Quizzes from Categorical Data Analysis

For a dataset with variables relating to heart disease you have a saturated model with maximized likelihood of 187 and df= 10 and a reduced model, where 3 dummy variables that categorized the blood pressure levels of each individual (blood pressure levels and had 4 levels) where removed, had a maximized loglikelihood of 182, and using level of 0.05 and can we conclude about blood pressure levels?

• The variable blood pressure levels improves the model.

• At least one of the betas for the dummy variables related to blood pressure levels are likely not equal to zero.

For a dataset with variables related to heart disease you have a statured model with maximized loglikelihood of 200 and df=10 and reduced model, where the 4 dummy variables that categorized the smoking status of each indviduals (smoking status has 5 levels) where removed, had a maximized loglikelihood of 193, and using an alpha level of 0.05 what can we conclude about smoking status?

-At least one of the betas for the dummy variables relating to smoking status are likely not to equal to zero.

-The variable smoking status improves the model.

If you are using a model with multiple interactions between explanatory variables when all the literature suggests no interactions are necessary, based on information alone the model is likely what?

-Model is too complex.

Why are unstable estimates a problem?

They cause non statistically significant variables to always appear statistically significant.

You can use a likelihood ratio test to compare the following two models.

Model 1: logit(P(Y-1)= interpret+ B1*Weight+ B2*Income+B3*Age

Model 2: logit(P(Y=1)= intercept+ B1*Weight+ B2*Income+ B3*Gender+B4*Weight*Income.

False.

You can use a likelihood ratio test to compare the following two models

Model 1: logit(P(Y=1)= intercept+B1*Age+B2*Gender+B3*Race

Model 2: logit(P(Y=1)= intercept+B1*Age+B2*Gender+B3*Salary

False

Only statistically significant variables should be included in the model.

False.

Based on the information provided in the data?

Model 7- 302.16 since it is the smallest value

gender

Based on the information provided which model best fits the data?

Model 2- 320.17 since it is the smallest in value of the data.

If we are conducting a study with a single binary predictor where we want to determine if the intervention will increase the proportion of students who want to go to college what sample size do we need if we have the following set parameters?

Alpha = .05

Power = .85

Control Group Proportion of students who want to go to college = 70%

Treatment Group of students who want to go to college = 80%

670

If we are conducting a study with a single binary predictor where we want to determine if the intervention will reduce teen pregnancy what Power do we have if we have the following set parameters?

Alpha = .1

Control Group Pregnancy Rate = 5%

Treatment Group Pregnancy Rate = 2.5%

Npergroup = 450

Round your answer to 3 decimal places.

0.631

The table below is the result of a SAS output where a multi-nominal logistic regression was conducted on the outcome of Deathcause with Cholesterol as the single explanatory variable.

Deathcause has the following values: Cancer, Cerebral Vascular Disease, and Coronary Heart Disease.  Cancer was used as the reference category for the multi-nominal logistic regression.

Cholesterol is a continuous measure in units of milligrams per deciliter (mg/dL).

Analysis of Maximum Likelihood Estimates
Parameter	DeathCause	DF	Estimate	Standard Error	Wald Chi-Square	Pr > ChiSq
Intercept	Cerebral Vascular Disease	1	-1.3068	0.3720	12.3431	0.0004
Intercept	Coronary Heart Disease	1	-2.0951	0.3359	38.9038	<.0001
Cholesterol	Cerebral Vascular Disease	1	0.00410	0.00158	6.7747	0.0092
Cholesterol	Coronary Heart Disease	1	0.00932	0.00140	44.2122	<.0001

Using the table above select the appropriate values that creates the prediction equation comparing the outcome values of Cancer to Coronary Heart Disease.

 

Pi1 means probability of Cerebral Vascular Disease

Pi2 means probability of Coronary Heart Disease

Pi3 means probability of Cancer

log(pi3/pi2=2.0951+0.00932*Cholesterol

The table below is the result of a SAS output where a multi-nominal logistic regression was conducted on the outcome of Deathcause with Cholesterol as the single explanatory variable.

Deathcause has the following values: Cancer, Cerebral Vascular Disease, and Coronary Heart Disease.  Cancer was used as the reference category for the multi-nominal logistic regression.

Cholesterol is a continuous measure in units of milligrams per deciliter (mg/dL).

