 Diabetes    0.5713619 0.3316513 1.003167   When I do a chi-squared test on these data I get the following:  data:  check X-squared = 3.4397, df = 1, p-value = 0.06365   If you'd like to calculate it on your own the distribution of diabetes in the cured and uncured groups are as follows:  Diabetic cure rate:      49 /  73 (67%) Non-diabetic cure rate: 268 / 343 (78%)   My question is: Why don't the p-values and the confidence interval including 1 agree?
60604
First I'm a little bit confused with the assumptions of a model with binomial response and logit link function. Since it is basically a logistic regression. Today one of my professors told me that I had to prove normality of my residuals, but of what I know the assumptions are:  First, binary logistic regression requires the dependent variable to be binary and ordinal logistic regression requires the dependent variable to be ordinal.  Second, logistic regression requires the observations to be independent of each other.  In other words, the observations should not come from repeated measurements or matched data.  Third, logistic regression requires there to be little or no multicollinearity among the independent variables.  This means that the independent variables should not be too highly correlated with each other.  Also these are the plots I have:     So basically my question is: what assumptions can I prove/not prove with these plots?
110823
I am trying to predict what are the determinants for foreign direct investments in Lithuanian regions from 2011 to 2017.   My dependent variable is foreign direct investments per capita in Lithuanian regions. And I have a variety of explanatory variables such as unemployment rate, labor cost, infrastructure quality and so on.   However, the data is really not normally distributed. Data does not show any linearity.     That is why I cannot use the multiple linear regression.     I found out that for the data which has a Poisson distribution, two regressions are suitable: Poisson and Negative binomial regression.   According to my calculations the dispersion is higher that the mean, so I should use the negative binomial regression.   Please correct me if I am wrong.   Also, how do you account for changing variables in time? (From 2011 to 2017)
2707
I have run proc freq to test association between two binary variables using the Fisher's exact test. However, the outputs seem contradict to each other as Two-sided Pr &lt;= P 0.0355 whereas the OR and the 95% Confidence Limits 0.1097 [0.0022, 1.1380] includes 1.  This means that p-value shows that they are significantly associated while the 95% CI does not indicate that.  My question is that based on the output from SAS, what should I use: p-value or CI?
53724
One of the assumption of logistic regression is the linearity in the logit. So once I got my model up and running I test for nonlinearity using Box-Tidwell test. One of my continuous predictors (X) has tested positive for nonlinearity. What am I suppose to do next?   As this is a violation of the assumptions shall I get rid of the predictor (X) or include the nonlinear transformation (X*X). Or transform the variable into a categorical? If you have a reference could you please point me to that too?
52262
I have fitted a binomial regression in R using glm.nb from the MASS package.  I have two questions and would be very thankful if you could answer any of them:  1a) Can I use the Anova (type II, car package) to analyse which explanatory variables are significant? Or should I use the summary() function?  However, the summary uses a z-test which requires normal distribution if i am not mistaken. When looking at examples in books and websites, mostly summary has been used. I get completely different outcomes for Anova test and summary. Based on visualisation of the data I feel that Anova is more accurate. (i only get different outcomes when I have included an interaction).  1b) When using the Anova, both an F-test, chi-square test and anova (type 1) give different (but pretty similar) results - is there any of these tests that is preferred for a negative binomial regression? Or is there any way to find out which test represents the most likely results?   2) When looking at the diagnostic plots, my qq-plot looks kinda off. I am wondering if this is fine - since the negative binomial is different from the normal distribution? Or should the residuals still be normally distributed?
43698
Is it appropriate to do a logistic regression where both the dependent and independent variables are binary? for example the dependent variable is 0 and 1 and the predictors are contrast coded variables -1 and 1 ?