Analysis of Maximum Likelihood Estimates
Parameter	DeathCause	DF	Estimate	Standard Error	Wald Chi-Square	Pr > ChiSq
Intercept	Cerebral Vascular Disease	1	-1.3068	0.3720	12.3431	0.0004
Intercept	Coronary Heart Disease	1	-2.0951	0.3359	38.9038	<.0001
Cholesterol	Cerebral Vascular Disease	1	0.00410	0.00158	6.7747	0.0092
Cholesterol	Coronary Heart Disease	1	0.00932	0.00140	44.2122	<.0001

 

Using the table above determine the value of Cholesterol when Pi1 = Pi2

 

Pi1 means probability of Cerebral Vascular Disease

Pi2 means probability of Coronary Heart Disease

Pi3 means probability of Cancer

151

The table below is the result of a SAS output where a multi-nominal logistic regression was conducted on the outcome of Deathcause with Cholesterol as the single explanatory variable.

Deathcause has the following values: Cancer, Cerebral Vascular Disease, and Coronary Heart Disease.  Cancer was used as the reference category for the multi-nominal logistic regression.

Cholesterol is a continuous measure in units of milligrams per deciliter (mg/dL).

Analysis of Maximum Likelihood Estimates
Parameter	DeathCause	DF	Estimate	Standard Error	Wald Chi-Square	Pr > ChiSq
Intercept	Cerebral Vascular Disease	1	-1.3068	0.3720	12.3431	0.0004
Intercept	Coronary Heart Disease	1	-2.0951	0.3359	38.9038	<.0001
Cholesterol	Cerebral Vascular Disease	1	0.00410	0.00158	6.7747	0.0092
Cholesterol	Coronary Heart Disease	1	0.00932	0.00140	44.2122	<.0001

 

Using the table above determine the probability of someone dying of Cancer when Cholesterol equals 450.

 

Do not round the values in the table during your calculations, calculate your final answer to 4 decimals.

0.092

The table below is the result of a SAS output where a multi-nominal logistic regression was conducted on the outcome of Deathcause with Cholesterol as the single explanatory variable.

Deathcause has the following values: Cancer, Cerebral Vascular Disease, and Coronary Heart Disease.  Cancer was used as the reference category for the multi-nominal logistic regression.

Cholesterol is a continuous measure in units of milligrams per deciliter (mg/dL).

Analysis of Maximum Likelihood Estimates
Parameter	DeathCause	DF	Estimate	Standard Error	Wald Chi-Square	Pr > ChiSq
Intercept	Cerebral Vascular Disease	1	-1.3068	0.3720	12.3431	0.0004
Intercept	Coronary Heart Disease	1	-2.0951	0.3359	38.9038	<.0001
Cholesterol	Cerebral Vascular Disease	1	0.00410	0.00158	6.7747	0.0092
Cholesterol	Coronary Heart Disease	1	0.00932	0.00140	44.2122	<.0001

 

Using the table above select the appropriate interpretation for the Odds Ratio related to Cholesterol where Cerebral Vascular Disease is the outcome of interest compared to Coronary Heart Disease.

As cholesterol increases by 1 md/L the odds that someone dies from Cerebral Vascular Disease rather than Coronary Heart Disease decreases by 0.5%

The table below is the result of a SAS output where a Ordinal logistic regression was conducted on the outcome of Smoking Status (number of cigarettes smoked per day) with Sex and Weight as the explanatory variables.

Smoking Status had the following values:

0 = Non-smoker

1 = Light (1-5)

2 = Moderate (6-15)

3 = Heavy (16-25)

4 = Very Heavy (26+)

The regression modeled logit(P(Smoking Status <= j)) where j equals the values of the variable smoking status

 

Sex had the values of Male and Female (Female was used as the reference category)

Weight is a continuous measure in units pounds (lbs)

 

Analysis of Maximum Likelihood Estimates
Parameter		DF	Estimate	Standard Error	Wald Chi-Square	Pr > ChiSq
Intercept	0	1	-1.7137	0.3178	29.0714	<.0001
Intercept	1	1	-1.298	0.3165	16.8223	<.0001
Intercept	2	1	-0.788	0.3153	6.2452	0.0125
Intercept	3	1	0.6098	0.3172	3.6966	0.0545
Weight		1	0.00520	0.00184	8.0234	0.0046
Sex	Male	1	-1.5177	0.1118	184.2406	<.0001

 

Based on the table above where there are multiple intercepts, but only a single estimate for each explanatory variable.  Select the answer below that explains why.

The proportional odds assumption is being applied.

The table below is the result of a SAS output where a Ordinal logistic regression was conducted on the outcome of Smoking Status (number of cigarettes smoked per day) with Sex and Weight as the explanatory variables.

Smoking Status had the following values:

0 = Non-smoker

1 = Light (1-5)

2 = Moderate (6-15)

3 = Heavy (16-25)

4 = Very Heavy (26+)

The regression modeled logit(P(Smoking Status <= j)) where j equals the values of the variable smoking status

 

Sex had the values of Male and Female (Female was used as the reference category)

Weight is a continuous measure in units pounds (lbs)

 

Analysis of Maximum Likelihood Estimates
Parameter		DF	Estimate	Standard Error	Wald Chi-Square	Pr > ChiSq
Intercept	0	1	-1.7137	0.3178	29.0714	<.0001
Intercept	1	1	-1.298	0.3165	16.8223	<.0001
Intercept	2	1	-0.788	0.3153	6.2452	0.0125
Intercept	3	1	0.6098	0.3172	3.6966	0.0545
Weight		1	0.00520	0.00184	8.0234	0.0046
Sex	Male	1	-1.5177	0.1118	184.2406	<.0001

 

What is the prediction equation for someone smoking 1-5 cigarettes per day or less?

 

logit(P(Smoking Status<=1)) = -1.298 + (0.0052*weight) + (-1.5177*Sex)

The table below is the result of a SAS output where a Ordinal logistic regression was conducted on the outcome of Smoking Status (number of cigarettes smoked per day) with Sex and Weight as the explanatory variables.

Smoking Status had the following values:

0 = Non-smoker

1 = Light (1-5)

2 = Moderate (6-15)

3 = Heavy (16-25)

4 = Very Heavy (26+)

The regression modeled logit(P(Smoking Status <= j)) where j equals the values of the variable smoking status

 

Sex had the values of Male and Female (Female was used as the reference category)

Weight is a continuous measure in units pounds (lbs)

 

Analysis of Maximum Likelihood Estimates
Parameter		DF	Estimate	Standard Error	Wald Chi-Square	Pr > ChiSq
Intercept	0	1	-1.7137	0.3178	29.0714	<.0001
Intercept	1	1	-1.298	0.3165	16.8223	<.0001
Intercept	2	1	-0.788	0.3153	6.2452	0.0125
Intercept	3	1	0.6098	0.3172	3.6966	0.0545
Weight		1	0.00520	0.00184	8.0234	0.0046
Sex	Male	1	-1.5177	0.1118	184.2406	<.0001

 

Using the table above select the appropriate interpretation for the Odds Ratio associated with Weight.

As weight increases by 1lb the odds that someone will smoke less rather than more increases by 0.5%.

The table below is the result of a SAS output where a Ordinal logistic regression was conducted on the outcome of Smoking Status (number of cigarettes smoked per day) with Race and Sex as the explanatory variables.

Smoking Status had the following values:

0 = Non-smoker

1 = Light (1-5)

2 = Moderate (6-15)

3 = Heavy (16-25)

4 = Very Heavy (26+)

The regression modeled logit(P(Smoking Status <= j)) where j equals the values of the variable smoking status

 

Race has the values of White, African American, and Other (where White was used as the reference category).

Sex has the values of Female and Male (Male was used as the reference category)

 

Analysis of Maximum Likelihood Estimates
Parameter		DF	Estimate	Standard Error	Wald Chi-Square	Pr > ChiSq
Intercept	0	1	0.5081	0.1105	21.1564	<.0001
Intercept	1	1	1.0219	0.1133	81.3440	<.0001
Intercept	2	1	1.6273	0.1176	191.4537	<.0001
Intercept	3	1	3.1698	0.1349	552.1106	<.0001
Race	Black	1	-1.8215	0.1396	170.1347	<.0001
Race	Other	1	-2.2165	0.1336	275.3643	<.0001
Sex	Female	1	1.3100	0.1100	141.7405	<.0001

 

Use the table above to Calculate P(Smoking Status = 3) where Race = Black and Sex = Female.

Do not round the values in the table above, do round your final answer to 4 decimal places.

 

Hint: The table above gives you values to create a prediction equation for logit(P(Y<=j)), the question is asking for P(Y=j)

0.1813

		Do you get a yearly flu shot
		Yes	No
Do you get a yearly physical	Yes	325	56
	No	36	100

 

Using the table above calculate the Test statistic for the McNemar Test.

4.348

		Do you get a yearly flu shot
		Yes	No
Do you get a yearly physical	Yes	125	15
	No	30	75

 

Select the appropriate conclusion about people who get yearly physicals and people who get yearly flu shots using the McNemar Test with an alpha of .05.

There is evidence to suggest that people are more willing to get a yearly flu shot than a yearly physical.