113847
Background and Problem  I have a question concerning a meta-analysis combining effects from between- and within-subject designs using log-odds ratios (OR) as the metric of interest. I am familiar with conducting meta-analyses and will be undertaking my calculations in R (using the metafor and lme4 packages). To provide greater context, the studies in question ask research subjects to make a binary decision with respect to a personal preference across one of two conditions. In some cases, each participant is assigned to a single condition (making only a single binary response); in others, each subject takes part in both conditions (making two binary responses). For now, presume I have the raw data in all cases. The issue I face is how best to calculate an OR that is comparable across design and whether I should take the correlation between conditions into account for the within-subject designs.  My Current Approach  I presently use logistic regression to estimate the OR for between-subject designs. The slope represents the OR and the sampling variance can be calculated by squaring the SE of the slope coefficient. Using this approach produces estimates comparable to equations reported in common texts such The Handbook of Research Synthesis and Meta-Analysis, 2nd Edition (p. 243). I then extend this approach to use a multilevel logistic regression model including a random intercept by subject to estimate the OR for within-subject designs while account for the dependency between conditions. The OR and sampling variance are otherwise calculated in the same fashion.   My Questions:  With this in mind, I would like to ask:   Is it reasonable to meta-analytically aggregate OR calculated using standard and multilevel logistic regression? Would it be better to use standard logistic regression for both designs (ignoring the correlation between conditions for the within-subject designs)?
19685
I'm quite new on this with binomial data tests, but needed to do one and now I´m not sure how to interpret the outcome. The y-variable, the response variable, is binomial and the explanatory factors are continuous. This is what I got when summarizing the outcome:  glm(formula = leaves.presence ~ Area, family = binomial, data = n)  Deviance Residuals:  Min      1Q  Median      3Q     Max   -1.213  -1.044  -1.023   1.312   1.344    Coefficients:                         Estimate Std. Error z value Pr(&gt;|z|)  (Intercept)           -0.3877697  0.0282178 -13.742  &lt; 2e-16 *** leaves.presence        0.0008166  0.0002472   3.303 0.000956 *** --- Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1  (Dispersion parameter for binomial family taken to be 1)  Null deviance: 16662  on 12237  degrees of freedom Residual deviance: 16651  on 12236  degrees of freedom (314 observations deleted due to missingness) AIC: 16655 Number of Fisher Scoring iterations: 4   There's a number of things I don't get here, what does this really say:                          Estimate Std. Error z value Pr(&gt;|z|)  (Intercept)           -0.3877697  0.0282178 -13.742  &lt; 2e-16 *** leaves.presence        0.0008166  0.0002472   3.303 0.000956 ***   And what does AIC and Number of Fisher Scoring iterations mean?  &gt; fit Call:  glm(formula = Lövförekomst ~ Areal, family = binomial, data = n)  Coefficients: (Intercept)        Areal   -0.3877697    0.0008166    Degrees of Freedom: 12237 Total (i.e. Null);  12236 Residual (314 observations deleted due to missingness) Null Deviance:      16660  Residual Deviance: 16650        AIC: 16650   And here what does this mean:  Coefficients: (Intercept)        Areal   -0.3877697    0.0008166
39424
When I analyze my variables in two separate (univariate) logistic regression models, I get the following:  Predictor 1:    B= 1.049,    SE=.352,    Exp(B)=2.85,    95% CI=(1.43, 5.69),    p=.003    Constant:    B=-0.434,    SE=.217,    Exp(B)=0.65,                            p=.046  Predictor 2:    B= 1.379,    SE=.386,    Exp(B)=3.97,    95% CI=(1.86, 8.47),    p&lt;.001    Constant:    B=-0.447,    SE=.205,    Exp(B)=0.64,                            p=.029   but when I enter them into a single multiple logistic regression model, I get:  Predictor 1:    B= 0.556,    SE=.406,    Exp(B)=1.74,    95% CI=(0.79, 3.86),    p=.171 Predictor 2:    B= 1.094,    SE=.436,    Exp(B)=2.99,    95% CI=(1.27, 7.02),    p=.012    Constant:    B=-0.574,    SE=.227,    Exp(B)=0.56,                            p=.012   Both predictors are dichotomous (categorical). I have checked for multicollinearity.  I am not sure if I have given enough info, but I cannot understand why predictor 1 has gone from being significant to non-significant and why the odds ratios are so different in the multiple regression model. Can anyone provide a basic explanation of what is going on?
28934
As we all know, there are 2 methods to evaluate the logistic regression model and they are testing very different things  Predictive power: Get a statistic that measures how well you can predict the dependent variable based on the independent variables. The well-known Pseudo R^2 are McFadden (1974) and Cox and Snell (1989).  Goodness-of-fit statistics The test is telling whether you could do even better by making the model more complicated, which is actually testing whether there are any non-linearities or interactions that you have missed.   I implemented both tests on my model, which added quadratic and interaction already:     &gt;summary(spec_q2)      Call:     glm(formula = result ~ Top + Right + Left + Bottom + I(Top^2) +       I(Left^2) + I(Bottom^2) + Top:Right + Top:Bottom + Right:Left,       family = binomial())       Coefficients:                  Estimate Std. Error z value Pr(&gt;|z|)         (Intercept)  0.955431   8.838584   0.108   0.9139         Top          0.311891   0.189793   1.643   0.1003         Right       -1.015460   0.502736  -2.020   0.0434 *       Left        -0.962143   0.431534  -2.230   0.0258 *       Bottom       0.198631   0.157242   1.263   0.2065         I(Top^2)    -0.003213   0.002114  -1.520   0.1285         I(Left^2)   -0.054258   0.008768  -6.188 6.09e-10 ***     I(Bottom^2)  0.003725   0.001782   2.091   0.0366 *       Top:Right    0.012290   0.007540   1.630   0.1031         Top:Bottom   0.004536   0.002880   1.575   0.1153         Right:Left  -0.044283   0.015983  -2.771   0.0056 **      ---     Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1     (Dispersion parameter for binomial family taken to be 1)     Null deviance: 3350.3  on 2799  degrees of freedom     Residual deviance: 1984.6  on 2789  degrees of freedom     AIC: 2006.6  and the predicted power is as below, the MaFadden is 0.4004, and the value between 0.2~0.4 should be taken to present very good fit of the model(Louviere et al (2000), Domenich and McFadden (1975))                                                :  &gt; PseudoR2(spec_q2)     McFadden     Adj.McFadden        Cox.Snell       Nagelkerke McKelvey.Zavoina           Effron            Count        Adj.Count     0.4076315        0.4004680        0.3859918        0.5531859        0.6144487        0.4616466        0.8489286        0.4712500           AIC    Corrected.AIC  2006.6179010     2006.7125925   and the goodness-of-fit statistics:  &gt; hoslem.test(result,phat,g=8)       Hosmer and Lemeshow goodness of fit (GOF) test    data:  result, phat   X-squared = 2800, df = 6, p-value &lt; 2.2e-16  As my understanding, GOF is actually testing the following null and alternative hypothesis:   H0: The models does not need interaction and non-linearity   H1: The models needs interaction and non-linearity  Since my models added interaction, non-linearity already and the p-value shows H0 should be rejected, so I came to the conclusion that my model needs interaction, non-linearity indeed. Hope my interpretation is correct and thanks for any advise in advance, thanks.
20128
I have two non-significant main binary variables in my binary logistic regression model, but their interaction is significant. The variables are centered and no multicollinearity is the case (all VIFs about 1.0). The main variables are nonsignificant, but their interaction is. I want to interpret that significant interaction of two non-significant estimates.   It would read something like this: the effect of the variable A is less visible in the level 1 of the variable B (B1) and more visible in the second level of B (B2). Or I can say the same thing about the effect of B being less visible in A1 and more visible in A2...  However, the problem is that neither the effect of A, nor the effect of B are significant! So the above interpretation, although seemingly correct, sounds inconsistent or strange. (How a non-significant effect is supposed to be boosted by the other variable?)...   On a second thought, it seems that it is actually possible. For example, if I exclude cases with B2 from my sample, now the effect of A in the sample would show up as significant (it is B2 cases in the sample that disallow A to appear as significant)... This is getting more clear in my head now, but do you still have something other than the above interpretation in mind?
97783
I'm trying to get caught up in some notes, and the topic is pooled, cross-sectional data. If we have the regression: $$\log{wage_i}=\beta_0+\beta_1\text{married}_i+\delta_0\text{yr10}_i+\delta_1\text{married}_i\times \text{yr10}_i+\varepsilon_i$$ Where $\text{married}$ is a dummy variable which $=1$ if a person is married and $0$ if not, and $\text{yr10}$ is a dummy variable indicating whether the observation was recorded in the year 2010, as opposed to being recorded in the year 2000. There's a blank spot in the notes that I didn't get, and it asks: How do we interpret $\delta_1$?  I think it's correct to say that $\delta_1$ measures how the return on whether or not someones married has changed in the past $10$ years. Is that correct? Or am I wrong? I read a little bit in my textbook and I think that's what it's saying.